@@ -16,7 +16,7 @@ events. This work aims to aid some of these applications by introducing the state-of-the-art in interpolation and motion estimation to \ac{TEC} mapping. To this end, work contained here pertains to the production of accurate -\ac{TEC} maps from sparse data, and the automated tracking of image derived +\ac{TEC} maps from sparse data, and the automated tracking of image-derived ionospheric features. As the ionosphere is the medium on which the majority of this work is based, @@ -25,4 +25,4 @@ this introductory chapters describes the ionosphere and its storms, considers for sensing its activity during geomagnetic storms. The introduction concludes with a chapter-by-chapter summary of the remainder -of the thesis. \ No newline at end of file +of the thesis. Introduction.tex @@ -18,7 +18,7 @@ Matthew Philip Foster \par\par A thesis submitted for the degree of Doctor of Philosophy \\ University of Bath \\ Department of Electronic and Electrical Engineering\par -% 2009 +April 2009 \par \vfill} \underline{COPYRIGHT}\par @@ -84,7 +84,7 @@ mother, Caroline and grandfather, Roy for imbibing me with curiosity and always believing in me. Without the help and support of these people I would probably not have started, let alone finished this undertaking. -Finally, I would like to thank the UK Engineering and Pysical Sciences Research Council (EPSRC) for giving me the opportunity to embark on this project. +Finally, I would like to thank the UK Engineering and Physical Sciences Research Council (EPSRC) for giving me the opportunity to embark on this project. \addcontentsline{toc}{chapter}{Table of Contents} \tableofcontents @@ -126,14 +126,21 @@ Finally, I would like to thank the UK Engineering and Pysical Sciences Research \include{motion_optical_corr} \include{boundary_motion} +\include{motion_comparisons} + \include{further_work} \appendix % \noappendicestocpagenum % \addappheadtotoc -\pagestyle{fancy} -\fancyhf{} +% \pagestyle{fancy} +% \fancyhf{} + +\lhead{\sffamily{\rightmark}} +\cfoot{\sffamily{\thepage}} +\renewcommand{\headrulewidth}{0.5pt} +\renewcommand{\footrulewidth}{0.5pt} \titleformat{\chapter}[display] {\filleft\sffamily\bfseries\Huge} % Format @@ -143,7 +150,6 @@ Finally, I would like to thank the UK Engineering and Pysical Sciences Research [\vspace{5ex}] % after \include{publications} -\include{motion_comparisons} \include{tec_image_sequences} \include{software} Thesis.tex @@ -3,7 +3,7 @@ <plist version="1.0"> <dict> <key>currentDocument</key> - <string>preamble.tex</string> + <string>intro_summary.tex</string> <key>documents</key> <array> <dict> @@ -45,12 +45,16 @@ <dict> <key>filename</key> <string>interp_summary.tex</string> + <key>lastUsed</key> + <date>2009-06-13T11:36:33Z</date> </dict> <dict> <key>filename</key> <string>intro_summary.tex</string> <key>lastUsed</key> - <date>2009-01-06T16:24:44Z</date> + <date>2009-06-13T11:43:56Z</date> + <key>selected</key> + <true/> </dict> <dict> <key>filename</key> @@ -62,7 +66,7 @@ <key>filename</key> <string>ionosphere.tex</string> <key>lastUsed</key> - <date>2009-01-14T14:45:05Z</date> + <date>2009-06-13T11:32:45Z</date> </dict> <dict> <key>filename</key> @@ -104,7 +108,7 @@ <key>filename</key> <string>normalised_convolution.tex</string> <key>lastUsed</key> - <date>2009-01-14T14:59:30Z</date> + <date>2009-06-13T11:36:57Z</date> </dict> <dict> <key>filename</key> @@ -116,7 +120,7 @@ <key>filename</key> <string>other_interp_methods.tex</string> <key>lastUsed</key> - <date>2009-01-15T11:40:59Z</date> + <date>2009-06-13T11:37:13Z</date> </dict> <dict> <key>filename</key> @@ -128,9 +132,7 @@ <key>filename</key> <string>preamble.tex</string> <key>lastUsed</key> - <date>2009-04-15T10:43:10Z</date> - <key>selected</key> - <true/> + <date>2009-06-13T11:30:13Z</date> </dict> <dict> <key>filename</key> @@ -172,7 +174,7 @@ <key>filename</key> <string>Thesis.tex</string> <key>lastUsed</key> - <date>2009-04-15T10:43:10Z</date> + <date>2009-05-19T21:03:07Z</date> </dict> <dict> <key>filename</key> @@ -204,30 +206,14 @@ <key>caret</key> <dict> <key>column</key> - <integer>41</integer> + <integer>6</integer> <key>line</key> - <integer>45</integer> + <integer>20</integer> </dict> - <key>columnSelection</key> - <false/> <key>firstVisibleColumn</key> <integer>0</integer> <key>firstVisibleLine</key> <integer>0</integer> - <key>selectFrom</key> - <dict> - <key>column</key> - <integer>36</integer> - <key>line</key> - <integer>45</integer> - </dict> - <key>selectTo</key> - <dict> - <key>column</key> - <integer>41</integer> - <key>line</key> - <integer>45</integer> - </dict> </dict> <key>acronyms.tex</key> <dict> @@ -313,14 +299,28 @@ <key>firstVisibleLine</key> <integer>145</integer> </dict> + <key>interp_summary.tex</key> + <dict> + <key>caret</key> + <dict> + <key>column</key> + <integer>71</integer> + <key>line</key> + <integer>16</integer> + </dict> + <key>firstVisibleColumn</key> + <integer>0</integer> + <key>firstVisibleLine</key> + <integer>0</integer> + </dict> <key>intro_summary.tex</key> <dict> <key>caret</key> <dict> <key>column</key> - <integer>33</integer> + <integer>0</integer> <key>line</key> - <integer>11</integer> + <integer>16</integer> </dict> <key>firstVisibleColumn</key> <integer>0</integer> @@ -332,14 +332,14 @@ <key>caret</key> <dict> <key>column</key> - <integer>12</integer> + <integer>47</integer> <key>line</key> - <integer>127</integer> + <integer>447</integer> </dict> <key>firstVisibleColumn</key> - <integer>0</integer> + <integer>78</integer> <key>firstVisibleLine</key> - <integer>105</integer> + <integer>403</integer> </dict> <key>main_bibliography.bib</key> <dict> @@ -446,14 +446,30 @@ <key>caret</key> <dict> <key>column</key> - <integer>0</integer> + <integer>30</integer> <key>line</key> - <integer>640</integer> + <integer>70</integer> </dict> + <key>columnSelection</key> + <false/> <key>firstVisibleColumn</key> <integer>0</integer> <key>firstVisibleLine</key> - <integer>624</integer> + <integer>46</integer> + <key>selectFrom</key> + <dict> + <key>column</key> + <integer>25</integer> + <key>line</key> + <integer>70</integer> + </dict> + <key>selectTo</key> + <dict> + <key>column</key> + <integer>30</integer> + <key>line</key> + <integer>70</integer> + </dict> </dict> <key>optical_flow_table.tex</key> <dict> @@ -474,28 +490,28 @@ <key>caret</key> <dict> <key>column</key> - <integer>29</integer> + <integer>91</integer> <key>line</key> - <integer>279</integer> + <integer>270</integer> </dict> <key>firstVisibleColumn</key> - <integer>0</integer> + <integer>68</integer> <key>firstVisibleLine</key> - <integer>242</integer> + <integer>172</integer> </dict> <key>preamble.tex</key> <dict> <key>caret</key> <dict> <key>column</key> - <integer>16</integer> + <integer>19</integer> <key>line</key> - <integer>40</integer> + <integer>9</integer> </dict> <key>firstVisibleColumn</key> <integer>0</integer> <key>firstVisibleLine</key> - <integer>33</integer> + <integer>0</integer> </dict> <key>publications.tex</key> <dict> @@ -588,6 +604,7 @@ <string>normalised_convolution.tex</string> <string>artefacts.tex</string> <string>ionosphere.tex</string> + <string>interp_summary.tex</string> <string>biases.tex</string> <string>sim_corr_uni_percentiles.tex</string> <string>sim_corr_percentiles.tex</string> @@ -627,6 +644,6 @@ <key>treeState</key> <dict/> <key>windowFrame</key> - <string>{{-1086, -23}, {594, 767}}</string> + <string>{{26, 11}, {594, 767}}</string> </dict> </plist> Thesis.tmproj @@ -5,7 +5,7 @@ \acro{ANC}{adaptive normalised convolution} \acro{BSI}{biharmonic spline interpolation} \acro{C/A}{coarse acquisition} - \acro{CCC}{cross correlation coefficient} + \acro{CCC}{cross-correlation coefficient} \acro{CME}{coronal mass ejection} \acro{CM}{curve matching} \acro{DD}{diffusion distance} @@ -44,7 +44,7 @@ \acro{TEC}{total electron content} \acro{TOI}{tongue of ionisation} \acro{TPS}{thin plate spline} - \acro{TSM}{thin sell model} + \acro{TSM}{thin shell model} \acro{TOA}{time of arrival} \acro{VMF}{vector-median filter} \acro{VHR}{very-high resolution} acronyms.tex @@ -29,7 +29,7 @@ interpolated output field which has been introduced by the interpolation technique used to create it. Examples of artefacts commonly seen are peaks, concave slopes and overshooting edges. This definition is deliberately loose, as interpolation is arguably the introduction of artefacts around a sparse set -of data points. As interpolation is ill-posed, there is an infinite number of +of data points. As interpolation is ill-posed, there are an infinite number of available outputs, all of which are interpolated versions of the input data, the vast majority of which are completely inappropriate. Of the remaining (miniscule fraction) of outputs deemed acceptable, only some will be @@ -38,17 +38,64 @@ of any interpolation method can be considered an \emph{artefact}, and so the following discussion will be kept fairly broad in scope. Fig.~\ref{fig:elev_zoomed} shows some example data from the Shuttle Radar -Topography Mission. These data have been downsampled by approximately 99\%, +Topography Mission. These data have been downsampled by approximately 99\% and then reconstructed using various interpolation methods. This figure -illustrates artefacts the produced, as well as giving a general \emph{feel} +illustrates artefacts produced, as well as giving a general \emph{feel} for the outputs produced by the different methods. + \begin{figure}[ht] - \centering - \includegraphics[width=10cm]{artefacts/rice_zoomed} - \caption[Close up of a single rice grain]{A greyscale image of rice grains, displayed using false colour, with the single grain used in Fig.~\ref{fig:images_rice_stack}.} - \label{fig:images_rice_zoomed} -\end{figure} + + \centerline{ + \subfloat[]{ + \includegraphics[width=5cm]{artefacts/rect_input} + \label{fig:images_rect_input} + } + \hfil + \subfloat[]{ + \includegraphics[width=5cm]{artefacts/rect_linear} + \label{fig:images_rect_linear} + } + } + + \centerline{ + \subfloat[]{ + \includegraphics[width=5cm]{artefacts/rect_rbf_linear} + \label{fig:images_rect_rbf_linear} + } + \hfil + \subfloat[]{ + \includegraphics[width=5cm]{artefacts/rect_tps} + \label{fig:images_rect_tps} + } + } + + \centerline{ + \subfloat[]{ + \includegraphics[width=5cm]{artefacts/rect_nn} + \label{fig:images_rect_nn} + } + \hfil + \subfloat[]{ + \includegraphics[width=5cm]{artefacts/rect_anc} + \label{fig:images_rect_anc} + } + } + + \caption[Example interpolated SRTM DEM data, showing artefacts]{Example elevation data from the SRTM, shown as a false colour surface. \subref{fig:images_rect_input} is the original input data, which were sampled to $\approx 99\%$ sparsity, and reconstructed by \subref{fig:images_rect_linear} was interpolated using linear triangulation based interpolation and \subref{fig:images_rect_rbf_linear} were interpolated using linear RBF interpolation. \subref{fig:images_rect_tps} TPS RBF interpolation, \subref{fig:images_rect_nn} NN interpolation, \subref{fig:images_rect_anc} ANC. +} + + \label{fig:elev_zoomed} + \end{figure} + + + \begin{figure}[ht] + \centering + \includegraphics[width=10cm]{artefacts/rice_zoomed} + \caption[Close up of a single rice grain]{A greyscale image of rice grains, displayed using false colour, with the single grain used in Fig.~\ref{fig:images_rice_stack}.} + \label{fig:images_rice_zoomed} + \end{figure} + \begin{figure}[ht] @@ -91,49 +138,8 @@ sampled image.} \label{fig:images_rice_stack} \end{figure} -\begin{figure}[ht] - - \centerline{ - \subfloat[]{ - \includegraphics[width=5cm]{artefacts/rect_input} - \label{fig:images_rect_input} - } - \hfil - \subfloat[]{ - \includegraphics[width=5cm]{artefacts/rect_linear} - \label{fig:images_rect_linear} - } - } - - \centerline{ - \subfloat[]{ - \includegraphics[width=5cm]{artefacts/rect_rbf_linear} - \label{fig:images_rect_rbf_linear} - } - \hfil - \subfloat[]{ - \includegraphics[width=5cm]{artefacts/rect_tps} - \label{fig:images_rect_tps} - } - } - - \centerline{ - \subfloat[]{ - \includegraphics[width=5cm]{artefacts/rect_nn} - \label{fig:images_rect_nn} - } - \hfil - \subfloat[]{ - \includegraphics[width=5cm]{artefacts/rect_anc} - \label{fig:images_rect_anc} - } - } - \caption[Example interpolated SRTM DEM data, showing artefacts]{Example elevation data from the SRTM, shown as a false colour surface. \subref{fig:images_rect_input} is the original input data, which was sampled to $\approx 99\%$ sparsity, and reconstructed by \subref{fig:images_rect_linear} was interpolated using linear triangulation based interpolation and \subref{fig:images_rect_rbf_linear} was interpolated using linear RBF interpolation., \subref{fig:images_rect_tps} TPS RBF interpolation, \subref{fig:images_rect_nn} NN interpolation, \subref{fig:images_rect_anc} ANC. -} - \label{fig:elev_zoomed} - \end{figure} Fig.~\ref{fig:images_rice_zoomed} shows an image of rice grains, and illustrates a small section which was sampled and interpolated to produce @@ -157,7 +163,7 @@ plates together over a frame whose vertices are the data points, and with edges following those of the triangles. There is not necessarily any continuity across any derivatives of the edges, and therefore the surfaces can appear highly jagged. However, because no continuity of derivatives is -enforced all points in the interpolated output will lie within the surfaces +enforced, all points in the interpolated output will lie within the surfaces defined by the triangulation. This means that linear interpolation of this kind never contains overshoots, which can be an advantage in some situations, and absolutely essential in others. The main downside is the faceting effect @@ -168,8 +174,8 @@ introduced by this method. \subsection{Linear RBF Interpolation} % (fold) \label{sub:linear_rbf_interpolation} -Linear \ac{RBF} interpolation uses a basis function which is varies linearly -with the distance from input datum. This yields results which are similar to +Linear \ac{RBF} interpolation uses a basis function which varies linearly +with the distance from input data. This yields results which are similar to those produced by linear triangulation-based interpolation, but which do not contain the faceted appearance. The trade-off here is that \ac{RBF} interpolation is a global interpolation method, which means it is @@ -194,7 +200,7 @@ Figs.~\ref{fig:images_artefacts_tps} and \ref{fig:images_rect_tps} were interpolated using \ac{TPS} \ac{RBF} interpolation, a cubic-order method which was introduced in Section~\ref{sec:paper_rbf}, on page~\pageref{sec:paper_rbf}. This produces results which are almost identical -to \ac{BSI}, and is characterised by smooth, isotropic surfaces. A \ac{TPS} is +to \ac{BSI}, and are characterised by smooth, isotropic surfaces. A \ac{TPS} is a kind of cubic spline, and as such produces similar outputs to triangulation based cubic interpolation. These outputs are all characterised by smooth surfaces, and a tendency to produce values which overshoot around extrema. @@ -213,19 +219,19 @@ amount, and whose joins with other plates must be continuous to at least the first derivative. This physical analogy is the idea around which splines were originally designed. -Other interpolation methods such as the venerable Akima method also -\citet{akima_method_1978,ripley_spatial_2004}, aim to reduce these overshoots -\footnote{which are themselves a well documented and analysed problem -\cite[see e.g.][]{fried_curve_1973,maeland_on-the-comparison_1988}} and -succeed in suppressing them. However, algorithms such as this are no longer -commonly used in modern software and tend only to be used in applications -where legacy code is heavily relied upon, such as in the interpolation of -precipitation information. \citet{chen_assessing_2008}, for example compares -three commonly used interpolation methods for interpolation global rainfall. -The methods tested include \citet{shepard_a-two-dimensional_1968}, which is -based on a modified inverse distance weighting function, designed when -computational methods for irregular interpolation was first being heavily -investigated, in the late 1960s. +Other interpolation methods such as the venerable Akima method +\citep{akima_method_1978,ripley_spatial_2004}, also aim to reduce these +overshoots \footnote{which are themselves a well documented and analysed +problem \cite[see e.g.][]{fried_curve_1973,maeland_on-the-comparison_1988}} +and succeed in suppressing them. However, algorithms such as this are no +longer commonly used in modern software and tend only to be used in +applications where legacy code is heavily relied upon, such as in the +interpolation of precipitation information. \citet{chen_assessing_2008}, for +example, compared three commonly used interpolation methods for interpolation +global of rainfall data. The methods tested include +\citet{shepard_a-two-dimensional_1968}, which is based on a modified inverse +distance weighting function, designed when computational methods for irregular +interpolation were first being heavily investigated in the late 1960s. \begin{figure}[ht] \centering @@ -251,7 +257,7 @@ triangulation. However, it differs from all other methods in that it uses the ratio of overlapping areas to determine the weighting of data points. This results in surfaces which vary more smoothly than linear interpolation based on triangulation. The most obvious artefact caused by \ac{NN} is the fact that -it tends to produce sharp points near the input datum. +it tends to produce sharp points near input data. Physically, the surfaces produced by \ac{NN} are similar in appearance to that of a heavy rubber sheet, stretched over and attached to input points. The artefacts.tex @@ -3,7 +3,7 @@ One very effective way of examining interpolation methods for possible problems is to create a histogram of the errors between an interpolated -output, and a simulated full-field input. This can also be attempted using a +output and a simulated full-field input. This can also be attempted using a cross-validation style method (see Chapter~\ref{cha:performance}), although often this will not yield enough error measurements for the creation of a full histogram. @@ -45,18 +45,17 @@ In ascending order the moments can be used as follows: \item The third moment describes the `skewness', or asymmetry of the distribution. A non zero skewness, is indicative of a tendency for the - interpolation method to under-, or over-estimate the output values which do - not lie on input datum. Asymmetry in distributions is known as `skew', and - is defined as the third-standardised moment of a given distribution. The sample skewness is estimated using: + interpolation method to under- or over-estimate the output values which do + not lie on an input datum. The sample skewness is estimated using: \begin{equation} - \gamma_1 = \frac{\frac{1}{N} \sum \limits_{n=1}^{N} ( x_i - \overline{x})^3}{(\sigma_2)^{3/2}}. + \gamma_1 = \frac{\frac{1}{N} \sum \limits_{n=1}^{N} ( x_i - \overline{x})^3}{(\sigma^2)^{3/2}}, \end{equation} - Where $\mu_3$ is the third moment about the mean, and $\sigma$ is the + where $\mu_3$ is the third moment about the mean and $\sigma$ is the standard deviation. \label{item:skew} - \item The fourth moments is the `kurtosis', which describes how + \item The fourth moment is the `kurtosis', which describes how outlier-prone a distribution is. Standard Gaussian distributions have a kurtosis of 3; distributions which are more outlier prone have higher kurtosis values, and those which are less outlier prone have lower vales. @@ -102,7 +101,7 @@ works in several stages, the first of which is the estimation of an of the data being interpolated. This then has a model fitted to it, which is then used as a basis function for a global interpolation. In this case, the image has patches with high levels, followed closely by patches with low -levels (the patches are actually grains of rice), because each grain of rice +levels (the patches are actually grains of rice). Because each grain of rice has a different orientation, the level of autocorrelation in the image varies significantly across the image, which is also highly anisotropic. This means that the semivariogram is unable to fully capture the spatial variation of the @@ -110,7 +109,7 @@ image, which in turn leads to a poorly fitting semivariogram model, which culminates in a poor interpolated output. The main consequence of the poorly fitting model is that the basis function chosen for the interpolation leads to concave surfaces in the output, which causes a large proportion of the output -positions to contain under estimates than overestimates, this is evidenced by +positions to contain under-estimates than overestimates; this is evidenced by the longer left hand tail in Fig.~\ref{fig:error_hist}. Problems with kriging are also discussed in Section \ref{sec:paper_conclusions}, page~\pageref{sec:paper_conclusions}. @@ -133,7 +132,7 @@ page~\pageref{sec:paper_conclusions}. } } - \caption[An example image with its semivariogram and a histogram of interpolation errors]{\subref{fig:recon_image}~(top) a reconstructed version of the sampled image (bottom), \subref{fig:kriging_variogram} the semivariogram for the sampled version of the sampled version of the bottom image in \subref{fig:recon_image}. \subref{fig:error_hist} a histogram showing the distribution of error values between the images in \subref{fig:recon_image}.} + \caption[An example image with its semivariogram and a histogram of interpolation errors]{\subref{fig:recon_image}~(top) a reconstructed version of the sampled image (bottom), \subref{fig:kriging_variogram} the semivariogram for the sampled version of the bottom image in \subref{fig:recon_image}. The green line represents the fitted semivariogram model. \subref{fig:error_hist} a histogram showing the distribution of error values between the images in \subref{fig:recon_image}.} \label{fig:images_kriging_hist} \end{figure*} @@ -143,14 +142,14 @@ page~\pageref{sec:paper_conclusions}. \label{sub:confidence_limits} Error distributions can be used to calculate confidence limits on output -errors. These can be calculated using the standard distribution of errors, or +errors. These can be calculated using the standard distribution of errors or, as absolute error bounds are probably more useful, the histogram of absolute errors could be used to calculate the limits. Fig.~\ref{fig:images_abs_error_hist} shows an example normalised histogram with the 90, 95 and 99\% confidence limits plotted as vertical lines (from -left to right). Other rank statistics, such as the median (the 50th -percentile) can also be calculated if desired, and the process can also be +left to right). Other rank statistics such as the median (the 50th +percentile), can also be calculated if desired, and the process can also be carried out using the normal error histogram, or histogram of other error measures, such as \ac{RMSE} or \ac{SSE}. @@ -163,7 +162,7 @@ Fig.~\ref{fig:simulated_error_distributions} shows some example histograms, created by interpolating simulated data as described and used in Section~\ref{sec:simulation_validation_results}, on page~\pageref{sec:simulation_validation_results}. A single field generated in -this way was downsampled to various sparsities and then reconstructing using +this way was downsampled to various sparsities and then reconstructed using the interpolation methods used in Section~\ref{sec:simulation_validation_results}. Histograms were then greated by subtracting the input and output data. These plots clearly show that the @@ -215,12 +214,12 @@ sparsity. They also show that the performance of different techniques is comparable. In Table~\ref{tab:perc_95}, for example, the 99th percentile values for \ac{BSI}, cubic and linear triangulation based interpolation and natural neighbour are all very similar. The worst performer by far is nearest -neighbour. Table~\ref{tab:perc_998}, shows similar trends although the +neighbour. Table~\ref{tab:perc_998} shows similar trends, although the performance gap has narrowed, and \ac{ANC} performs worst in terms of the 99th percentile. Examining Fig.~\ref{fig:hist_998} reveals that this is probably because the distribution of errors for nearest neighbour has a low kurtosis, meaning that most errors are grouped around an approximately zero mean. All of -the plotted error distributions appear to be approximately Gaussian, and are +the plotted error distributions appear to be approximately Gaussian and are centred close to zero, indicating that the methods work well on this type of simulated data. @@ -235,9 +234,9 @@ be used to examine the behaviour of these methods, and discussed and demonstrated the use of percentiles to specify error performance. The main conclusion that can be drawn from this chapter is that all of the -interpolation methods behave well, and have symmetrical distributions which +interpolation methods behave well and have symmetrical distributions which are centred on zero (see Fig.~\ref{fig:simulated_error_distributions}). Simple -tests done on the \ac{TEC} data in Chpater~\ref{cha:performance} provided +tests done on the \ac{TEC} data in Chapter~\ref{cha:performance} provided similar results. The following chapters changes topic to the estimating the motion of a feature biases.tex @@ -54,7 +54,7 @@ and hence studying its evolution. \end{figure} A very large number of segmentation techniques exist, but are not suitable for -the data being considered here. For example, \emph{optimal thresholding}, a +the data being considered here: for example, \emph{optimal thresholding}, a simple technique for separating objects from background or clutter \citep{nixon_feature_2008}. This approach is appropriate when the object of interest has a different range of values than the background, as is the case @@ -62,13 +62,13 @@ with the \ac{TOI}. It is also designed for use on data with a bi-modal intensity distribution. However, histograms of the \ac{TEC} data for the four images from Fig.~\ref{fig:images_frames} (on page \pageref{fig:images_frames}), shown in Fig.~\ref{fig:hist}, show that the -\ac{TEC} data is characterised by a distribution with only a single peak, +\ac{TEC} data are characterised by a distribution with only a single peak, which corresponds to the background value. The \ac{TEC} values which correspond to the \ac{TOI} occur in the tails (on the right hand side) of the illustrated distributions. This, coupled with the presence of noise, and the -fact that the maximum \ac{TEC} value changes over time means that simple -thresholding is doomed to failure. Other segmentation methods, such as those -based on image texture are also inappropriate due to the low resolution and +fact that the maximum \ac{TEC} value changes over time, means that simple +thresholding is doomed to failure. Other segmentation methods such as those +based on image texture,s are also inappropriate due to the low resolution and smoothness of the data. % subsection segmentation_methods (end) @@ -85,7 +85,7 @@ Segmentation can be carried out using various different methodologies, from simple thresholding to more complex methods such as the watershed transform, or graph connectivity \citep[e.g.,][]{soille_constrained_2008}, and new methods are continually being developed. The main segmentation framework -considered here is mathematical morphology and more specifically, attribute +considered here is mathematical morphology and, more specifically, attribute morphology, which is described below. Mathematical morphology provides a robust toolkit for segmentation and feature @@ -124,7 +124,7 @@ described in more detail below. \label{sub:morphological_toi_segmentation} Whilst the segmentation schemes proposed in -\citet{soille_advances_2002,pesaresi_a-new-approach_2001,akcay_morphological_2007,akcay_automatic_2008} +\citep{soille_advances_2002,pesaresi_a-new-approach_2001,akcay_morphological_2007,akcay_automatic_2008} were developed for application to \ac{VHR} images, the images in this study are characterised by extremely low resolution. In these images, the lack of texture and small size mean that multi-scale segmentation methods are @@ -191,7 +191,7 @@ overall loss in performance. } } - \caption[Comparing area and correlation of contrast parameters]{Comparisons of area difference \subref{fig:area_comp} and correlation \subref{fig:correlation_comp} between frames segmented at various contrasts, and hand segmented frames. In both cases the contrast with the closest matches to the hand segmented frames was 33 TEC Units.} + \caption[Comparing area and correlation of contrast parameters]{Comparisons of area difference \subref{fig:area_comp} and correlation \subref{fig:correlation_comp} between frames segmented at various contrasts, and hand segmented frames. The black plotted points show the lowest difference in area, and highest correction values respectively. In both cases the contrast with the mean closest match to the hand segmented frames was 33 TEC Units.} \label{fig:correlation_area_comparisons} \end{figure} @@ -285,7 +285,7 @@ After boundaries have been extracted and described using a chain code or coordinates, it is necessary to compute the correspondences between boundary points. It may also be appropriate to resample them so that the number of points in each boundary is equal, a process which can be made easier by -converting the boundaries to a spine-based representation. Splines are +converting the boundaries to a spline-based representation. Splines are piecewise parametric polynomials which are an extremely powerful tool for compactly and smoothly representing complex curves. Using splines allows smoothing of shape boundaries as well as arbitrary resampling along the @@ -348,7 +348,7 @@ A shape context is histogram which describes the distribution of boundary points \item choose an origin on the shape boundary; \item subtract the origin coordinates from the other boundary coordinates; \item convert the new coordinates into polar form to get $r$ and $\theta$; - \item create a 2-D histogram by binning $log(r)$ and $\theta$ (\citet{belongie_shape_2002} uses five bins for $log(r)$ and 12 bins for $\theta$) + \item create a 2-D histogram by binning $\log(r)$ and $\theta$ (\citet{belongie_shape_2002} uses five bins for $\log(r)$ and 12 bins for $\theta$). \end{itemize} In order to establish point correspondences between boundaries, shape contexts @@ -361,14 +361,14 @@ given by: \begin{equation} C_ij \equiv \chi^2(p_i, p_j) = \frac{1}{2} \sum\limits_{k = 1}^{K} - \frac{[h_i(k) - h_j(k)]^2}{h_i(k) + h_j(k)}, + \frac{[h_i(k) - h_j(k)]^2}{h_i(k) + h_j(k)}. \end{equation} As this only compares histogram bins with corresponding bins in the second histogram, other methods, such as as the \ac{EMD}~\citep{ling_an-efficient_2007} or \ac{DD}~\citep{ling_diffusion_2006} (a dissimilarity measure found to be more robust and accurate than the -\ac{EMD} under certain conditions) can be used. These metrics include +\ac{EMD} under certain conditions), can be used. These metrics include cross-bin comparisons and so are more robust to problems such as boundary occlusion and noise. The \ac{DD} is particularly attractive due to its simplicity (it makes use of a Gaussian pyramid and simple filtering @@ -384,7 +384,7 @@ where, d_1(\mathbf{x}) & = [d_{l-1} * \phi(\mathbf{x}, \sigma)] \downarrow_2 \;\;\; l = 1, \ldots, L \end{align} -Where $l$ represents the current layer of the Gaussian pyramid with $L$ +where $l$ represents the current layer of the Gaussian pyramid with $L$ layers, $\downarrow_2$ denotes downsampling to half-size. $\sigma$ is the standard deviation of the Gaussian filter $\phi(\ldots)$. @@ -402,12 +402,12 @@ Hungarian/Munkres method, which attempts to find an optimal path through the matrix \citep{kuhn_the-hungarian_1955}. The result of minimising (\ref{eqn:context_minimise}) is a permutation -$\pi(i)$, describing the optimal mapping between shape boundary points. +$\pi(i)$ describing the optimal mapping between shape boundary points. Constraints and extras costs can be added to this technique by modifying the cost matrix to include them as necessary. For example, a distance weighting -could be added to help ensure that the minimisation returns points close in +could be added to help ensure that the minimisation returns points close to the boundary order. Metrics relating to image properties could also be added, -although finding suitable metrics is problematic, as many, such as curvature, +although finding suitable metrics is problematic as many, such as curvature, can be very noisy and introduce `pits', very low values, into the cost matrix. These serve to pull the match towards them, which can give poor vectors as it can leads to bad boundary correspondences. Fig.~\ref{fig:cost_matrix} shows an @@ -457,25 +457,25 @@ where $A$ is a matrix describing rotation and scaling, and $o$ is a translation \hat{A} = (Q^+P)^t, \end{equation} $P$ and $Q$ contain the homogeneous coordinates of the boundaries described by -$p$ and $q$, in the same form as equation \ref{eqn:homogeneous_coordinates}. +$p$ and $q$, in the same form as (\ref{eqn:homogeneous_coordinates}). $Q^+$ is the pseudo-inverse of $Q$. The outputs, $\hat{A}$ and $\hat{o}$ can then be used in place of $A$ and $o$ in equation \ref{eqn:affine_model}. Typical fields produced by affine models and are characterised by an area where the vectors are very small (an origin). Affine modelled fields tend to be have insufficient degrees of freedom to accurately describe complex motion, -such as exhibited by the \ac{TOI} in the \ac{TEC} images. +such as that exhibited by the \ac{TOI} in the \ac{TEC} images. \subsubsection{RBF Fitting and Regularisation} % (fold) \label{sub:rbf_fitting_and_regularisation} -\citet{belongie_shape_2002} uses two separate \ac{TPS} surfaces (one for the $x$-axis mapping and on for the $y$-axis), fitted using \ac{RBF}, giving a model of the form: +\citet{belongie_shape_2002} uses two separate \ac{TPS} surfaces (one for the $x$-axis mapping and one for the $y$-axis), fitted using \ac{RBF}, giving a model of the form: \begin{equation} T(x,y) = \left ( f_x(x,y), f_y(x,y) \right ). \end{equation} The fitting is carried out by considering the boundary positions of the first shape $p_i = (x_i, y_i)$ as the input coordinates, and then taking the -$x$-component second shapes' coordinate as $z_i$. \ac{RBF} interpolation is +$x$-component second shape's coordinate as $z_i$. \ac{RBF} interpolation is then performed to give $f_x$. The same process is then performed using the $y$-component of the displacement to get $f_y$. @@ -488,7 +488,7 @@ it with: \begin{equation} A + \lambda I \end{equation} -Where $\lambda$ is a scale dependent \emph{regularisation parameter} which +where $\lambda$ is a scale dependent \emph{regularisation parameter} which controls the amount of smoothing, and $I$ is an identity matrix. Setting $\lambda=0$ corresponds to interpolation, and setting $\lambda$ to large values creates outputs which are similar to those from a fitted affine model. @@ -533,14 +533,14 @@ this section of the data-set, the motion is highly constrained, and the \label{fig:initial_outputs} \end{figure} -As described in section \ref{sec:data_sources}, on page +As described in Section~\ref{sec:data_sources}, on page \pageref{sec:data_sources}, the image sequence corresponds to a patch over the polar cap. One consequence of this is that one side of the image is always in sunlight, and one is in darkness. Because of the nature of the ionosphere, the side in sunlight is continually injected with electrons and ions, and the side in darkness undergoes depletion due to recombination effects. This results in the \ac{TOI} being drained at its tip, in a fashion similar to the snout of a -glacier, where ice melts, and drains away. If the rate of melting increases, +glacier, where ice melts and drains away. If the rate of melting increases, the snout will appear to retreat whilst water will always flow away. If only the position of the snout was being measured, the glacier would appear to be flowing backwards, which is clearly never the case. This effect is illustrated @@ -611,11 +611,11 @@ This method detects vectors which are significantly different from those in the previous frame, but is very sensitive to the threshold parameter chosen as the histograms of displacements vectors tend to be very flat. -\item Marking vectors in a manor similar to the above method, but making use +\item Marking vectors in a manner similar to the above method, but making use of angle instead of magnitude. This method was found to be unreliable because of the wide variety of vector directions between frames. -\item Marking entire frames based on the mean and standard deviation of the vectors differenced with those from the previous frame. A combination of a mean value of 5, and standard deviation of 3 was found to be effective. +\item Marking entire frames based on the mean and standard deviation of the vectors differenced with those from the previous frame. A combination of a mean value of 5 and standard deviation of 3 was found to be effective. \end{itemize} @@ -729,14 +729,14 @@ relaxation-labelling (see Section~\ref{sec:relaxation_labelling}, on page set of available vectors, but uses fitted smooth surfaces. The regularisation is also part of the `interpolation' method, rather than a add-on step. Fig.~\ref{fig:images_regularisation_effect} shows the how changing the -scale-dependent regularisation parameter, $\lambda$ changes the smoothness of +scale-dependent regularisation parameter $\lambda$ changes the smoothness of a surface being reconstructed. In this example, a sparsely sampled field has had an \ac{RBF} surface fitted with various different $\lambda$ values, -starting at zero and ending and one, in steps of a quarter. This shows the +starting at zero and ending and one, in steps of 0.25. This shows the effect that modifying the regularisation parameter has on the smoothness of the reconstructed field. Fig.~\ref{fig:reg_masked_fields} then shows the same frames as Fig.~\ref{fig:interped_masked_fields}, but regularised using a -$\lambda$ of 0.5. This produces smoothed vectors, with a tendency for the +$\lambda$ value of 0.5. This produces smoothed vectors, with a tendency for the field to be less curved than in the non-regularised case. \begin{figure}[ht!] @@ -819,8 +819,8 @@ histogram comparison metric for use with shape context matching, and lastly, vector field density can be increased using regularised radial-basis functions, in order to get smooth dense motion fields. -Appendix~\ref{cha:comparisons_of_tec_motion_estimation_methods} compares the -different motion estimation techniques against one-another, in order to +Chapter~\ref{cha:comparisons_of_tec_motion_estimation_methods} compares the +different motion estimation techniques against one another, in order to illustrate how they differ. % section conclusions (end) boundary_motion.tex @@ -9,7 +9,7 @@ further work that could be carried out are also listed. \section{Summary of Conclusions} % (fold) \label{sec:summary_of_conclusions} -Chapter~\ref{cha:introduction} introduced the background, upon which the +Chapter~\ref{cha:introduction} introduced the background upon which the remainder of this work is based: the ionosphere. Ionospheric mapping methods and storms were introduced, providing context for the work in later chapters. @@ -85,7 +85,7 @@ boundaries. One particularly notable feature of the segmentation method designed here is the use of temporal feedback, which stabilises the area of the segmented objects by examining the properties of previous frames. This technique was found to perform well, once several problems had been overcome. -The main problem were object joins, due to saddle points, and the +The main problems were object joins, due to saddle points, and the \emph{retreating boundary problem} which manifests as a reversal in the direction of boundary motion. The problems were solved using the watershed transform, and by selectively replacing boundary vectors respectively. @@ -104,7 +104,7 @@ paradigm can be adapted to the estimation of shape-motion. A by-product of any long term project must surely be a large list of unanswered questions. This section lists a few such questions, collected over -the course of the work that completes into this document. +the course of the work that completes this document. \subsection{Interpolation and TEC Mapping} % (fold) \label{sub:interpolation_and_tec_mapping} @@ -112,12 +112,12 @@ the course of the work that completes into this document. A large number of older interpolation methods exist which have not been tested in recent studies \citep[e.g.][]{akima_method_1978,shepard_a-two-dimensional_1968,ripley_spatial_2004}. -Many of these are also implemented in languages such as FORTRAN (or older -languages). Porting these methods to C or C++ and then including them in the -studies in Chapter~\ref{cha:performance} would be a useful benchmark. It would -show how well these methods can cope with highly-sparse data (something which -seems to have only been given attention recently), as well as how well they -compare to more modern methods. +Many of these are also implemented in languages such as FORTRAN. Porting these +methods to C or C++, or making them available to MATLAB, and then including +them in the studies in Chapter~\ref{cha:performance} would be a useful +benchmark. It would show how well these methods can cope with highly-sparse +data (something which seems to have only been given attention recently), as +well as how well they compare to more modern methods. Another useful advancement would be improving the speed of the \ac{RBF} interpolation methods by implementing domain decomposition. This was briefly @@ -131,7 +131,7 @@ Work on examining how sampling patterns alter interpolation outputs should also prove very interesting and informative. This should concentrate on the spatial frequency content that can be reconstructed for different sampling methods and sparsities, and might pave the way for a universal description of -the limits of reconstruction quality at differing sparsity. A good sampling +the limits of reconstruction quality at differing sparsities. A good sampling point for this work would be \citet{ripley_spatial_2004} and references therein. @@ -157,13 +157,13 @@ allow the use of the same parameter on many different storms. Independent data sources such as vector data from the SuperDARN \citep{greenwald_darn_superdarn_1995} or EISCAT radars could also be used both -for validation of results and perhaps more interestingly, the production of +for validation of results and, perhaps more interestingly, the production of improved motion fields by combining them estimates of boundary positions. Comparisons and validation with assimilation algorithms, such AMIE (described by \citet{bust_tracking_2007}). Implementation of a tracking system, using for example, a Kalman filter -\citep{m_sonka_image_1999} would be a useful extension of the work, which +\citep{m_sonka_image_1999}, would be a useful extension of the work, which could allow for forecasting of storms motion they progress. These results could also be of scientific interest. @@ -177,7 +177,7 @@ ground truth. This data would have to be generated in such a way as to ensure realism, whilst ensuring confidence in the estimated vectors. Examining warping methods \citep[e.g.][]{wolberg_digital_1994} which could be modified for image generation would be a good first-step towards implementing this -study. Although it should be noted that simple warping models, such as the +study, although it should be noted that simple warping models, such as the affine model, can not appropriately capture the complex motion of the \ac{TOI}. further_work.tex gnuplot/.DS_Store @@ -12,7 +12,6 @@ set xlabel 'lag [h]' # textcolor rgb 'white' set grid lw 2 set key off -set xtics rotate by 90 #set pointsize 0.6 @@ -31,4 +30,4 @@ set key off #set pointsize 0.6 plot 'gnuplot/data/good_variogram.dat' using 1:2 with points lw 4 pt 7 ps 2 title 'Semivariogram', \ - 'gnuplot/data/good_variogram.dat' using 1:3 with lines lt 2 lw 4 title 'Fitted Spherical Model' \ No newline at end of file + 'gnuplot/data/good_variogram.dat' using 1:3 with lines lt 2 lw 4 title 'Fitted Spherical Model' gnuplot/bias_variogram.gp @@ -6,4 +6,4 @@ set output 'gnuplot/output/perimeters.pdf' set key bottom outside center horizontal plot 'gnuplot/data/shape_perimeters' using 1 with linespoints title "Total perimeters" lw 3 lt 1 ps 3, \ -'gnuplot/data/shape_perimeters' using 2 with linespoints title "First shape perimeter" lw 3 lt 2 ps 3 \ No newline at end of file +'gnuplot/data/shape_perimeters' using 2 with linespoints title "First shape perimeter" lw 3 lt 2 ps 3 gnuplot/boundaries.gp @@ -5,7 +5,6 @@ set ylabel 'Normalised Count' # set yrange [0:2000] set xlabel 'Error Value' -set xtics rotate by 90 # set title 'Error Histogram' set grid lw 2 set key off gnuplot/confidence_hist.gp @@ -1,6 +1,6 @@ # cd ~/Work/matlab/interp_comparison/simulation/; ls *.dat -set grid lw 2 +set grid lw 4 set xrange [-0.7:0.7] set yrange [0:1000] set xlabel 'Difference' gnuplot/hist_plots.gp @@ -8,7 +8,7 @@ set ylabel 'Count' # set yrange [0:2000] set xlabel 'Error Value' -set xtics rotate by 90 +#set xtics rotate by 90 # set title 'Error Histogram' set grid lw 2 set key off gnuplot/kriging_hist.gp @@ -10,7 +10,7 @@ set ytics out unset ztics -unset colorbox +set colorbox set size ratio 37/16 set xrange[1:16] @@ -18,6 +18,7 @@ set yrange[37:1] set xlabel "TEC Units" set ylabel "Frame number" +set cblabel "Area difference" # set size 1,1 # set origin 0,0 @@ -40,7 +41,7 @@ set ytics out unset ztics -unset colorbox +set colorbox set size ratio 37/16 set xrange[1:16] @@ -48,6 +49,7 @@ set yrange[37:1] set xlabel "TEC Units" set ylabel "Frame number" +set cblabel "Correlation" # set size 1,1 # set origin 0,0 gnuplot/plot_comparison_images.gp @@ -11,7 +11,7 @@ set ylabel 'Count' # set yrange [0:2000] set xlabel 'Error Value' -set xtics rotate by 90 +#set xtics rotate by 90 # set title 'Error Histogram' set grid lw 2 set key off gnuplot/sim_val_hist.gp @@ -1,7 +1,7 @@ \section{Interpolating TEC Data} -This chapter has introduced variously commonly used and state-of-the art +This chapter has introduced various commonly used and state-of-the art interpolation methods. These methods have ranged from ubiquitous triangulation based methods, such as the cubic and linear methods, to more obscure methods such as natural neighbour. It also included \ac{RBF} interpolation, kriging interp_summary.tex @@ -66,8 +66,8 @@ frequency} -- the frequency at which the electrons and ions in a slab of plasma will oscillate when perturbed -- the wave will be re-radiated, otherwise it will be pass through. The plasma frequency is given by $f_N = \sqrt{80.5 N}$, where $N$ is the electron density. The \emph{critical -frequency} of a layer is the maximum frequency which can be reflected the -layer at vertical incidence. The critical frequency, of a layer is given by +frequency} of a layer is the maximum frequency which can be reflected by the +layer at vertical incidence. The critical frequency of a layer is given by $f_c \approx 9 \times 10^{-6}\sqrt{N_m}$, where $N_m$ is the maximum electron density of the layer (in electrons per $m^3$). Critical frequencies in the various layers (which are described below) are denoted $f_oE$, $f_0F_1$ and @@ -109,7 +109,7 @@ the Sun's surface magnetic field due to sunspots means that the orientation of the \ac{IMF} varies with time. The magnitude of the `vertical' component of the \ac{IMF} is known as $B_z$, and its orientation determines whether solar wind plasma can enter the ionosphere. Regions of open magnetic-field lines, -known as polar cusps form between the sunward and tailward areas of the +known as polar cusps, form between the sunward and tailward areas of the geomagnetic field. In the northern polar cusp, the magnetic field is directed towards Earth, and in the southern cusp, the magnetic field lines point away. @@ -159,8 +159,9 @@ created using several methods, the most common of which make use of data derived from \ac{GPS} satellites and receivers. These data are then interpolated or inverted to provided full 2- or 3-D fields. Incoherent scatter radars, such as EISCAT can also be used to provided electron density profiles, -although spatial coverage is much more limited that with \ac{GPS}, which can -in theory, image the entire ionosphere. +although spatial coverage is much more limited than with \ac{GPS}, which can +in theory, image the entire ionosphere +\citep[][\emph{e.g.,}]{foster_multiradar_2005}. % subsection imaging_the_ionosphere (end) @@ -168,7 +169,7 @@ in theory, image the entire ionosphere. \label{sec:gps} The \ac{GPS} is a timing and positioning system run by the US Department of -Defence. The system is divided into three segments; known as the control, +Defense. The system is divided into three segments; known as the control, space and user segments. The \emph{control segment} consists of various tracking stations around the world, with the main control centre at Schriever Air Force Base, Colorado, USA. These stations combine measured satellite @@ -184,7 +185,7 @@ Earth. Each of the satellites transmits its own \ac{NS}, containing information on the satellite, clock corrections, ephemeris and other information. This signal -is created, and then added to a \ac{PRN} code known as the coarse \ac{C/A} code. The resulting code is modulated on to carrier wave, known as $L_1$, +is created and then added to a \ac{PRN} code known as the coarse \ac{C/A} code. The resulting code is modulated on to carrier wave, known as $L_1$, creating a spread-spectrum signal which can be used for ranging. A second spread spectrum signal known as $L_2$ is also transmitted. @@ -269,7 +270,7 @@ interpolation~\cite[e.g.][]{arikan_regularized_2007,meggs_simulations_2002}. Tomographic methods use ray-tracing to project path measurements onto a grid of voxels. Non-linear inversion techniques can then be used to reconstruct the -electron content data at each voxel. Basis functions, and model based +electron content data at each voxel. Basis functions and model based interpolation can be also used to help improve output quality. Generally, tomographic inversions can provide high resolution 3-D imagery, but require large amounts of data to do so. This means that in cases when tomography @@ -287,12 +288,12 @@ body of literature surrounding inverse problems and tomography. In order to use standard 2-D interpolation methods, \ac{TEC} data must first be converted from path measurements to spot values on a fixed height shell. This is known as the \ac{TSM} approach, and models the ionosphere as an -infinitesimally thin shell, at a given height, normally between 300 and 400 km +infinitesimally thin shell at a given height, normally between 300 and 400 km \citep[][pp. 102]{hoffmann-wellenhof_gps_2001}. The disadvantage of this approach is that information on the vertical structure is completely lost. -However, it has to potential to be computationally simple (depending on the +However, it has the potential to be computationally simple (depending on the interpolation method used, and especially in comparison to large matrix -inversions), and allows for analysis of data which are too sparse for other +inversions) and allows for analysis of data which are too sparse for other methods to reconstruct. Various methods have been developed for extracting \ac{TEC} information from the amplitude and phase of~\ac{GPS} signals, e.g.~\citet{warnant_the-increase_2000,arikan_regularized_2007}. @@ -421,7 +422,7 @@ components: regions of high-electron density, noise and artefacts corresponding to other maxima (and minima), and the remainder of the image which can be considered background. This allows \ac{TEC} maps to be used for the the examination of changes in electron density during geomagnetic storms: -The most obvious high-values feature of note during large storms is the +The most obvious high-valued feature of note during large storms is the \ac{TOI}. Tracking and analysing its motion allows the effects of a given storm to be evaluated, and helps to improve scientists' understanding of the behaviour of the Earth's atmosphere and magnetic field under varying @@ -445,7 +446,7 @@ available, removing a major limitation relative to previous techniques. This thesis presents the results of applying several different motion estimation -methods, for the first time, (described in Chapter~\ref{cha:motion}) to +methods (described in Chapter~\ref{cha:motion}), for the first time, to ionospheric \ac{TEC} data in Chapter~\ref{cha:motion_estimation_using_optical_flow_and_corr}. ionosphere.tex @@ -2,7 +2,7 @@ %% http://bibdesk.sourceforge.net/ -%% Created for Matt Foster at 2009-04-13 16:02:36 +0100 +%% Created for Matt Foster at 2009-06-13 20:23:33 +0100 %% Saved with string encoding Unicode (UTF-8) @@ -13,6 +13,18 @@ @string{tgars = {IEEE Trans. Geosci. Remote Sens.}} +@phdthesis{foster_reconstruction_2009, + Address = {University of Bath}, + Author = {Matthew P. Foster}, + Date-Added = {2009-05-09 16:56:26 +0200}, + Date-Modified = {2009-05-09 16:57:37 +0200}, + Keywords = {Ionosphere, image processing, remote sensing, motion analysis, motion estimation}, + Location = {University of Bath, United Kingdom}, + Month = {April}, + School = {Dept. of Electronic and Electrical Engineering}, + Title = {Reconstruction and Motion Estimation of Sparsely Sampled Ionospheric Data}, + Year = {2009}} + @inproceedings{4779784, Abstract = {Interpolation methods are widely used in geoscience applications to reconstruct multivariate data from irregular samples. This paper describes a quantitative methodology for assessing the performance of various state-of-the-art interpolation methods. The methodology consists of simulation-validation and cross-validation using simulated and real data respectively, and has recently been applied to study the reconstruction of total electron content maps of the ionosphere. These two approaches are described and a study of the various artefacts associated with different interpolation methods also presented, including their origins and typical locations. Finally, the use of the statistical moments of error histograms as a method of evaluating techniques for biases and skew is described, as well as providing confidence bounds on error values. The methodology and artefact analysis should be of use to anyone who uses multivariate interpolation methods.}, Author = {Foster, M.P. and Evans, A.N.}, @@ -40,7 +52,7 @@ Url = {http://www.ann-geophys.net/24/107/2006/}, Volume = {24}, Year = {2006}, - Bdsk-File-1 = {YnBsaXN0MDDUAQIDBAUGCQpYJHZlcnNpb25UJHRvcFkkYXJjaGl2ZXJYJG9iamVjdHMSAAGGoNEHCFRyb290gAFfEA9OU0tleWVkQXJjaGl2ZXKoCwwXGBkdJCVVJG51bGzTDQ4PEBEUViRjbGFzc1dOUy5rZXlzWk5TLm9iamVjdHOAB6ISE4ACgAOiFRaABIAGWWFsaWFzRGF0YVxyZWxhdGl2ZVBhdGjSDRobHFdOUy5kYXRhgAVPEQHiAAAAAAHiAAIAAAxNYWNpbnRvc2ggSEQAAAAAAAAAAAAAAAAAAADE037MSCsAAAAI4twfc3RvbGxlX29ic2VydmluZyB0aGUjNEI2MkM4LnBkZgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAEtiyMWIuLdQREYgcHJ2dwADAAMAAAkgAAAAAAAAAAAAAAAAAAAABlBhcGVycwAQAAgAAMTTcLwAAAARAAgAAMWIuLcAAAABABAACOLcAAjGcQAIuuYAAHmIAAIASE1hY2ludG9zaCBIRDpVc2VyczptYXR0OkRvY3VtZW50czpQYXBlcnM6c3RvbGxlX29ic2VydmluZyB0aGUjNEI2MkM4LnBkZgAOAFAAJwBzAHQAbwBsAGwAZQBfAG8AYgBzAGUAcgB2AGkAbgBnACAAdABoAGUAIABuAG8AcgB0AGgAXwAyADAAMAA2AF8AMAAwADAALgBwAGQAZgAPABoADABNAGEAYwBpAG4AdABvAHMAaAAgAEgARAASAENVc2Vycy9tYXR0L0RvY3VtZW50cy9QYXBlcnMvc3RvbGxlX29ic2VydmluZyB0aGUgbm9ydGhfMjAwNl8wMDAucGRmAAATAAEvAAAVAAIAC///AADSHh8gIVgkY2xhc3Nlc1okY2xhc3NuYW1loyEiI11OU011dGFibGVEYXRhVk5TRGF0YVhOU09iamVjdF8QQS4uLy4uLy4uL0RvY3VtZW50cy9QYXBlcnMvc3RvbGxlX29ic2VydmluZyB0aGUgbm9ydGhfMjAwNl8wMDAucGRm0h4fJieiJyNcTlNEaWN0aW9uYXJ5AAgAEQAaAB8AKQAyADcAOgA/AEEAUwBcAGIAaQBwAHgAgwCFAIgAigCMAI8AkQCTAJ0AqgCvALcAuQKfAqQCrQK4ArwCygLRAtoDHgMjAyYAAAAAAAACAQAAAAAAAAAoAAAAAAAAAAAAAAAAAAADMw==}, + Bdsk-File-1 = {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}, Bdsk-Url-1 = {http://www.ann-geophys.net/24/107/2006/}} @article{bust_tracking_2007, @@ -58,7 +70,7 @@ Title = {{Tracking of polar cap ionospheric patches using data assimilation}}, Volume = 112, Year = 2007, - 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A. and Zucker, S. W.}, @@ -98,9 +110,9 @@ Bdsk-Url-1 = {http://dx.doi.org/10.1109/TSMC.1976.4309519}} @article{spencer_imaging_2007, - Author = {Spencer, PSJ and Mitchell, CN}, + Author = {Spencer, P. S. J and Mitchell, C. N.}, Date-Added = {2009-01-21 15:04:11 +0000}, - Date-Modified = {2009-01-21 15:04:44 +0000}, + Date-Modified = {2009-06-13 20:04:50 +0100}, Journal = {Annals of Geophysics}, Month = {June}, Number = {3}, @@ -153,7 +165,7 @@ Url = {http://www.informaworld.com/10.1080/01431160601105876}, Volume = {28}, Year = {2007}, - Bdsk-File-1 = {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}, + Bdsk-File-1 = {YnBsaXN0MDDUAQIDBAUGCQpYJHZlcnNpb25UJHRvcFkkYXJjaGl2ZXJYJG9iamVjdHMSAAGGoNEHCFRyb290gAFfEA9OU0tleWVkQXJjaGl2ZXKoCwwXGBkdJCVVJG51bGzTDQ4PEBEUViRjbGFzc1dOUy5rZXlzWk5TLm9iamVjdHOAB6ISE4ACgAOiFRaABIAGWWFsaWFzRGF0YVxyZWxhdGl2ZVBhdGjSDRobHFdOUy5kYXRhgAVPEQH8AAAAAAH8AAIAAAxNYWNpbnRvc2ggSEQAAAAAAAAAAAAAAAAAAADGPfMrSCsAAAATVhofYm91dGlvdXRhX21vbml0b3JpbmcjMTM1NjNGLnBkZgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABNWP8Uwj60AAAAAAAAAAAADAAMAAAkgAAAAAAAAAAAAAAAAAAAABlBhcGVycwAQAAgAAMY95RsAAAARAAgAAMUwj60AAAABABAAE1YaABNKNQAS5tgAEubFAAIASE1hY2ludG9zaCBIRDpVc2VyczptYXR0OkRvY3VtZW50czpQYXBlcnM6Ym91dGlvdXRhX21vbml0b3JpbmcjMTM1NjNGLnBkZgAOAGIAMABiAG8AdQB0AGkAbwB1AHQAYQBfAG0AbwBuAGkAdABvAHIAaQBuAGcAIAB0AGgAZQAgAGkAbwBuAG8AcwBwAGgAZQByAGUAXwAyADAAMAA3AF8AMAAwADAALgBwAGQAZgAPABoADABNAGEAYwBpAG4AdABvAHMAaAAgAEgARAASAExVc2Vycy9tYXR0L0RvY3VtZW50cy9QYXBlcnMvYm91dGlvdXRhX21vbml0b3JpbmcgdGhlIGlvbm9zcGhlcmVfMjAwN18wMDAucGRmABMAAS8AABUAAgAL//8AANIeHyAhWCRjbGFzc2VzWiRjbGFzc25hbWWjISIjXU5TTXV0YWJsZURhdGFWTlNEYXRhWE5TT2JqZWN0XxBKLi4vLi4vLi4vRG9jdW1lbnRzL1BhcGVycy9ib3V0aW91dGFfbW9uaXRvcmluZyB0aGUgaW9ub3NwaGVyZV8yMDA3XzAwMC5wZGbSHh8mJ6InI1xOU0RpY3Rpb25hcnkACAARABoAHwApADIANwA6AD8AQQBTAFwAYgBpAHAAeACDAIUAiACKAIwAjwCRAJMAnQCqAK8AtwC5ArkCvgLHAtIC1gLkAusC9ANBA0YDSQAAAAAAAAIBAAAAAAAAACgAAAAAAAAAAAAAAAAAAANW}, Bdsk-Url-1 = {http://www.informaworld.com/10.1080/01431160601105876}} @article{wu_a-correlation-relaxation-labeling_1995, @@ -165,7 +177,7 @@ Publisher = {IEEE Computer Society}, Title = {{A Correlation-Relaxation-Labeling Framework for Computing Optical Flow Template Matching from a New Perspective}}, Year = {1995}, - 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P. and Evans, A. N.}, @@ -472,7 +484,7 @@ Publisher = {ACM New York, NY, USA}, Title = {{A two-dimensional interpolation function for irregularly-spaced data}}, Year = {1968}, - Bdsk-File-1 = {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}} + Bdsk-File-1 = {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}} @article{chen_assessing_2008, Author = {Chen, M. and Shi, W. and Xie, P. and Silva, V. and Kousky, V. E. and W. Higgins, R. and Janowiak, J. E.}, @@ -497,7 +509,7 @@ Title = {On the comparison of interpolation methods}, Volume = {7}, Year = {1988}, - Bdsk-File-1 = {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}, + Bdsk-File-1 = {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}, Bdsk-Url-1 = {http://dx.doi.org/10.1109/42.7784}} @article{wu_local_1993, @@ -511,7 +523,7 @@ Title = {Local error estimates for radial basis function interpolation of scattered data}, Volume = {13}, Year = {1993}, - 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It has a very wide application in the analysis of management problems, in business and industry, in economic studies, in military problems and in many other fields of our present day activities. In this keen competetive world, the problems are getting more and more complicated ahnd efforts are being made to deal with these challenging problems. This book presents from the origin to the recent developments in mathematical programming. The book has wide coverage and is self-contained. It is suitable both as a text and as a reference.* A wide ranging all encompasing overview of mathematical programming from its origins to recent developments* A result of over thirty years of teaching experience in this feild* A self-contained guide suitable both as a text and as a reference}, @@ -592,7 +604,7 @@ Ty = {JOUR}, Volume = {109}, Year = {2008}, - Bdsk-File-1 = {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}, + Bdsk-File-1 = {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}, Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/B6WCX-4P192R4-1/1/81915e33f2536404bac636cbb1d4ff5d}} @article{dinh_reconstructing_2001, @@ -607,7 +619,7 @@ Title = {Reconstructing surfaces using anisotropic basis functions}, Volume = {2}, Year = {2001}, - 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Successive images of the combustion process captured in controlled experiments are smoothed by nonlinear diffusion filtering then active contour models are used to obtain the curves that most accurately describe the frame boundary. These curves are matched using the concept of shortest path (geodesic) computation on a cost surface. The level set representation is employed so that complex curve evolutions including those with topological changes in their structures could be handled. A critical point detection algorithm is used to identify important curve landmarks that are then used to modify the cost surface so as to improve the quality and stability of the matching. Accordingly, the propagation of curves representing successive flame contours within a sequence is obtained and used for studying the flame dynamics}, @@ -704,17 +716,18 @@ Abstract = {We propose EMD-L1: a fast and exact algorithm for computing the earth mover's distance (EMD) between a pair of histograms. The efficiency of the new algorithm enables its application to problems that were previously prohibitive due to high time complexities. The proposed EMD-L1 significantly simplifies the original linear programming formulation of EMD. Exploiting the L1 metric structure, the number of unknown variables in EMD-L1 is reduced to O(N) from O(N2) of the original EMD for a histogram with N bins. In addition, the number of constraints is reduced by half and the objective function of the linear program is simplified. Formally, without any approximation, we prove that the EMD-L1 formulation is equivalent to the original EMD with a L1 ground distance. To perform the EMD-L1 computation, we propose an efficient tree-based algorithm, Tree-EMD. Tree-EMD exploits the fact that a basic feasible solution of the simplex algorithm-based solver forms a spanning tree when we interpret EMD-L1 as a network flow optimization problem. We empirically show that this new algorithm has an average time complexity of O(N2), which significantly improves the best reported supercubic complexity of the original EMD. The accuracy of the proposed methods is evaluated by experiments for two computation-intensive problems: shape recognition and interest point matching using multidimensional histogram-based local features. For shape recognition, EMD-L1 is applied to compare shape contexts on the widely tested MPEG7 shape data set, as well as an articulated shape data set. For interest point matching, SIFT, shape context and spin image are tested on both synthetic and real image pairs with large geometrical deformation, illumination change, and heavy intensity noise. The results demonstrate that our EMD-L1-based solutions outperform previously reported state- -of-the-art features and distance measures in solving the two tasks}, Author = {H. Ling and Okada, K.}, Date-Added = {2008-02-26 15:17:31 +0000}, - Date-Modified = {2008-04-07 11:45:16 +0100}, + Date-Modified = {2009-06-13 19:52:10 +0100}, Doi = {10.1109/TPAMI.2007.1058}, Issn = {0162-8828}, Journal = {Pattern Analysis and Machine Intelligence, IEEE Trans.}, Keywords = {computational complexity, image matching, linear programming, object recognitioncomputation-intensive problems, earth movers distance, interest point matching, linear programming formulation, multidimensional histogram-based local features, network flow optimization problem, shape context, shape recognition, spin image, supercubic complexity, time complexity, tree-based algorithm}, + Month = {May}, Number = {5}, Pages = {840-853}, Title = {An Efficient Earth Mover's Distance Algorithm for Robust Histogram Comparison}, Volume = {29}, - Year = {May 2007}, - Bdsk-File-1 = {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}, + Year = {2007}, + Bdsk-File-1 = {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}, Bdsk-Url-1 = {http://dx.doi.org/10.1109/TPAMI.2007.1058}} @article{jonker_a-shortest_1987, @@ -732,17 +745,18 @@ @article{belongie_shape_2002, Author = {Belongie, S. and Malik, J. and Puzicha, J.}, Date-Added = {2008-02-05 11:33:22 +0000}, - Date-Modified = {2008-02-05 11:33:29 +0000}, + Date-Modified = {2009-06-13 14:31:55 +0100}, Doi = {10.1109/34.993558}, Issn = {0162-8828}, Journal = {Transactions on Pattern Analysis and Machine Intelligence}, Keywords = {handwritten character recognition, image matching, image registration, object recognition, splines (mathematics)COIL data set, MPEG, aligning transform, deformable templates, handwritten digits, image matching, image registration, nearest-neighbor classification, object recognition, object similarity, regularized thin-plate splines, shape alignment, shape context, shape matching, shape point correspondence, silhouettes, trademarks}, + Month = {April}, Number = {4}, Pages = {509-522}, Title = {Shape matching and object recognition using shape contexts}, Volume = {24}, - Year = {Apr 2002}, - Bdsk-File-1 = {YnBsaXN0MDDUAQIDBAUGCQpYJHZlcnNpb25UJHRvcFkkYXJjaGl2ZXJYJG9iamVjdHMSAAGGoNEHCFRyb290gAFfEA9OU0tleWVkQXJjaGl2ZXKoCwwXGBkdJCVVJG51bGzTDQ4PEBEUViRjbGFzc1dOUy5rZXlzWk5TLm9iamVjdHOAB6ISE4ACgAOiFRaABIAGWWFsaWFzRGF0YVxyZWxhdGl2ZVBhdGjSDRobHFdOUy5kYXRhgAVPEQHYAAAAAAHYAAIAAAxNYWNpbnRvc2ggSEQAAAAAAAAAAAAAAAAAAADE037MSCsAAAAI4twfYmVsb25naWVfc2hhcGUgbWF0Y2hpIzhFMkYyLnBkZgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAji8sPN+doAAAAAAAAAAAADAAMAAAkgAAAAAAAAAAAAAAAAAAAABlBhcGVycwAQAAgAAMTTcLwAAAARAAgAAMPN+doAAAABABAACOLcAAjGcQAIuuYAAHmIAAIASE1hY2ludG9zaCBIRDpVc2VyczptYXR0OkRvY3VtZW50czpQYXBlcnM6YmVsb25naWVfc2hhcGUgbWF0Y2hpIzhFMkYyLnBkZgAOAEoAJABiAGUAbABvAG4AZwBpAGUAXwBzAGgAYQBwAGUAIABtAGEAdABjAGgAaQBuAGcAXwAyADAAMAAyAF8AMAAwADAALgBwAGQAZgAPABoADABNAGEAYwBpAG4AdABvAHMAaAAgAEgARAASAEBVc2Vycy9tYXR0L0RvY3VtZW50cy9QYXBlcnMvYmVsb25naWVfc2hhcGUgbWF0Y2hpbmdfMjAwMl8wMDAucGRmABMAAS8AABUAAgAL//8AANIeHyAhWCRjbGFzc2VzWiRjbGFzc25hbWWjISIjXU5TTXV0YWJsZURhdGFWTlNEYXRhWE5TT2JqZWN0XxA+Li4vLi4vLi4vRG9jdW1lbnRzL1BhcGVycy9iZWxvbmdpZV9zaGFwZSBtYXRjaGluZ18yMDAyXzAwMC5wZGbSHh8mJ6InI1xOU0RpY3Rpb25hcnkACAARABoAHwApADIANwA6AD8AQQBTAFwAYgBpAHAAeACDAIUAiACKAIwAjwCRAJMAnQCqAK8AtwC5ApUCmgKjAq4CsgLAAscC0AMRAxYDGQAAAAAAAAIBAAAAAAAAACgAAAAAAAAAAAAAAAAAAAMm}, + Year = {2002}, + Bdsk-File-1 = {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}, Bdsk-Url-1 = {http://dx.doi.org/10.1109/34.993558}} @article{belongie_matching_2001, @@ -761,7 +775,7 @@ Title = {Matching Shapes}, Volume = {01}, Year = {2001}, - 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Date-Modified = {2008-01-15 10:32:00 +0000}, + Date-Modified = {2009-06-13 19:48:40 +0100}, Doi = {10.1109/83.663500}, Issn = {1057-7149}, Journal = {IEEE Trans. on Image Processing}, Keywords = {entropy, filtering theory, image reconstruction, image representation, image sequences, image texture, mathematical morphology, mathematical operators, motion estimation, optimisation, trees (mathematics)Viterbi algorithm, antiextensive connected operators, binary opening by reconstruction, contour information, entropy-oriented operators, filtering, flat zones, formal definition, image processing, image texture, mathematical morphology, max-tree, morphological operators, motion-oriented operators, sequence processing, simplicity-oriented operators, structured image representation}, + Month = {April}, Number = {4}, Pages = {555-570}, Title = {Antiextensive connected operators for image and sequence processing }, Volume = {7}, - Year = {Apr 1998}, - Bdsk-File-1 = {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}, + Year = {1998}, + Bdsk-File-1 = {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}, Bdsk-Url-1 = {http://dx.doi.org/10.1109/83.663500}} @article{bangham_image_1998, @@ -826,7 +841,7 @@ Url = {http://link.aip.org/link/abstract/ECEJE9/v10/i3/p117/s1}, Volume = {10}, Year = {1998}, - 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The method is similar to, but gives better results than, a method described in an earlier paper.}, @@ -1114,7 +1129,7 @@ vectors for texture analysis}, Title = {An Improved Method of Angle Detection on Digital Curves}, Volume = {C-24}, Year = {Sept. 1975}, - Bdsk-File-1 = {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}} + Bdsk-File-1 = {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}} @article{acton_fast_2001, Abstract = { Acton, S. T., Fast Algorithms for Area Morphology, Digital Signal Processing11 (2001) 187-203 Efficient algorithms are developed for area morphology. As opposed to traditional morphological operations that alter grayscale images via a concatenation of order statistic filters, the area morphological operators manipulate connected components within the image level sets. Essentially, the area morphology filters are capable of removing objects based on the object area solely. These operators can then be effectively used in important multiscale and scale space tasks such as object-based coding and hierarchical image searches. Unfortunately, the traditional implementation of these filters based on level set theory precludes real-time implementation. This paper reviews previous fast algorithms and introduces a pyramidal approach. The full pyramidal algorithm is over 1000 times faster than the standard algorithm for typical image sizes. 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At Scott Base station, Antarctica (GEO: -77.85[degree sign], 166.76[degree sign]; CGM: -79.94[degree sign], 327.23[degree sign]), the partial solar eclipse was observed with the magnitude of 0.769. This solar eclipse event was a rare event due to its mixed eclipse-storm-TID. A severe magnetic storm which lasted for three days took place on 20th November 2003 with disturbance storm time index (Dst) reading of -465 nT and the planetary indices Kp and Ap of 9 and 117, respectively, and on the day of the solar eclipse minor storm activities was detected. A strong and rapid TEC oscillation with 3-4 oscillations and ranging from 20 to 30 min, a signature of Traveling Ionospheric Disturbances (TIDs) event was observed at the onset of eclipse event. Investigation on the TEC responses during the day before and after the eclipse event, showed that the TID event exist at about the same time period of the eclipse event on these days. Several TID events were also observed on other time of the day during the major storm period. At the time of maximum eclipse (at zero time delay), sudden decrease in TEC or TEC dip of 1.7 TECU with duration of 9 min was observed and the overall TEC level decreased during the eclipse period. Comparison of TEC levels at the time window of the eclipse period on 22nd and 24th November show that the TEC levels decreased by about 17% and 30% with respect to the day before and the day after the eclipse, respectively. Measurement of TEC for each GPS satellites within the observation window of the solar eclipse on 22nd, 23rd and 24th showed some satellites experienced TEC dip of about 1.5-1.7 TECU at the maximum solar eclipse period than on the day before and after the solar eclipse. The ionosonde measurements at Scott Base station show a similar behavior. The TEC dip observed from GPS and ionosonde measurement is in good agreement. During the eclipse event, a noise was detected by SuperDARN Syowa East Radar, which confirms the existence of the TID observations at the onset of the eclipse. Results of TEC measurements at McMurdo (GEO: -77.84[degree sign], 166.95[degree sign] and CGM: -79.95[degree sign], 325[degree sign], eclipse magnitude 0.769) and Davis station (GEO: -68.58[degree sign], 77.97[degree sign] and CGM: -74.91[degree sign], 101.91[degree sign], eclipse magnitude 0.983) shows a significant TEC depletion of 1.5 TECU at McMurdo station and 2.2 TECU at Davis station. The observed delay and duration of eclipse at McMurdo station are 0 and 9 min while at Davis station they are 5 and 12 min, respectively. A linear relationship between the eclipse magnitude and TEC depletion was observed from the results obtained from these stations. At McMurdo station, rapid noise in the TEC measurements was observed prior to the maximum eclipse time and also on the day before and after the eclipse. The observation of the TID waves before and after the eclipse day suggested that the TID event on the eclipse period cannot be resulted from the solar eclipse, but they could be resulted from the tropospheric origin, however, further investigation is required to examine the sources behind these waves.}, @@ -1272,7 +1287,7 @@ vectors for texture analysis}, Url = {http://www.sciencedirect.com/science/article/B6VHB-4K1X88F-1/2/ba6ae338f7a81042069802e2ad0e202b}, Volume = {68}, Year = {2006}, - Bdsk-File-1 = {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}, + Bdsk-File-1 = {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}, Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/B6VHB-4K1X88F-1/2/ba6ae338f7a81042069802e2ad0e202b}} @article{hernandez-pajares_egnos_2005, @@ -1291,7 +1306,7 @@ vectors for texture analysis}, Ty = {JOUR}, Volume = {43}, Year = {2005}, - Bdsk-File-1 = {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}} + Bdsk-File-1 = {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}} @article{pallares_ionospheric_2005, Abstract = {We report a preliminary analysis of the impact of Global Navigation Satellite System Reflections (GNSS-R) data on ionospheric monitoring over the oceans. The focus is on a single polar Low Earth Orbiter (LEO) mission exploiting GNSS-R as well as Navigation (GNSS-N) and Occultation (GNSS-O) total electron content (TEC) measurements. In order to assess impact of the data, we have simulated GNSS-R/O/N TEC data as would be measured from the LEO and from International Geodesic Service (IGS) ground stations, with an electron density (ED) field generated using a climatic ionospheric model. We have also developed a new tomographic approach inspired by the physics of the hydrogen atom and used it to effectively retrieve the ED field from the simulated TEC data near the orbital plane. The tomographic inversion results demonstrate the significant impact of GNSS-R: three-dimensional ionospheric ED fields are retrieved over the oceans quite accurately, even as, in the spirit of this initial study, the simulation and inversion approaches avoided intensive computation and sophisticated algorithmic elements (such as spatio-temporal smoothing). We conclude that GNSS-R data over the oceans can contribute significantly to a Global/GNSS Ionospheric Observation System (GIOS).}, @@ -1323,7 +1338,7 @@ vectors for texture analysis}, Ty = {JOUR}, Volume = {18}, Year = {1997}, - Bdsk-File-1 = {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}, + Bdsk-File-1 = {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}, Bdsk-Url-1 = {http://www.informaworld.com/10.1080/014311697218980}} @article{irani_detecting_1992, @@ -1347,7 +1362,7 @@ vectors for texture analysis}, Title = {{GPS} {TEC} and scintillation measurements from the polar ionosphere during the October 2003 storm}, Volume = {32}, Year = {2005}, - 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J. and Petrou, M. and Kittler, J.}, @@ -1446,7 +1461,7 @@ vectors for texture analysis}, Title = {{On the Foundations of Probabilistic Relaxation with Product Support}}, Volume = {9}, Year = {1998}, - Bdsk-File-1 = {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}} + Bdsk-File-1 = {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}} @article{sommer_the-svd-approach_, Author = {Sommer, G. and Michaelis, M. and Herpers, R.}, @@ -1467,7 +1482,7 @@ vectors for texture analysis}, Title = {{Filling-in by joint interpolation of vector fields and gray levels}}, Volume = {10}, Year = {2001}, - 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C. and Coster, A. J. and Erickson, P. J. and Holt, J. M. and Lind, F. D. and Rideout, W. and McCready, M. and van Eyken, A. and Barnes, R. J. and Greenwald, R. A. and others}, @@ -1578,7 +1593,7 @@ vectors for texture analysis}, Title = {{Multiradar observations of the polar tongue of ionization}}, Volume = {110}, Year = {2005}, - Bdsk-File-1 = {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}} + Bdsk-File-1 = {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}} @article{evans_full_1997, Author = {Evans, A. N.}, @@ -1595,7 +1610,7 @@ vectors for texture analysis}, Ty = {CONF}, Volume = {2}, Year = {1997}, - Bdsk-File-1 = {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}} + Bdsk-File-1 = {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}} @article{evans_mode_1995, Author = {Evans, AN and Nixon, MS}, @@ -1608,7 +1623,7 @@ vectors for texture analysis}, Title = {{Mode filtering to reduce ultrasound speckle for feature extraction}}, Volume = {142}, Year = {1995}, - Bdsk-File-1 = {YnBsaXN0MDDUAQIDBAUGCQpYJHZlcnNpb25UJHRvcFkkYXJjaGl2ZXJYJG9iamVjdHMSAAGGoNEHCFRyb290gAFfEA9OU0tleWVkQXJjaGl2ZXKoCwwXGBkdJCVVJG51bGzTDQ4PEBEUViRjbGFzc1dOUy5rZXlzWk5TLm9iamVjdHOAB6ISE4ACgAOiFRaABIAGWWFsaWFzRGF0YVxyZWxhdGl2ZVBhdGjSDRobHFdOUy5kYXRhgAVPEQGaAAAAAAGaAAIAAAxNYWNpbnRvc2ggSEQAAAAAAAAAAAAAAAAAAADE037MSCsAAAAI4twTZXZhbnNfbW9kZV8xOTk1LnBkZgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAjjEMLiMIEAAAAAAAAAAAADAAMAAAkgAAAAAAAAAAAAAAAAAAAABlBhcGVycwAQAAgAAMTTcLwAAAARAAgAAMLiInEAAAABABAACOLcAAjGcQAIuuYAAHmIAAIAPE1hY2ludG9zaCBIRDpVc2VyczptYXR0OkRvY3VtZW50czpQYXBlcnM6ZXZhbnNfbW9kZV8xOTk1LnBkZgAOACgAEwBlAHYAYQBuAHMAXwBtAG8AZABlAF8AMQA5ADkANQAuAHAAZABmAA8AGgAMAE0AYQBjAGkAbgB0AG8AcwBoACAASABEABIAL1VzZXJzL21hdHQvRG9jdW1lbnRzL1BhcGVycy9ldmFuc19tb2RlXzE5OTUucGRmAAATAAEvAAAVAAIAC///AADSHh8gIVgkY2xhc3Nlc1okY2xhc3NuYW1loyEiI11OU011dGFibGVEYXRhVk5TRGF0YVhOU09iamVjdF8QLS4uLy4uLy4uL0RvY3VtZW50cy9QYXBlcnMvZXZhbnNfbW9kZV8xOTk1LnBkZtIeHyYnoicjXE5TRGljdGlvbmFyeQAIABEAGgAfACkAMgA3ADoAPwBBAFMAXABiAGkAcAB4AIMAhQCIAIoAjACPAJEAkwCdAKoArwC3ALkCVwJcAmUCcAJ0AoICiQKSAsICxwLKAAAAAAAAAgEAAAAAAAAAKAAAAAAAAAAAAAAAAAAAAtc=}} + Bdsk-File-1 = {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}} @article{huang_motion_1995, Abstract = { Scene motion is characterized by the orientation of its spectrum in the frequency domain. An image sequence can be divided into small regions which contain only translating information; thus, detecting the image motion corresponds to detecting the orientation of the spectrum of a moving image. In this paper, we use `steerable filters' to estimate the motion of a scene. The steerable filters are synthesized by the interpolation of some `basis functions' and `steered' to arbitrary orientations. These filters measure the `oriented energy' along certain orientations. When the oriented energy is minimized, the spectrum plane can be identified, for which the orientation indicates the velocity. Using steerable filters has two advantages: first, we have no orientation selection problem -- the conventional `Gabor-type' filters can have only certain directional pairs of filters; and second, it is computationally efficient because the output of steerable filters can be interpolated by the outputs of its basis filters. In our experiments, we show the accuracy and simplicity of our method using steerable filters.}, @@ -1625,7 +1640,7 @@ vectors for texture analysis}, Url = {http://www.sciencedirect.com/science/article/B6V09-3Y45125-24/2/faec293798bc020e2eb746d29370411d}, Volume = {13}, Year = {1995}, - Bdsk-File-1 = {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}, + Bdsk-File-1 = {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}, Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/B6V09-3Y45125-24/2/faec293798bc020e2eb746d29370411d}} @article{buhmann_motion_1998, @@ -1642,7 +1657,7 @@ vectors for texture analysis}, Ty = {CONF}, Volume = {5}, Year = {1998}, - 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J.}, @@ -1666,7 +1681,7 @@ vectors for texture analysis}, Title = {{High-Resolution 2-D Cloud-Top Advection From Geostationary Satellite Imagery}}, Volume = {44}, Year = {2006}, - Bdsk-File-1 = {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}} + Bdsk-File-1 = {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}} @article{beatson_fast_2000, Author = {Beatson, RK and Light, WA and Billings, S.}, @@ -1680,7 +1695,7 @@ vectors for texture analysis}, Title = {{Fast Solution of the Radial Basis Function Interpolation Equations: Domain Decomposition Methods}}, Volume = {22}, Year = {2000}, - 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We assume that similar patterns of motion contain similar events with consistent motion across image sequences. Using this assumption, we formulate the problem of motion recognition as a matching of corresponding events in image sequences. To enable the matching, we present and evaluate a set of motion descriptors that exploit the spatial and the temporal coherence of motion measurements between corresponding events in image sequences. As the motion measurements may depend on the relative motion of the camera, we also present a mechanism for local velocity adaptation of events and evaluate its influence when recognizing image sequences subjected to different camera motions. When recognizing motion patterns, we compare the performance of a nearest neighbor (NN) classifier with the performance of a support vector machine (SVM). We also compare event-based motion representations to motion representations in terms of global histograms. A systematic experimental evaluation on a large video database with human actions demonstrates that (i) local spatio-temporal image descriptors can be defined to carry important information of space-time events for subsequent recognition, and that (ii) local velocity adaptation is an important mechanism in situations when the relative motion between the camera and the interesting events in the scene is unknown. The particular advantage of event-based representations and velocity adaptation is further emphasized when recognizing human actions in unconstrained scenes with complex and non-stationary backgrounds.}, @@ -1698,7 +1713,7 @@ vectors for texture analysis}, Url = {http://www.sciencedirect.com/science/article/B6WCX-4N919RH-1/2/a4368ad23cf182fd918b1f4ce123d7ca}, Volume = {108}, Year = {2007}, - Bdsk-File-1 = {YnBsaXN0MDDUAQIDBAUGCQpYJHZlcnNpb25UJHRvcFkkYXJjaGl2ZXJYJG9iamVjdHMSAAGGoNEHCFRyb290gAFfEA9OU0tleWVkQXJjaGl2ZXKoCwwXGBkdJCVVJG51bGzTDQ4PEBEUViRjbGFzc1dOUy5rZXlzWk5TLm9iamVjdHOAB6ISE4ACgAOiFRaABIAGWWFsaWFzRGF0YVxyZWxhdGl2ZVBhdGjSDRobHFdOUy5kYXRhgAVPEQGiAAAAAAGiAAIAAAxNYWNpbnRvc2ggSEQAAAAAAAAAAAAAAAAAAADE037MSCsAAAAI4twVbGFwdGV2X2xvY2FsXzIwMDcucGRmAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAjjL8NUmt8AAAAAAAAAAAADAAMAAAkgAAAAAAAAAAAAAAAAAAAABlBhcGVycwAQAAgAAMTTcLwAAAARAAgAAMNUmt8AAAABABAACOLcAAjGcQAIuuYAAHmIAAIAPk1hY2ludG9zaCBIRDpVc2VyczptYXR0OkRvY3VtZW50czpQYXBlcnM6bGFwdGV2X2xvY2FsXzIwMDcucGRmAA4ALAAVAGwAYQBwAHQAZQB2AF8AbABvAGMAYQBsAF8AMgAwADAANwAuAHAAZABmAA8AGgAMAE0AYQBjAGkAbgB0AG8AcwBoACAASABEABIAMVVzZXJzL21hdHQvRG9jdW1lbnRzL1BhcGVycy9sYXB0ZXZfbG9jYWxfMjAwNy5wZGYAABMAAS8AABUAAgAL//8AANIeHyAhWCRjbGFzc2VzWiRjbGFzc25hbWWjISIjXU5TTXV0YWJsZURhdGFWTlNEYXRhWE5TT2JqZWN0XxAvLi4vLi4vLi4vRG9jdW1lbnRzL1BhcGVycy9sYXB0ZXZfbG9jYWxfMjAwNy5wZGbSHh8mJ6InI1xOU0RpY3Rpb25hcnkACAARABoAHwApADIANwA6AD8AQQBTAFwAYgBpAHAAeACDAIUAiACKAIwAjwCRAJMAnQCqAK8AtwC5Al8CZAJtAngCfAKKApECmgLMAtEC1AAAAAAAAAIBAAAAAAAAACgAAAAAAAAAAAAAAAAAAALh}, + Bdsk-File-1 = {YnBsaXN0MDDUAQIDBAUGCQpYJHZlcnNpb25UJHRvcFkkYXJjaGl2ZXJYJG9iamVjdHMSAAGGoNEHCFRyb290gAFfEA9OU0tleWVkQXJjaGl2ZXKoCwwXGBkdJCVVJG51bGzTDQ4PEBEUViRjbGFzc1dOUy5rZXlzWk5TLm9iamVjdHOAB6ISE4ACgAOiFRaABIAGWWFsaWFzRGF0YVxyZWxhdGl2ZVBhdGjSDRobHFdOUy5kYXRhgAVPEQGiAAAAAAGiAAIAAAxNYWNpbnRvc2ggSEQAAAAAAAAAAAAAAAAAAADGPfMrSCsAAAATVhoVbGFwdGV2X2xvY2FsXzIwMDcucGRmAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABNWecNUmt8AAAAAAAAAAAADAAMAAAkgAAAAAAAAAAAAAAAAAAAABlBhcGVycwAQAAgAAMY95RsAAAARAAgAAMNUmt8AAAABABAAE1YaABNKNQAS5tgAEubFAAIAPk1hY2ludG9zaCBIRDpVc2VyczptYXR0OkRvY3VtZW50czpQYXBlcnM6bGFwdGV2X2xvY2FsXzIwMDcucGRmAA4ALAAVAGwAYQBwAHQAZQB2AF8AbABvAGMAYQBsAF8AMgAwADAANwAuAHAAZABmAA8AGgAMAE0AYQBjAGkAbgB0AG8AcwBoACAASABEABIAMVVzZXJzL21hdHQvRG9jdW1lbnRzL1BhcGVycy9sYXB0ZXZfbG9jYWxfMjAwNy5wZGYAABMAAS8AABUAAgAL//8AANIeHyAhWCRjbGFzc2VzWiRjbGFzc25hbWWjISIjXU5TTXV0YWJsZURhdGFWTlNEYXRhWE5TT2JqZWN0XxAvLi4vLi4vLi4vRG9jdW1lbnRzL1BhcGVycy9sYXB0ZXZfbG9jYWxfMjAwNy5wZGbSHh8mJ6InI1xOU0RpY3Rpb25hcnkACAARABoAHwApADIANwA6AD8AQQBTAFwAYgBpAHAAeACDAIUAiACKAIwAjwCRAJMAnQCqAK8AtwC5Al8CZAJtAngCfAKKApECmgLMAtEC1AAAAAAAAAIBAAAAAAAAACgAAAAAAAAAAAAAAAAAAALh}, Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/B6WCX-4N919RH-1/2/a4368ad23cf182fd918b1f4ce123d7ca}} @article{jain_segregation_2007, @@ -1717,7 +1732,7 @@ vectors for texture analysis}, Url = {http://www.sciencedirect.com/science/article/B6WCX-4NF4F84-1/2/57933ee9a30957c27d98e563035f0524}, Volume = {108}, Year = {2007}, - 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Previous methods are based on shape matching and level set. In this paper, a method based on snake model is used for cloud tracking. Snakes are known to be more efficient than level set for contour detection however they do not handle topological changes. Therefore, geometrical criteria are introduced to characterize topological transformations. Geometrical techniques are then combined and inserted in the tracking algorithm to perform morphological operations. By applying this method, a history of the positions of the clouds is obtained. In a second stage, a data model is presented for cloud interrogation. Physical information is introduced and data are organized so that spatiotemporal queries can be performed. Results obtained with the tracking method on a real data set are presented and some query examples are given. }, @@ -1812,7 +1827,7 @@ vectors for texture analysis}, Url = {http://dx.doi.org/10.1007/s10707-006-0008-6}, Volume = {11}, Year = {2007}, - Bdsk-File-1 = {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}, + Bdsk-File-1 = {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}, Bdsk-Url-1 = {http://dx.doi.org/10.1007/s10707-006-0008-6}} @article{mukherjee_cloud_2002, @@ -1830,7 +1845,7 @@ vectors for texture analysis}, Ty = {JOUR}, Volume = {40}, Year = {2002}, - 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It does this by combining an affine representation of local image motions with a local structure model based on Gaussian functions. After a brief review of its symmetry and completeness properties, the representation is applied to the analysis of image motions in a typical video sequence}, @@ -1847,7 +1862,7 @@ vectors for texture analysis}, Ty = {CONF}, Volume = {2}, Year = {1998}, - Bdsk-File-1 = {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}} + Bdsk-File-1 = {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}} @article{kass_snakes_1988, Author = {Kass, M. and Witkin, A. and Terzopoulos, D.}, @@ -1860,7 +1875,7 @@ vectors for texture analysis}, Title = {{Snakes: Active contour models}}, Volume = {1}, Year = {1988}, - 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Because of non-fronto-parallel viewing of an object or due to relative motion between the camera and the object, the resultant image may undergo affine or projective object-to-image transformations. In a recent paper we have shown that in the case of object tracking, frame-to-frame deformations of an initial curve obtained through Euler-Lagrange descent equations of a curve functional can be used to enact a desired Lie group of plane transformations [A.-R. Mansouri, D. P. Mukherjee, S. T. Acton, Constraining active contour evolution via Lie groups of transformation, IEEE Trans. Image Process. 13 (2004) 853-863]. In this work, we propose an energy functional that encodes the Lie group transformation parameters, which in turn guide shape distortion due to oblique viewing. Additional constraints, such as transformation smoothness, are imposed on the active contour by modifying the energy functional. The functional is minimized using numerical schemes similar to the conjugate gradient technique, and the convergence properties are discussed. The success of the technique for affine and projective scenes is demonstrated with both synthetic and real image examples and compared with the related approaches.}, @@ -1887,7 +1902,7 @@ vectors for texture analysis}, Url = {http://www.sciencedirect.com/science/article/B6V14-4KJV2YY-2/2/befabdd8361ea03d4af0825f4c30f3b1}, Volume = {40}, Year = {2007}, - Bdsk-File-1 = {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}, + Bdsk-File-1 = {YnBsaXN0MDDUAQIDBAUGCQpYJHZlcnNpb25UJHRvcFkkYXJjaGl2ZXJYJG9iamVjdHMSAAGGoNEHCFRyb290gAFfEA9OU0tleWVkQXJjaGl2ZXKoCwwXGBkdJCVVJG51bGzTDQ4PEBEUViRjbGFzc1dOUy5rZXlzWk5TLm9iamVjdHOAB6ISE4ACgAOiFRaABIAGWWFsaWFzRGF0YVxyZWxhdGl2ZVBhdGjSDRobHFdOUy5kYXRhgAVPEQGyAAAAAAGyAAIAAAxNYWNpbnRvc2ggSEQAAAAAAAAAAAAAAAAAAADGPfMrSCsAAAATVhoZbXVraGVyamVlX2FmZmluZV8yMDA3LnBkZgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABNWiMNDvk8AAAAAAAAAAAADAAMAAAkgAAAAAAAAAAAAAAAAAAAABlBhcGVycwAQAAgAAMY95RsAAAARAAgAAMNDsD8AAAABABAAE1YaABNKNQAS5tgAEubFAAIAQk1hY2ludG9zaCBIRDpVc2VyczptYXR0OkRvY3VtZW50czpQYXBlcnM6bXVraGVyamVlX2FmZmluZV8yMDA3LnBkZgAOADQAGQBtAHUAawBoAGUAcgBqAGUAZQBfAGEAZgBmAGkAbgBlAF8AMgAwADAANwAuAHAAZABmAA8AGgAMAE0AYQBjAGkAbgB0AG8AcwBoACAASABEABIANVVzZXJzL21hdHQvRG9jdW1lbnRzL1BhcGVycy9tdWtoZXJqZWVfYWZmaW5lXzIwMDcucGRmAAATAAEvAAAVAAIAC///AADSHh8gIVgkY2xhc3Nlc1okY2xhc3NuYW1loyEiI11OU011dGFibGVEYXRhVk5TRGF0YVhOU09iamVjdF8QMy4uLy4uLy4uL0RvY3VtZW50cy9QYXBlcnMvbXVraGVyamVlX2FmZmluZV8yMDA3LnBkZtIeHyYnoicjXE5TRGljdGlvbmFyeQAIABEAGgAfACkAMgA3ADoAPwBBAFMAXABiAGkAcAB4AIMAhQCIAIoAjACPAJEAkwCdAKoArwC3ALkCbwJ0An0CiAKMApoCoQKqAuAC5QLoAAAAAAAAAgEAAAAAAAAAKAAAAAAAAAAAAAAAAAAAAvU=}, Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/B6V14-4KJV2YY-2/2/befabdd8361ea03d4af0825f4c30f3b1}} @article{kittler_probabilistic_2000, @@ -1905,7 +1920,7 @@ vectors for texture analysis}, Url = {http://www.sciencedirect.com/science/article/B6V14-3YF9WNJ-F/2/0bd496608417f69c98bcda9f380aecec}, Volume = {33}, Year = {2000}, - 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R. and Anandan, P. and Hanna, K. 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D}, @@ -2336,7 +2351,7 @@ vectors for texture analysis}, Pages = {982-987}, Title = {Motion Estimation using Ordinal Measures}, Year = {1997}, - Bdsk-File-1 = {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}} + Bdsk-File-1 = {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}} @book{cressie_statistics_1991, Author = {N. 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H. McClellan and R. W. Schafer and M. A. Yoder}, @@ -2407,9 +2422,9 @@ vectors for texture analysis}, Year = {1973}} @article{fan_hardware_2005, - Author = {Q Fan and A Efrat and V Koltun and S Krishnan and S Venkatasubramanian}, + Author = {Q. Fan and A. Efrat and V. Koltun and S. Krishnan and S. Venkatasubramanian}, Date-Added = {2007-08-25 12:06:38 +0100}, - Date-Modified = {2007-08-25 12:06:38 +0100}, + Date-Modified = {2009-06-13 20:06:14 +0100}, Journal = {Proc. 7th Workshop on Algorithm Engineering and Experiments (ALENEX)}, Title = {Hardware assisted natural neighbour interpolation}, Year = {2005}} @@ -2429,7 +2444,7 @@ vectors for texture analysis}, Url = {http://comjnl.oxfordjournals.org/cgi/content/abstract/24/2/167}, Volume = {24}, Year = {1981}, - Bdsk-File-1 = {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}, + Bdsk-File-1 = {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}, Bdsk-Url-1 = {http://comjnl.oxfordjournals.org/cgi/content/abstract/24/2/167}} @article{hou_cubic_1978, @@ -2464,7 +2479,7 @@ vectors for texture analysis}, Title = {Normalized averaging using adaptive applicability functions with applications in image reconstruction from sparsely and randomly sampled data}, Volume = {2749}, Year = {2003}, - 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M. Ruohoniemi and K. B. Baker}, Date-Added = {2007-08-25 12:06:38 +0100}, - Date-Modified = {2007-11-05 10:31:27 +0000}, - Journal = {jgr}, + Date-Modified = {2009-06-13 20:05:27 +0100}, + Journal = {Journal of Geophysical Research}, Keywords = {ionosphere}, Local-Url = {file://localhost/Users/matt/Documents/Papers/ruohoniemi_large-scale_1998.pdf}, Pages = {20797-20811}, - Title = {Large-scale imaging of high-latitude convection with Super Dual Auroral Radar Network HF radar observations}, + Title = {Large-scale imaging of high-latitude convection with {Super Dual Auroral Radar Network HF} radar observations}, Volume = {03}, Year = {1998}, - Bdsk-File-1 = {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}} + Bdsk-File-1 = {YnBsaXN0MDDUAQIDBAUGCQpYJHZlcnNpb25UJHRvcFkkYXJjaGl2ZXJYJG9iamVjdHMSAAGGoNEHCFRyb290gAFfEA9OU0tleWVkQXJjaGl2ZXKoCwwXGBkdJCVVJG51bGzTDQ4PEBEUViRjbGFzc1dOUy5rZXlzWk5TLm9iamVjdHOAB6ISE4ACgAOiFRaABIAGWWFsaWFzRGF0YVxyZWxhdGl2ZVBhdGjSDRobHFdOUy5kYXRhgAVPEQHKAAAAAAHKAAIAAAxNYWNpbnRvc2ggSEQAAAAAAAAAAAAAAAAAAADGPfMrSCsAAAATVhofcnVvaG9uaWVtaV9sYXJnZS1zY2FsZV8xOTk4LnBkZgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABNWlcLiMIwAAAAAAAAAAAADAAMAAAkgAAAAAAAAAAAAAAAAAAAABlBhcGVycwAQAAgAAMY95RsAAAARAAgAAMLiInwAAAABABAAE1YaABNKNQAS5tgAEubFAAIASE1hY2ludG9zaCBIRDpVc2VyczptYXR0OkRvY3VtZW50czpQYXBlcnM6cnVvaG9uaWVtaV9sYXJnZS1zY2FsZV8xOTk4LnBkZgAOAEAAHwByAHUAbwBoAG8AbgBpAGUAbQBpAF8AbABhAHIAZwBlAC0AcwBjAGEAbABlAF8AMQA5ADkAOAAuAHAAZABmAA8AGgAMAE0AYQBjAGkAbgB0AG8AcwBoACAASABEABIAO1VzZXJzL21hdHQvRG9jdW1lbnRzL1BhcGVycy9ydW9ob25pZW1pX2xhcmdlLXNjYWxlXzE5OTgucGRmAAATAAEvAAAVAAIAC///AADSHh8gIVgkY2xhc3Nlc1okY2xhc3NuYW1loyEiI11OU011dGFibGVEYXRhVk5TRGF0YVhOU09iamVjdF8QOS4uLy4uLy4uL0RvY3VtZW50cy9QYXBlcnMvcnVvaG9uaWVtaV9sYXJnZS1zY2FsZV8xOTk4LnBkZtIeHyYnoicjXE5TRGljdGlvbmFyeQAIABEAGgAfACkAMgA3ADoAPwBBAFMAXABiAGkAcAB4AIMAhQCIAIoAjACPAJEAkwCdAKoArwC3ALkChwKMApUCoAKkArICuQLCAv4DAwMGAAAAAAAAAgEAAAAAAAAAKAAAAAAAAAAAAAAAAAAAAxM=}} @article{young_recursive_1995, Author = {I. T. Young and L. J. van Vliet}, Date-Added = {2007-08-25 12:06:38 +0100}, - Date-Modified = {2007-11-05 10:30:05 +0000}, + Date-Modified = {2009-06-13 20:03:36 +0100}, Journal = {Signal Processing}, Keywords = {Filter,Gaussian}, Local-Url = {file://localhost/Users/matt/Documents/Papers/young_recursive_1995.pdf}, Pages = {139-151}, - Title = {Recursive implementation of the Gaussian filter}, + Title = {Recursive implementation of the {Gaussian} filter}, Volume = {44}, Year = {1995}, - Bdsk-File-1 = {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}} + Bdsk-File-1 = {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}} @article{sandwell_biharmonic_1987, Author = {D. T. 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Samardjiev and P. A. Bradley and L. R. Cander and M. I. Dick}, @@ -2834,9 +2849,9 @@ vectors for texture analysis}, Year = {2006}} @article{watson_neighborhood-based_1987, - Author = {DF Watson and GM Philip}, + Author = {D. F. Watson and G. M. Philip}, Date-Added = {2007-08-25 12:06:38 +0100}, - Date-Modified = {2007-08-25 12:06:38 +0100}, + Date-Modified = {2009-06-13 20:04:04 +0100}, Journal = {Geobyte}, Number = {2}, Pages = {12-16}, @@ -2856,7 +2871,7 @@ vectors for texture analysis}, Title = {Fast Anisotropic Gauss Filtering}, Volume = {12}, Year = {2002}, - Bdsk-File-1 = {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}} + Bdsk-File-1 = {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}} @inproceedings{meggs_simulations_2002, Address = {Maastricht, Netherlands}, @@ -2871,7 +2886,7 @@ vectors for texture analysis}, Title = {SIMULATIONS OF THIN SHELL AND 4-D INVERSION TECHNIQUES FOR MAPPING OF TOTAL ELECTRON CONTENT.}, Volume = {15}, Year = {2002}, - 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E. Danielsson}, @@ -2933,7 +2948,7 @@ vectors for texture analysis}, School = {Link\"{o}ping University, Sweden}, Title = {Polynomial Expansion for Orientation and Motion Estimation}, Year = {2002}, - Bdsk-File-1 = {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}} + Bdsk-File-1 = {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}} @article{heiri_model-based_2006, Author = {C. Heiri and H. Buggmann and W. Tinner and O. Heiri and H. Lischke}, @@ -2964,7 +2979,7 @@ vectors for texture analysis}, Local-Url = {file://localhost/Users/matt/Documents/Papers/wilson_relational_1999.pdf}, Title = {Relational matching by discrete relaxation}, Year = {1999}, - Bdsk-File-1 = {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}} + Bdsk-File-1 = {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}} @article{meijering_chronology_2002, Author = {E. Meijering}, @@ -2988,7 +3003,7 @@ vectors for texture analysis}, Title = {Glacier Surface Motion Computation from Digital Image Sequences}, Volume = {38}, Year = {2000}, - Bdsk-File-1 = {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}} + Bdsk-File-1 = {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}} @article{sambridge_geophysical_1995, Author = {M Sambridge and J Braun and H McQueen}, @@ -3012,7 +3027,7 @@ vectors for texture analysis}, Month = {April}, Title = {Measuring Sparseness of Noisy Signals}, Year = {2003}, - 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This problem can be solved by constructing the Voronoi diagram of the griven sites and then locating the query point inone of its regions. Two algorithms are given, one that constructs the Voronoi diagram in O(n log n) time, and another that inserts a new sit on O(n) time. Both are based on the use of the Voronoi dual, or Delaunay triangulation, and are simple enough to be of practical value. the simplicity of both algorithms can be attributed to the separation of the geometrical and topological aspects of the problem and to the use of two simple but powerful primitives, a geometric predicate and an operator for manipulating the topology of the diagram. The topology is represented by a new data structure for generalized diagrams, that is, embeddings of graphs in two-dimensional manifolds. This structure represents simultaneously an embedding, its dual, and its mirror image. Furthermore, just two operators are sufficients for building and modifying arbitrary diagrams.}, @@ -3038,7 +3053,7 @@ vectors for texture analysis}, Title = {The Potential of the Maximum Cross-Correlation Technique to Estimate Surface Currents From Thermal {AVHRR} Global Area Coverage Data}, Volume = {3}, Year = {2006}, - Bdsk-File-1 = {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}} + Bdsk-File-1 = {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}} @phdthesis{blanch_using_2003, Author = {J. Blanch}, @@ -3049,7 +3064,7 @@ vectors for texture analysis}, School = {Dept. of Aeronautics and Astronautics, Stanford University}, Title = {Using Kriging to Bound Satellite Ranging Errors Due to the Ionosphere}, Year = {2003}, - Bdsk-File-1 = {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}} + Bdsk-File-1 = {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}} @article{de_boor_bicubic_1962, Author = {C de Boor}, @@ -3063,12 +3078,14 @@ vectors for texture analysis}, @inproceedings{jong_gradient_1998, Author = {F. de Jong and L. J. van Vliet and P. P. Jonker}, + Booktitle = {MVA'98 IAPR Workshop on Machine Vision Applications}, Date-Added = {2007-08-25 12:06:38 +0100}, - Date-Modified = {2007-11-05 10:30:17 +0000}, + Date-Modified = {2009-06-13 20:22:48 +0100}, Local-Url = {file://localhost/Users/matt/Documents/Papers/jong_gradient_1998.pdf}, + Pages = {144--147}, Title = {Gradient estimation in uncertain data}, Year = {1998}, - Bdsk-File-1 = {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}} + Bdsk-File-1 = {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}} @inproceedings{knutsson_normalized_1993, Address = {New York City, USA}, @@ -3081,7 +3098,7 @@ vectors for texture analysis}, Pages = {515-523}, Title = {Normalized and Differential Convolution: Methods for Interpolation and Filtering of Incomplete and Uncertain data}, Year = {1993}, - 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The output signal is estimated using integration of signals over a neighbourhood employing a local model of the signal using discrete filters. The strength of the method is demonstrated in motion compensation examples by comparing to traditional techniques. @@ -3108,7 +3125,7 @@ vectors for texture analysis}, Pages = {457-460}, Title = {On the Equivalence of Normalized Convolution and Normalized Differential Convolution}, Year = {1994}, - Bdsk-File-1 = {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}} + Bdsk-File-1 = {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}} @book{leick_gps_1995, Author = {A. Leick}, @@ -3130,7 +3147,7 @@ vectors for texture analysis}, Title = {Vector Median Filters}, Volume = {78}, Year = {1990}, - Bdsk-File-1 = {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}} + Bdsk-File-1 = {YnBsaXN0MDDUAQIDBAUGCQpYJHZlcnNpb25UJHRvcFkkYXJjaGl2ZXJYJG9iamVjdHMSAAGGoNEHCFRyb290gAFfEA9OU0tleWVkQXJjaGl2ZXKoCwwXGBkdJCVVJG51bGzTDQ4PEBEUViRjbGFzc1dOUy5rZXlzWk5TLm9iamVjdHOAB6ISE4ACgAOiFRaABIAGWWFsaWFzRGF0YVxyZWxhdGl2ZVBhdGjSDRobHFdOUy5kYXRhgAVPEQGmAAAAAAGmAAIAAAxNYWNpbnRvc2ggSEQAAAAAAAAAAAAAAAAAAADGPfMrSCsAAAATVhoWYXN0b2xhX3ZlY3Rvcl8xOTkwLnBkZgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABNWLsLiMIIAAAAAAAAAAAADAAMAAAkgAAAAAAAAAAAAAAAAAAAABlBhcGVycwAQAAgAAMY95RsAAAARAAgAAMLiInIAAAABABAAE1YaABNKNQAS5tgAEubFAAIAP01hY2ludG9zaCBIRDpVc2VyczptYXR0OkRvY3VtZW50czpQYXBlcnM6YXN0b2xhX3ZlY3Rvcl8xOTkwLnBkZgAADgAuABYAYQBzAHQAbwBsAGEAXwB2AGUAYwB0AG8AcgBfADEAOQA5ADAALgBwAGQAZgAPABoADABNAGEAYwBpAG4AdABvAHMAaAAgAEgARAASADJVc2Vycy9tYXR0L0RvY3VtZW50cy9QYXBlcnMvYXN0b2xhX3ZlY3Rvcl8xOTkwLnBkZgATAAEvAAAVAAIAC///AADSHh8gIVgkY2xhc3Nlc1okY2xhc3NuYW1loyEiI11OU011dGFibGVEYXRhVk5TRGF0YVhOU09iamVjdF8QMC4uLy4uLy4uL0RvY3VtZW50cy9QYXBlcnMvYXN0b2xhX3ZlY3Rvcl8xOTkwLnBkZtIeHyYnoicjXE5TRGljdGlvbmFyeQAIABEAGgAfACkAMgA3ADoAPwBBAFMAXABiAGkAcAB4AIMAhQCIAIoAjACPAJEAkwCdAKoArwC3ALkCYwJoAnECfAKAAo4ClQKeAtEC1gLZAAAAAAAAAgEAAAAAAAAAKAAAAAAAAAAAAAAAAAAAAuY=}} @article{akima_method_1978, Author = {H. Akima}, @@ -3160,7 +3177,7 @@ vectors for texture analysis}, School = {University of Bath}, Title = {Ionospheric total electron content mapping using {GNSS}}, Year = {2005}, - Bdsk-File-1 = {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}} + Bdsk-File-1 = {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}} @book{sabins_remote_1987, Author = {Jr. Sabins}, @@ -3231,7 +3248,7 @@ vectors for texture analysis}, Title = {A study of cross-validation and bootstrap for accuracy estimation and model selection}, Volume = {2}, Year = {1995}, - 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S. J. Estepar and M. Martin-Fernandez and C. Alberola-Lopez and J. Ellsmere and R. Kikinis and C.-F Westin}, @@ -3281,7 +3298,7 @@ vectors for texture analysis}, Title = {On orientation and anisotropy estimation for online fingerprint authentication}, Volume = {53}, Year = {2005}, - Bdsk-File-1 = {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}} + Bdsk-File-1 = {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}} @book{gonzalez_digital_2001, Author = {R. C. Gonzalez and R. E. 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Guinehut and P-Y. Le Traon and G. Larnicol and S. Philipps}, @@ -3338,7 +3355,7 @@ vectors for texture analysis}, Title = {The quickhull algorithm for convex hulls}, Volume = {22}, Year = {1996}, - Bdsk-File-1 = {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}} + Bdsk-File-1 = {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}} @book{kernighan_c_1988, Author = {B. W. Kernighan and D. M. Ritchie}, @@ -3409,7 +3426,7 @@ vectors for texture analysis}, Title = {Cloud Tracking Using Ordinal Measures and Relaxation Labelling}, Volume = {2}, Year = {1999}, - Bdsk-File-1 = {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}} + Bdsk-File-1 = {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}} @article{brad_cloud_2002, Author = {R[emus] Brad and I[oan] A. Letia}, @@ -3425,7 +3442,7 @@ vectors for texture analysis}, Url = {http://link.aip.org/link/?PSI/4875/408/1}, Volume = {4875}, Year = {2002}, - Bdsk-File-1 = {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}, + Bdsk-File-1 = {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}, Bdsk-Url-1 = {http://link.aip.org/link/?PSI/4875/408/1}} @article{matheron_intrinsic_1973, @@ -3498,7 +3515,7 @@ numerically controlled (CNC) mill}, Title = {Surface interpolation with radial basis functions for medical imaging}, Volume = {16}, Year = {1997}, - 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K. Beatson and W. A. Light and S. Billings}, @@ -3511,7 +3528,7 @@ numerically controlled (CNC) mill}, Title = {Fast Solution of the Radial Basis Function Interpolation Equations: Domain Decomposition Methods}, Volume = {22}, Year = {2001}, - Bdsk-File-1 = {YnBsaXN0MDDUAQIDBAUGCQpYJHZlcnNpb25UJHRvcFkkYXJjaGl2ZXJYJG9iamVjdHMSAAGGoNEHCFRyb290gAFfEA9OU0tleWVkQXJjaGl2ZXKoCwwXGBkdJCVVJG51bGzTDQ4PEBEUViRjbGFzc1dOUy5rZXlzWk5TLm9iamVjdHOAB6ISE4ACgAOiFRaABIAGWWFsaWFzRGF0YVxyZWxhdGl2ZVBhdGjSDRobHFdOUy5kYXRhgAVPEQGiAAAAAAGiAAIAAAxNYWNpbnRvc2ggSEQAAAAAAAAAAAAAAAAAAADE037MSCsAAAAI4twVYmVhdHNvbl9mYXN0XzIwMDEucGRmAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAji78LiMLMAAAAAAAAAAAADAAMAAAkgAAAAAAAAAAAAAAAAAAAABlBhcGVycwAQAAgAAMTTcLwAAAARAAgAAMLiIqMAAAABABAACOLcAAjGcQAIuuYAAHmIAAIAPk1hY2ludG9zaCBIRDpVc2VyczptYXR0OkRvY3VtZW50czpQYXBlcnM6YmVhdHNvbl9mYXN0XzIwMDEucGRmAA4ALAAVAGIAZQBhAHQAcwBvAG4AXwBmAGEAcwB0AF8AMgAwADAAMQAuAHAAZABmAA8AGgAMAE0AYQBjAGkAbgB0AG8AcwBoACAASABEABIAMVVzZXJzL21hdHQvRG9jdW1lbnRzL1BhcGVycy9iZWF0c29uX2Zhc3RfMjAwMS5wZGYAABMAAS8AABUAAgAL//8AANIeHyAhWCRjbGFzc2VzWiRjbGFzc25hbWWjISIjXU5TTXV0YWJsZURhdGFWTlNEYXRhWE5TT2JqZWN0XxAvLi4vLi4vLi4vRG9jdW1lbnRzL1BhcGVycy9iZWF0c29uX2Zhc3RfMjAwMS5wZGbSHh8mJ6InI1xOU0RpY3Rpb25hcnkACAARABoAHwApADIANwA6AD8AQQBTAFwAYgBpAHAAeACDAIUAiACKAIwAjwCRAJMAnQCqAK8AtwC5Al8CZAJtAngCfAKKApECmgLMAtEC1AAAAAAAAAIBAAAAAAAAACgAAAAAAAAAAAAAAAAAAALh}} + Bdsk-File-1 = {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}} @comment{BibDesk Static Groups{ <?xml version="1.0" encoding="UTF-8"?> main_bibliography.bib @@ -1,11 +1,11 @@ -The field of \ac{MM} in the mid nineteen-sixties, in France, where it was -initially used to analyse the geometry of porous media. Initial work on was -completed by G. Matheron and J. Serra, and the seminal work entitled: +The field of \ac{MM} originated in the mid nineteen-sixties, in France, where +it was initially used to analyse the geometry of porous media. Initial work +was completed by G. Matheron and J. Serra, and the seminal work entitled: \emph{El\'{e}ments pour une th\'{e}orie des milieux poreux} was published by -Matheron in 1967. In this paper, he formalised various concepts, such as -granulometries, or morphological profiles which are still heavily used today. +Matheron in 1967. In this paper, he formalised various concepts such as +granulometries or morphological profiles which are still heavily used today. -\ac{MM} has its roots in geoscience and interestingly, the Matheron mentioned +\ac{MM} has its roots in geoscience and, interestingly, the Matheron mentioned here is the very same person who was later credited with pioneering the field of Geostatistics, mentioned in Section~\ref{sec:paper_kriging}, on page~\pageref{sec:paper_kriging}. @@ -22,7 +22,7 @@ the connectivity of level-sets. \end{figure} For example, imagine the grey-level of a greyscale image to be a vertical -displacement. A level-set is a horizontal slice through the image, at a +displacement. A level-set is a horizontal slice through the image at a specific value. This means that a given pixel value can be a member of several level-sets (up to 256 for a typical, 8-bit greyscale image). Fig.~\ref{fig:component_morphology} shows an example image cross-section, @@ -61,8 +61,8 @@ meet the specified criterion. Area opening is equivalent to moving down from the top of the connected component graph until the area is exceeded, and area closing is the equivalent to moving up from the bottom until the criterion is exceeded. Fig.~\ref{fig:area_morphology} shows how an area opening using an -area of three would alter an example image, and its connected component graph. -in the image, A, B, C, D, and F would be removed, as they all correspond to +area of three would alter an example image and its connected component graph. +In the image, A, B, C, D, and F would be removed, as they all correspond to components with areas of less than three. \begin{figure} [!ht] morphology.tex @@ -8,7 +8,7 @@ evaluating their suitability to estimating motion in polar ionospheric \ac{TEC} data which contains storm features, such as \ac{TOI}. First, in Section~\ref{sec:data_sources}, the data being examined are -described, example frames and a schematic diagram are presented to illustrate +described. Example frames and a schematic diagram are presented to illustrate the spatial extent of the data. Section~\ref{sec:assumptions} then introduces some of the assumptions which are common to all motion estimation techniques. Section~\ref{sec:differential_analysis} describes \emph{differential @@ -29,13 +29,13 @@ Section~\ref{sec:suitability}. % this is specific to the motion study. -The chief source of data considered in this, and later chapters on motion +The chief source of data considered in this and later chapters on motion estimation (\ref{cha:motion_estimation_using_optical_flow_and_corr} and \ref{cha:motion_estimation_curve_matching}), was gathered by \ac{GPS} -receivers during the `Halloween Storm', which occurred during the 29---31 +receivers during the `Halloween Storm', which occurred during the 29--31 October 2003. This was a large geomagnetic storm, with peak activity that occurred between about 20:00 and 23:00 UTC, over North America. During this -time, a large region of \ac{SED} developed over mainland USA, and moved +time, a large region of \ac{SED} developed over mainland USA and moved northward over Canada and through the polar region to the night-side of the Earth. This storm caused a great many operational problems and failures for satellites as well as many problems for land-based communications and power @@ -44,7 +44,7 @@ systems. The available data consist of images created using the \acf{MIDAS} software from the \depteee, at the \uob~\citep{spencer_imaging_2007}. These images were generated by extracting integrated electron measurements from paths between -\ac{GPS} receivers and satellites, and performing a 4-D tomographic +\ac{GPS} receivers and satellites and performing a 4-D tomographic pseudo-inversion. The region covered by the inversion is a 3-D grid extending radially in an approximate square of dimension $96^{\circ}$ around the north geographic pole, such that the voxels have a horizontal resolution of @@ -66,10 +66,10 @@ under examination contain data ranging in value from close to zero to $\approx 250$ TECU\footnote{1 TECU or \ac{TEC} unit, corresponds to an electron concentration of $10^{16}$ electrons per $m^2$ }, meaning that a compact representation using 8-bit unsigned integers is possible. This is advantageous -because many image processing techniques, such as mathematical morphology are +because many image processing techniques such as mathematical morphology are able to operate more efficiently on integer classes. -Also of note, is the fact the motion occurring in the latter part of the +Also of note is the fact the motion occurring in the latter part of the sequence is confusing and hard to ascertain \emph{by eye}. This suggests that all motion-estimation techniques will have difficulty analysing the motion in this section; what is hard for humans is likely to be very hard for computer @@ -149,7 +149,7 @@ tomographic images. \includegraphics[width=0.5\textwidth]{exb_30} } } - \caption[Modelled TOI vectors]{Plots of modelled $E \times B$ vectors.} + \caption[Modelled TOI vectors]{Plots of modelled $\mathbf{E} \times \mathbf{B}$ vectors.} \label{fig:exb} \end{figure} @@ -167,7 +167,7 @@ allow the electric field to be modelled with time, which when combined with an estimate of the magnetic field allow plasma velocity estimates to be made \citep{spencer_imaging_2007}. -Fig.~\ref{fig:exb} clearly show a simple precessing two-cell convective +Fig.~\ref{fig:exb} clearly shows a simple precessing two-cell convective pattern. Within this pattern, the \ac{TOI} moves through the centre of the two cells, which are surrounded by concentric rings of vectors. Various different convection patterns can occur, depending on the orientation and strength of @@ -230,7 +230,7 @@ made by most motion estimation systems are given in \citet{m_sonka_image_1999}, \item The motion of any given object does not exceed some \emph{maximum velocity}. This means that if the object's position in one frame is known, it must be within a circle of radius $v_m.dt$, which is centred on the last known -position, in the next. Where $v_m$ is the maximum velocity of the object, and +position, in the next. Here $v_m$ is the maximum velocity of the object, and $dt$ is the time between frames. \item The acceleration of objects is small. @@ -249,12 +249,12 @@ The third of these is known as the \emph{velocity smoothness constraint} and is the cornerstone of optical flow techniques. This means that object motion should vary smoothly across an image: a very reasonable assumption (similar to the theory of regionalised variables, see Section~\ref{sec:paper_kriging}) -which arises from the fact that images tend have regional autocorrelation +which arises from the fact that images tend to have regional autocorrelation which may be characterised by measuring autocorrelation distance, or using a semivariogram. If this autocorrelation is not present, an image is essentially -random noise. This does not necessarily hold where multiple objects are moving -in different directions, which would be expected to cause discontinuities in -the motion field. +random noise. This condition does not necessarily hold where multiple objects +are moving in different directions, which would be expected to cause +discontinuities in the motion field. It should be noted that the final two assumptions do not necessarily hold unless the objects being analysed are rigid. Nevertheless, these are the @@ -281,12 +281,12 @@ image $d(x, y)$, by subtracting the two images and thresholding the result: \begin{equation} \begin{array}{cccl} - d(x, y) & = & 0 & if \;\;\; \mbox{if} |f_1(x, y) - f_2(x, y)| \leq \epsilon \\ + d(x, y) & = & 0 & \;\;\; \mbox{if} |f_1(x, y) - f_2(x, y)| \leq \epsilon \\ & = & 1 & \mbox{otherwise}. \end{array} \end{equation} -Where $\epsilon$ is a small positive constant. This allows detection of any +Here $\epsilon$ is a small positive constant. This allows detection of any motion relative to the background (provided images are registered correctly) but cannot distinguish between different motion directions. Cumulative difference images (essentially moving averages) can be used to acquire more @@ -324,12 +324,12 @@ a threshold applied and have a scaled colour map. In all of these cases, whilst some motion \emph{would} be detected, this method cannot accurately capture the motion of the \ac{TOI} and gives the highest values in regions outside of the areas where motion can most easily be seen. This is because of -the change in noise and background between the images is too high Similarly, +the change in noise and background between the images is too high. Similarly, there is a change in average value through the sequence, making a static threshold ineffective. This technique is commonly improved by detecting moving -edges \citet{nixon_feature_2008}. However, in this case edge detection +edges, \citep[\emph{e.g.,}][]{nixon_feature_2008}. However, in this case edge detection operators, such as the Sobel operator, which typically uses a $3 \times 3$ (or larger) kernel, are too large relative to the scale of the image to provide meaningful results. Applying a simple Sobel magnitude edge detector to the @@ -355,7 +355,7 @@ points across an image. In this thesis, the term is used to denote a specific class of techniques which aim to calculate motion fields by differentiating in time and space, and applying smoothness constraints on the produced flow fields. The main additional assumption on which optical flow computation is -based, is that an object point's brightness is constant over time. This is the +based is that an object point's brightness is constant over time. This is the \emph{constant brightness} criterion. Optical flow's derivation \citep[see e.g.][]{nixon_feature_2008} uses this to give the motion constraint equation: \begin{equation} @@ -363,14 +363,14 @@ based, is that an object point's brightness is constant over time. This is the + \nabla t = 0 \label{eqn:motion_constraint} \end{equation} -Where $ \nabla x = \frac{\delta \mathbf{P}}{\delta x}$, $\nabla y = +where $ \nabla x = \frac{\delta \mathbf{P}}{\delta x}$, $\nabla y = \frac{\delta \mathbf{P}}{\delta y}$, $\nabla t = \frac{\delta \mathbf{P}}{\delta t}$, $u$ and $v$ are the horizontal and vertical \emph{optical flow} components, and $\mathbf{P}$ is an input image image. This equation describes how an image changes in time or \emph{moves}, and shows that `optical flow' or the motion of each pixel, plus the rate of -spatial intensity produce this effect together. To extract the optical flow, +spatial intensity, produce this effect together. To extract the optical flow, this equation can be solved by estimating $\nabla_x$, $\nabla_y$ and $\nabla_z$ using image derivatives. However, this problem is ill-posed, since many values of $u$ and $v$ will satisfy (\ref{eqn:motion_constraint}). @@ -384,10 +384,10 @@ minimisation of: e = \lambda \times ec + es \label{eqn:optical_flow} \end{equation} -Where $\lambda$ is a regularisation parameter, or smoothness constraint. This +where $\lambda$ is a regularisation parameter, or smoothness constraint. This can then be implemented in discrete form using first-order differences and solved in an iterative process. Gradients can be calculated by examining $2 -\times 2 $ pixel, or larger neighbourhoods (or using scale-space methods). +\times 2 $ pixel, or larger, neighbourhoods (or using scale-space methods). However, in the context of these small images, larger neighbourhood sizes will not be as effective. Also, using even-sized neighbourhoods will result in a slight offset to the estimates. @@ -413,10 +413,10 @@ evaluations of the methods' performances. Where images are noisy, region based motion estimation methods may prove to be more appropriate motion estimators than those based on image -derivatives~\citep{barron_performance_1994}. In these cases, region matching -methods, such as template matching may be used instead. +derivatives~\citep{barron_performance_1994}. In these cases region matching +methods such as template matching may be used instead. -Template and block matching arose from the need to of find \emph{template} +Template and block matching arose from the need to find \emph{template} images, or small objects, in other images \citep{nixon_feature_2008, gonzalez_digital_2001}. @@ -428,8 +428,8 @@ gonzalez_digital_2001}. \end{figure} This can by carried out by sliding the template image throughout the source -and using a similarity or dissimilarity measure (such as cross-correlation, or -\ac{SSD}) to measure compatibility between the two. In a more general case, +and using a similarity or dissimilarity measure [such as cross-correlation, or +\ac{SSD}] to measure compatibility between the two. In a more general case, rotation and scale must often also be considered, although in motion analysis these are not usually necessary when the motion between frames is small. @@ -479,7 +479,7 @@ below, in approximate order of complexity: \begin{equation} SSD(f,g) = \sum\limits_i \sum\limits_j \left ( f(i,j) - g(i,j) \right )^2 \end{equation} - Although the mean intensity is commonly subtracted, as described above. + although the mean intensity is commonly subtracted, as described above. \item The normalised \ac{CCC} is widely regarded as the most effective measure, and is a \emph{similarity} measure, returning $1$ when blocks are @@ -496,9 +496,9 @@ resistant to noise. { \sqrt{ \left ( f - \overline{f} \right )^2} \times \sqrt{ \left ( g - \overline{g} \right )^2} - }. + } \end{equation} - Where $\overline{f}$ and $\overline{g}$ are the mean values of $f$ and $g$ respectively. + where $\overline{f}$ and $\overline{g}$ are the mean values of $f$ and $g$ respectively. \item Ordinal measures \citep{evans_cloud_1999,evans_on-the-use-of-ordinal_2000,bhat_ordinal_1998} @@ -514,8 +514,8 @@ each vector. The most simple systems use the vector associated with maximum \ac{MCC} method. However, when using additional smoothing stages, a more sophisticated approach is to use the top $n$ vectors. As an additional analysis step, the \ac{CCC} values can be plotted again the vector components -as a 2-D surface. These \emph{correlation surfaces} are often noisy -multi-modal, and have indistinct peaks, which can make choosing the best +as a 2-D surface. These \emph{correlation surfaces} are often noisy, +multi-modal and have indistinct peaks, which can make choosing the best vectors difficult \citep{anandan_a-computational_1989,evans_glacier_2000}. This is especially true when using remotely sensed data which is characterised by a lack of texture and contrast, and a tendency to contain non-rigid @@ -654,7 +654,7 @@ illustrated graphically in Fig~\ref{fig:relaxation_labelling_terms}: \frac{\rho(J \rightarrow j)} {\sum\limits_{\lambda \in \Omega_{2J}} \rho(J \rightarrow \lambda)} \end{equation} - Where $\Omega_{2J}$ is the set of all candidate vectors for a block $J$. + where $\Omega_{2J}$ is the set of all candidate vectors for a block $J$. \item The probabilities are updated using the non-linear relaxation formula (\ref{eqn:relax_update}). This formula uses several nested support functions to judge a given vector's similarity with its neighbours in an iterative fashion. These similarity measures are then used to update the probability attached to each vector. The vector from each block with the highest probability attached is chosen as the output. \begin{equation} @@ -664,15 +664,15 @@ illustrated graphically in Fig~\ref{fig:relaxation_labelling_terms}: {\sum\limits_{\lambda \in \Omega_{2J}} P^{(n)}(J \rightarrow \lambda) Q(J \rightarrow \lambda)} \end{equation} - Where $Q(\cdot)$ is the following compatibility measuring function, which judges a vector $j$'s compatibility against those in neighbouring blocks. + where $Q(\cdot)$ is the following compatibility measuring function, which judges a vector $j$'s compatibility against those in neighbouring blocks. \begin{equation} Q(J \rightarrow j) = \prod \limits_{I \in G_j} \sum \limits_{i \in \Omega_{2J}}P^{(n)}(I \rightarrow I) R(I, J, i, j) \end{equation} The output from this will depend on both the probabilities of the -neighbouring block's vectors, and the output of the function $R(\cdot)$, is -the mutual information measure, which depends on vector similarity, and has +neighbouring block's vectors. The output of the function $R(\cdot)$ is +the mutual information measure, which depends on vector similarity and has the following form: \begin{equation} \label{eqn:relax_dist} @@ -685,7 +685,7 @@ the following form: | \right ) D(I, J) \end{equation} - Where $x_{I,i}$ and $x_{J,j}$ are the $x$-components of the displacement + where $x_{I,i}$ and $x_{J,j}$ are the $x$-components of the displacement vectors $i$ and $j$ in blocks $I$ and $J$ respectively. $\sigma$ is a parameter that controls the convergence during the iterative procedure of updating the probabilities. In practice, it is usually set to 1. $D(I, J)$ is @@ -697,10 +697,10 @@ given by: \end{equation} In (\ref{eqn:distance}), $D_{I,J}$ is the sum of the horizontal and vertical distances between the blocks, normalised to the block dimension. The form used -for (\ref{eqn:relax_dist}) and (\ref{eqn:distance}) are that of -\citet{evans_glacier_2000}. Others may also be used, provided they measure vector similarity in some way. Previous studies, such as \citet{wu_a-correlation-relaxation-labeling_1995} have used polar comparisons arguments in place of the Cartesian form used here. +for (\ref{eqn:relax_dist}) and (\ref{eqn:distance}) is that of +\citet{evans_glacier_2000}. Others may also be used, provided they measure vector similarity in some way. Previous studies, such as \citet{wu_a-correlation-relaxation-labeling_1995}, have used polar comparison arguments in place of the Cartesian form used here. - \item This process is repeated, until the probabilities are stable to within a given absolute value, or for a given number of iterations. + \item This process is repeated until the probabilities are stable to within a given absolute value, or for a given number of iterations. \end{enumerate} @@ -756,7 +756,7 @@ minimum value, any satisfying vector may be chosen. Correlation-relaxation labelling is the extension of template matching using the \ac{CCC} by the addition of a relaxation-labelling stage, as described -above. The process may be further augmented with a vector-median post-filter +above. The process may be further augmented with a vector-median post-filter. The \ac{CCC} has been shown to be particularly suitable for use with \ac{RL}. For example, a good comparison of (many of) the similarity measures in @@ -779,7 +779,7 @@ were representative of small-scale ocean currents. correlation measure as the first stage in constructing a mesh to represent a topological transformation. \citet{evans_cloud_2006} applied correlation-relaxation labelling to multichannel MSG cloud imagery and found -that it gave locally consistent dense vector fields. \citet{evans_cloud_1999}, +that it gave locally consistent dense vector fields. \citet{evans_cloud_1999} also showed the effectiveness of relaxation labelling when used to ordinal measures (based on rank-statistics). These previous results suggest that template matching and correlation-relaxation labelling may be effectively @@ -791,12 +791,12 @@ applied to \ac{TEC} images. \label{sub:vector_field_masking} When using the \ac{CCC} to estimate image motion, areas of image which contain -little texture lead to bad matches. This is because flat, or almost flat areas -match one-another very well. Areas of this type contain little in the way of +little texture lead to bad matches. This is because flat or almost flat areas +match one another very well. Areas of this type contain little in the way of information, and can be considered \emph{background}. Using a suitable mask to -disable such areas is an effective way of removing mitigating the problems -they cause, whilst limiting motion estimates to areas in which they are -useful. One example of an effective masking procedure is the use of a variance filter, with a threshold. By tuning the threshold, it is possible to create a mask which disables areas with low variances. These areas correspond to background regions. +disable such areas is an effective way of mitigating the problems +they cause whilst limiting motion estimates to areas in which they are +useful. One example of an effective masking procedure is the use of a variance filter with a threshold. By tuning the threshold, it is possible to create a mask which disables areas with low variances. These areas correspond to background regions. % subsection vector_field_masking (end) @@ -807,13 +807,12 @@ useful. One example of an effective masking procedure is the use of a variance f Sparse velocity fields can be estimated by using the correspondence of \emph{points of interest}. The definition of points of interest is fairly -broad, and includes both feature detector outputs and object properties, such +broad, and includes both feature detector outputs and object properties such as shape boundaries. The \emph{feature} based process process works by detecting points of interest using operators such as the Moravec operator or \ac{SIFT} features -\citep{lowe_object_1999}. These operators generally search for corners (or -intersecting straight edges). The points returned from two or more adjacent +\citep{lowe_object_1999}. The points returned from two or more adjacent frames are then used to estimate inter-frame motion, using, for example a probabilistic relaxation framework \citep[e.g.][]{m_sonka_image_1999}, or rectangular assignment \citep{kuhn_the-hungarian_1955}. The result of this @@ -844,10 +843,10 @@ further processed if necessary. \section{Snakes} % (fold) \label{sec:snakes} -Snakes, or active contours \citep{kass_snakes_1988} are a method of iterativly -finding objects with an image. A common analogy is with the deflation of a -balloon around an object, once a certain amount of air has been let out of the -balloon, its boundary will describe a hull around the object +Snakes, or active contours \citep{kass_snakes_1988}, are a method of +iterativly finding objects within an image. A common analogy is with the +deflation of a balloon around an object: once a certain amount of air has been +let out of the balloon, its boundary will describe a hull around the object \citep[e.g.][]{nixon_feature_2008}. Snakes model this process mathematically, using a cost function (known as an energy functional) to try and match image features, such as edge intensity and brightness, whilst minimising length and motion.tex @@ -4,7 +4,7 @@ This chapter briefly compares the motion estimation methods described in Chapters~\ref{cha:motion_estimation_using_optical_flow_and_corr} and \ref{cha:motion_estimation_curve_matching} with the modelled motion described in Section~\ref{sec:data_sources}. To this end, motion vectors from each method were aggregated, converted to -magnitude and subtracted from those of the other methods. Fig.~\ref{fig:exb_rel_diff} shows the difference between vectors from the $E \times B$ model and relaxation labelling. +magnitude and subtracted from those of the other methods. Fig.~\ref{fig:exb_rel_diff} shows the difference between vectors from the $\mathbf{E} \times \mathbf{B}$ model and relaxation labelling. \begin{figure}[ht] @@ -14,7 +14,7 @@ magnitude and subtracted from those of the other methods. Fig.~\ref{fig:exb_rel_ } \subfloat[20:50]{ \includegraphics[width=0.5\textwidth]{exb_rel_diff_10} - } + } } \centerline{ \subfloat[21:40]{ @@ -24,7 +24,7 @@ magnitude and subtracted from those of the other methods. Fig.~\ref{fig:exb_rel_ \includegraphics[width=0.5\textwidth]{exb_rel_diff_30} } } - \caption[Model and Relaxation Labelling differences.]{Frames illustrating the difference between $E \times B$ and relaxation labelling vector fields.} + \caption[Model and Relaxation Labelling differences.]{Frames illustrating the difference between $\mathbf{E} \times \mathbf{B}$ and relaxation labelling vector fields.} \label{fig:exb_rel_diff} \end{figure} @@ -37,7 +37,7 @@ Figs.~\ref{fig:relaxation_labelling_field_histograms}, overall difference in vector magnitude between each of the methods. Examination of these figures allows several conclusions to be drawn. -First, the magnitudes of the $E \times B$, optical flow and boundary derived +First, the magnitudes of the $\mathbf{E} \times \mathbf{B}$, optical flow and boundary derived vectors are all quite similar. This can be seen in the symmetrical zero-mode histograms of these methods. @@ -54,7 +54,7 @@ generated using regularisation. \begin{figure}[ht] \centering \includegraphics[width=0.9\textwidth]{exb_motion_field_histograms} - \caption{$E \times B$ vector magnitude comparisons.} + \caption{$\mathbf{E} \times \mathbf{B}$ vector magnitude comparisons.} \label{fig:exb_motion_field_histograms} \end{figure} motion_comparisons.tex @@ -6,15 +6,14 @@ This chapter discusses the application of optical flow and template matching based techniques to estimating the motion of the \ac{TOI} in \ac{TEC} images. As these methods are data-driven, they are largely de-coupled from the underlying physics and have the potential to provide a set of techniques for -analysing specific storm events that is not reliant on physical models -\citep{weimer_models_1995,bilitza_international_2001}. +analysing specific storm events that is not reliant on physical models, for example \citep{weimer_models_1995,bilitza_international_2001}. Optical flow was introduced in Section~\ref{sec:optical_flow}, on page~\pageref{sec:optical_flow} and template matching and correlation-relaxation labelling were introduced in Section~\ref{sec:template_matching_intro}, on page~\pageref{sec:template_matching_intro}. In the following case studies, -field entropy values, will be specified, as a proxy for field smoothness. +field entropy values will be specified as a proxy for field smoothness. These entropy values can be used to assess improvements made to the various methods, and will allow their relative performances to be compared. @@ -75,7 +74,7 @@ ensure stable results. Figs.~\ref{fig:images_optical_flow_0.1}, \ref{fig:images_optical_flow_1}, and \ref{fig:images_optical_flow_5} show the results from processing the images using regularisation parameters of 0.1, 1 and 5 respectively. The main thing -to note, with regards to these images, is their high degree of similarity. +to note with regards to these images is their high degree of similarity. \begin{figure}[!ht] \centering @@ -151,7 +150,7 @@ to note, with regards to these images, is their high degree of similarity. Table~\ref{tab:optical_flow_results} shows the average vector entropy values for output fields with different regularisation parameters. The first set shows the median, mean and standard deviations of field entropy values and the -second shows the result of masking the same vector field using a thresholded a +second shows the result of masking the same vector field using a thresholded standard deviation filter ($\sigma = 4$), as in Section~\ref{sec:motion_template_matching} These values are similar in magnitude to those in Table~\ref{tab:entropies} (on page @@ -180,7 +179,7 @@ part of the frame. The vector fields in Figs.~\ref{fig:images_optical_flow_0.1}, \ref{fig:images_optical_flow_1}, and \ref{fig:images_optical_flow_5} all show a tendency towards over-smoothing, even when the lowest regularisation -parameter was used. Also notable is the propensity for vectors to appear to +parameter is used. Also notable is the propensity for vectors to appear to spread outward around `bumps'. This can be seen in Fig.~\ref{fig:optical_flow_3}, in the top-left of the image. @@ -211,11 +210,10 @@ should also be noted that optical flow techniques produce vector fields with floating-point magnitudes, a factor which will definitely increase entropy. Future work in this area would benefit from the application of more recent -advancements to optical flow techniques, such as scale-space estimation. This -would allow the detection of larger displacements which might more accurately -capture the motion of the features in the end of the sequence. However, care -would need to be taken not to use filters which were too large, due to the -small size of the images. +advancements to optical flow techniques. This would allow the detection of +larger displacements which might more accurately capture the motion of the +features in the end of the sequence. However, care would need to be taken not +to use filters which were too large, due to the small size of the images. % section conclusions (end) @@ -236,7 +234,7 @@ Fig.~\ref{fig:template_matching}. Template matching (described in Section~\ref{sec:template_matching_intro}, on page~\pageref{sec:template_matching_intro}) using the \ac{MCC} method has been -used widely to estimate motion in many geoscience applications, for example, +used widely to estimate motion in many geoscience applications, for example deriving cloud motion vectors~\citep{schmetz_operational_1993} and estimating sea surface currents~\citep{dransfeld_potential_2006}. @@ -351,12 +349,12 @@ application of a \ac{VMF} to the relaxed motion field is proposed The effectiveness of the various motion estimation methods was evaluated using the \ac{TEC} image sequence described in Section~\ref{sec:data_sources} (on page \pageref{sec:data_sources}). All experiments used $5 \times 5$ blocks and -a search radius 5 pixels. Motion vectors were found to a half-pixel accuracy -which gives rise to a spatial resolution of 1\textdegree. Templates in the -image background were not considered for matching, these were determined by -thresholding the variance of the templates, such that $\sigma^2 > 16$. -Finally, for display purposes, the vector fields were all down-sampled by a -factor of three, allowing easier comparisons to be made throughout, and +a search radius of 5 pixels. Motion vectors were found to a half-pixel +accuracy which gives rise to a spatial resolution of 1\textdegree. Templates +in the image background were not considered for matching, these were +determined by thresholding the variance of the templates, such that $\sigma^2 +> 16$. Finally, for display purposes, the vector fields were all down-sampled +by a factor of three, allowing easier comparisons to be made throughout, and between, the images in the sequences. Fig.~\ref{fig:standard} shows the motion fields produced using the \ac{MCC} @@ -398,9 +396,9 @@ especially along the ridge towards the top-right. Nevertheless, they show a substantial improvement in vector quality, especially when compared with Figs.~\ref{fig:standard} and~\ref{fig:overlap}. -In addition to comparing the motion fields with the observable motion in the +In addition to comparing the motion fields with the observable motion in the \ac{TEC} sequences, an indication of the expected, underlying motion -fields can be obtained by running the $E \times B$ model provided by the MIDAS +fields can be obtained by running the $\mathbf{E} \times \mathbf{B}$ model provided by the MIDAS software package~\citep{spencer_imaging_2007} for the storm event. Comparing Fig.~\ref{fig:vmf_relaxed_overlap} with the modelled vectors shown in Fig.~\ref{fig:exb} shows some common features. For motion_optical_corr.tex @@ -19,7 +19,7 @@ regularisation \citep{westin_tensor_2003}, motion compensation work represents the first foray into the application of \ac{NC} techniques to the reconstruction of geophysical data. -The most basic form of \ac{NC}, known as zero-order \ac{NC} is described by +The most basic form of \ac{NC}, known as zero-order \ac{NC}, is described by the following equation: \begin{equation} \label{eqn:normconv} @@ -40,10 +40,10 @@ normalise the filtered input data. Zero-order \ac{NC} is similar in output to linear interpolation. The input image is convolved with a suitably sized filter kernel, in order to determine the contribution to the output by different input data. A confidence map, -describing the positions of input points is then convolved with the same -filter, in order to give the contribution of the filter kernel to each point +describing the positions of input points, is then convolved with the same +filter in order to give the contribution of the filter kernel to each point in the filtered input. The filtered input is then divided by the filtered -confidence map, removing the contribution from the filter, and leaving the +confidence map, removing the contribution from the filter and leaving the interpolated output. An alternative explanation is that \ac{NC} produces a local model of the input @@ -69,7 +69,7 @@ In order to improve output quality of zero-order \ac{NC}, the filter size can be adapted, and a suitable filter size for each pixel chosen. The simplest possible adaptation of this kind is to vary the filter radii so that the filter used at any given point is related to the distance to the nearest -sample. This, and other adaptations are known as \ac{ANC}. +sample. This and other adaptations are known as \ac{ANC}. % subsection zero_order_normalised_convolution (end) @@ -78,14 +78,14 @@ sample. This, and other adaptations are known as \ac{ANC}. So far, discussion has been limited to \ac{NC} using constant bases. This section discusses higher order \ac{NC}, where projection onto higher order -bases is carried out, using matrix inversions. Due to the irregularity of +bases is carried out using matrix inversions. Due to the irregularity of sample positions, inversions must be carried out at every output position. For this reason, first- and higher-order \ac{NC} methods are more computationally expensive than zero-order \ac{NC}. First order \ac{NC} is the simplest improvement over zero-order \ac{NC}, and uses bi-quadratic basis functions, where zero-order \ac{NC} uses a constant. -Nine-convolutions are required in all: six for the numerator, and three for +Nine convolutions are required in all: six for the numerator and three for the denominator. The following equation describes the process mathematically: \begin{equation} \label{eqn:first_order_nc} @@ -123,11 +123,11 @@ the denominator. The following equation describes the process mathematically: where $g$, $g\cdot x$, $g\cdot y$, $g\cdot x^2$, $g\cdot xy$, and $g\cdot y^2$ are filter kernels ($g$) that have been multiplied by surfaces of various orders, this can be seen in Fig.~\ref{fig:images_tilted_const}. The form of -(\ref{eqn:first_order_nc}) is similar to (\ref{eqn:normconv}), but involves an -inversion, instead of a division, because of the introduction of multiple +(\ref{eqn:first_order_nc}) is similar to (\ref{eqn:normconv}) but involves an +inversion instead of a division because of the introduction of multiple basis functions. It also outputs $f_x$ and $f_y$, the first derivatives in the $x$- and $y$-directions. The overall process of first-order \ac{NC} is -therefore one of fitting basis functions, and then normalising the output. +therefore one of fitting basis functions and then normalising the output. Orders of higher than one are possible, but are again more computationally expensive. However, second-order \ac{NC} would yield second derivatives, which @@ -169,6 +169,24 @@ faceted appearance) when filters are sized such that there are no output gaps. The main advantage is the fact that gradients are returned in addition to the interpolated image. +This and several of the following sections are illustrated using example images of a dockside crane. + +\begin{figure}[ht] + \centering + \centerline{ + \subfloat[]{ + \includegraphics[width=0.4\textwidth]{octave/data/crane.jpg} + \label{fig:crane-orig} + } + \subfloat[]{ + \includegraphics[width=0.4\textwidth]{crane_samples_inverted.png} + \label{fig:crane-sampled} + } + } + \caption[A crane image and sampled version.]{\subref{fig:crane-orig} the original version of the image used in several examples. \subref{fig:crane-sampled} a version of the crane image sampled to $\approx 90\%$ sparsity.} + \label{fig:crane} +\end{figure} + \begin{figure}[ht] % \centering \centerline{ @@ -185,16 +203,16 @@ interpolated image. \label{fig:nc_crane_first} } } - \caption[Examples of zero- and first-order NC]{\subref{fig:nc_crane_input} Small section of an image of a dockside crane. This was sampled to $\approx 90\%$ sparsity, and reconstructed using \subref{fig:nc_crane_zero} zero-order \ac{NC}, and \subref{fig:nc_crane_first} first-order \ac{NC}.} + \caption[Examples of zero- and first-order NC]{\subref{fig:nc_crane_input} Small section of the crane image (shown in Fig.~\ref{fig:crane-orig}). This was sampled to $\approx 90\%$ sparsity (as shown in Fig.~\ref{fig:crane-sampled}), and reconstructed using \subref{fig:nc_crane_zero} zero-order \ac{NC}, and \subref{fig:nc_crane_first} first-order \ac{NC}.} \label{fig:images_linear_90} \end{figure} -First order \ac{NC} is more computationally expensive that zero-order \ac{NC} -because of the use of multiple basis functions, and matrix inversions. -However, in general first-order \ac{NC} is more sensitive to filter size than +First order \ac{NC} is more computationally expensive than zero-order \ac{NC} +because of the use of multiple basis functions and matrix inversions. +However, in general, first-order \ac{NC} is more sensitive to filter size than zero-order \ac{NC}. This is illustrated in Fig.~\ref{fig:images_nc_rms_errors}, which shows the \ac{RMSE} associated with -reconstructing the crane image (Fig.~\ref{fig:images_linear_90}. A strong +reconstructing the crane image (Fig.~\ref{fig:images_linear_90}). A strong negative gradient is visible in the left-hand section of Fig.~\ref{fig:first_order_rms}. This section coincides with small filter sizes, demonstrating its high sensitivity to changes in the size of small @@ -221,7 +239,7 @@ filters. \subsection{Zero Order Adaptive Normalised Convolution} % (fold) \label{sub:adaptive_normalised_conv} -The most simple form of \ac{ANC}, known as \emph{size adaptive} \ac{NC} adapts +The most simple form of \ac{ANC}, known as \emph{size adaptive} \ac{NC}, adapts the filters such that the kernel standard deviation at any given point is specified by the Euclidean distance transform \citep[e.g.][]{m_sonka_image_1999} (or other distance transform) of the input @@ -266,18 +284,17 @@ interpolated and then differentiated, usually along both the $x$- and $y$-axes. There are two \ac{NC} based methods of estimating gradient. This first, -\emph{first-order \ac{NC}} was described in section -\ref{sub:higher_order_normalised_convolution} \citep{pham_robust_2006}, and -produces gradients as a product of its normal process. The second, -\emph{\ac{DoNC}} uses differentiated zero-order \ac{NC}, and is described -below. +\emph{first-order \ac{NC}}, was described in Section~ +\ref{sub:higher_order_normalised_convolution}, and produces gradients as a +product of its normal process. The second, \emph{\ac{DoNC}}, uses +differentiated zero-order \ac{NC} and is described below. \subsubsection{Differential of Normalised Convolution} % (fold) \label{ssub:donc} The \ac{DoNC} method is formed by applying derivative operators to the \ac{NC} equation (\ref{eqn:normconv}), in two directions. This gives the following -equations for the $x$-axis \citet{westin_tensor_2003,piroddi_dealing_2004}: +equations for the $x$-axis \citep{westin_tensor_2003,piroddi_dealing_2004}: \begin{equation} \label{eqn:donc-1} @@ -296,7 +313,7 @@ and: N_x(x,y) = x.g(x,y) \otimes c_i(x,y). \end{equation} -In the (\ref{eqn:donc-2}) and (\ref{eqn:donc-3}), $x \cdot +In (\ref{eqn:donc-2}) and (\ref{eqn:donc-3}), $x \cdot g(x,y)$ is an edge enhancement filter which could be any arbitrary (normally Gaussian) filter multiplied by a variable $x$. This effectively tilts the filter relative to the $x$-axis. @@ -343,7 +360,7 @@ image. Gradients calculated using first-order \ac{NC} are similar to those produced by \ac{DoNC}, but can be slightly more accurate for some images, such as those with a large amount of high-frequency content \citep{jong_gradient_1998}. The -lower computational complexity, and similar performance of \ac{DoNC} suggest +lower computational complexity and similar performance of \ac{DoNC} suggest that it is a sensible choice in practical situations where speed is important. % subsubsection gradients_from_first_order_nc (end) @@ -357,20 +374,20 @@ that it is a sensible choice in practical situations where speed is important. Once estimates of image gradients are available, they can be analysed in order to provide information on image structure, including local energies, orientations and anisotropies. These properties describe gradient, edge -direction and how non-uniformly varying a give image is. +direction and how non-uniformly varying a given image is. These properties can then be used to set the size and orientation of the -\ac{NC} filters in order to maintain features, and high frequency detail, +\ac{NC} filters in order to maintain features and high frequency detail, whilst ensuring that no gaps appear in the output. This process has been used in the past by \citet{nitzberg_nonlinear_1992,almansa_fingerprint_2000}, and specifically adapted for use in \ac{ANC} by \citet{pham_normalized_2003}. \citet{kass_analyzing_1987} describe that fact that anisotropy can be detected -by examining local power spectra, and noting that high-frequency energy will -tend to lie perpendicular to the direction of flow. It is then suggested that +by examining local power spectra and noting that high-frequency energy tends +to lie perpendicular to the direction of flow. It is then suggested that orientation-selective linear filters can be used to detect this clustering energy, and hence the anisotropy of the local area. -\citet{vliet_estimators_1995} develop this idea by using smooth +\citet{vliet_estimators_1995} developed this idea by using smooth local-gradient measures to form matrices known as \ac{GST}, which are approximately equivalent to covariance matrices of the gradients, and are given by: @@ -410,7 +427,7 @@ operators.} The effect of smoothing is the localisation of the matrix, so that when its eigenvectors are calculated, they correspond to the local area. Each pixel will have an associated \ac{GST}, and calculating these gives the various -pieces of information, which are summarised in Table~\ref{tab:gst}. +pieces of information which are summarised in Table~\ref{tab:gst}. \begin{table}[ht] \centering @@ -439,7 +456,7 @@ the `local direction', which is given by: \begin{equation} \label{eqn:varphi_2} - \varphi_2 = tan^{-1}\left ( \frac{g_{xy}}{\lambda_2 - g^2_y} \right ). + \varphi_2 = \tan^{-1}\left ( \frac{g_{xy}}{\lambda_2 - g^2_y} \right ). \end{equation} These measures are then used to set the size of the filters at any given point @@ -457,14 +474,13 @@ and where $u$ and $v$ denote filter axes, and $\sigma_u$ and $\sigma_v$ correspond to Gaussian standard deviations along those axes. These three parameters ($\sigma_u, \sigma_v, \varphi_2$) can then be used to set the size and -rotation of the filter used at any given output point -Fig.~\ref{fig:images_rotated_filter} shows how these parameters relate to a +rotation of the filter used at any given output point. Fig.~\ref{fig:images_rotated_filter} shows how these parameters relate to a rotated Gaussian kernel. \begin{figure}[ht] \centering \includegraphics[height=3in]{rotated_filter} - \caption[Rotated 2-D Gaussian Filter]{A schematic diagram showing shape, and salient parameters of a rotated 2-D Gaussian. The oval indicates $3\sigma$ confidence limits in each axis, which corresponds to a $99.7\%$ confidence interval, and is a good place to truncate filters.} + \caption[Rotated 2-D Gaussian Filter]{A schematic diagram showing the shape and salient parameters of a rotated 2-D Gaussian. The oval indicates $3\sigma$ confidence limits in each axis, which corresponds to a $99.7\%$ confidence interval, and is a good place to truncate filters.} \label{fig:images_rotated_filter} \end{figure} @@ -476,7 +492,7 @@ filters~\citep{ginkel_curvature_1999}. \label{sub:implementation} Various points in the above processes require filtering with Gaussian kernels -for either smoothing, or in the case of \ac{NC} localisation of output +for either smoothing or, in the case of \ac{NC}, localisation of output contributions. Multiple filtering stages can quickly lead to high computation times, making it prudent to investigate methods of speeding up these processes. @@ -491,7 +507,7 @@ improvements. These are dealt with separately below. Generation of 2-D Gaussian filter kernels can be sped up appreciably by using the property of separability, which allows symmetrical functions to be split down into orthogonal components. This is possible when a filter kernel can be -written as the output product of two vectors. For example, consider the Sobel +written as the outer product of two vectors. For example, consider the Sobel kernel: \begin{equation} \left [ @@ -520,26 +536,26 @@ vectors: \begin{equation} \label{eqn:gauss_sep} g(u,v ; \sigma_u, \sigma_v) = - \frac{1}{\sqrt{2\pi}\sigma_u} exp \left \{ - \frac{1}{2} + \frac{1}{\sqrt{2\pi}\sigma_u} \exp \left \{ - \frac{1}{2} \frac{u^2}{\sigma_u^2} \right \} \otimes - \frac{1}{\sqrt{2\pi}\sigma_v} exp \left \{ - \frac{1}{2} + \frac{1}{\sqrt{2\pi}\sigma_v} \exp \left \{ - \frac{1}{2} \frac{v^2}{\sigma_v^2} \right \} \end{equation} Alternatively, since convolution is associative, this property can be used to -quickly filter images by using two 1-D processes, instead of a single 2-D +quickly filter images by using two 1-D processes instead of a single 2-D process. The image is first filtered in one dimension, using one kernel, to give an -intermediate image. This image is then filtered in the other dimension, using +intermediate image. This image is then filtered in the other dimension using the other kernel. The output is exactly the same as if a more complex 2-D filtering process had been used, but is much faster thanks to the lower complexity. Complexity of filtering operations which can be decomposed drops from $M^2P^2$ -multiplies and additions to $M^2(2P)$. Where $M$ is the image dimension, and +multiplies and additions to $M^2(2P)$, where $M$ is the image dimension, and $P$ is the filter dimension. Therefore, the relative speedup is a factor of -$\frac{M^2}{2P}$. +$\frac{P}{2}$. A great many filters can be separated into orthogonal components, using the following algorithm: @@ -549,9 +565,9 @@ following algorithm: \begin{equation} K = USV^* \end{equation} - Where $*$ denotes the conjugate matrix transpose. + where $*$ denotes the conjugate matrix transpose. \item Take the rank of the singular values. This corresponds to the number of independent rows in $S$. If $\mbox{rank}(S) = 1$, then the filter kernel is separable. - \item Two separate the kernel, two 1-D vectors are formed by multiplying $U$ and $V$ by the square root of the non-zero value from $S$: + \item To separate the kernel, two 1-D vectors are formed by multiplying $U$ and $V$ by the square root of the non-zero value from $S$: \begin{equation} \begin{array}{c} K_u = U \sqrt{s},\\ @@ -581,14 +597,14 @@ following filter: g_x(x,y) = w_of(x,y) + \sum \limits_{i=1}^{\lfloor N/2 \rfloor} w_i(f(x-i,y) + f(x_i,y)) \end{equation} -Where $N$ is the size of the Gaussian filter, whose weights are given by $w_o\ldots w_N$. The filter standard deviation is: +where $N$ is the size of the Gaussian filter, whose weights are given by $w_o\ldots w_N$. The filter standard deviation is: \begin{equation} \sigma_x = \frac{\sigma_u \sigma_v} { \sqrt{\sigma_u^2 \cos^2{\theta} \sigma_v^2 \sin^2{\theta} } - } + }. \end{equation} In this equation, $\theta$ is the filter orientation and $\sigma_u$ and $\sigma_v$ are the standard deviations of the filter before rotation. The @@ -606,7 +622,7 @@ following form: \end{array} \end{equation} -Where $\mu = \tan{\varphi}$ is the direction along which this filtering +where $\mu = \tan{\varphi}$ is the direction along which this filtering operation occurs. This term arises from the equation for the Gaussian standard deviation for this pass, which is: @@ -653,7 +669,7 @@ after sampling, and after reconstruction using \ac{ANC}. \label{fig:dunnock} }} \centerline{ - \subfloat[Sampled to $\approx 98\%$]{ + \subfloat[Sampled to $\approx 98\%$ sparsity.]{ \framebox{\includegraphics[height=2in]{dunnock_98_sampled}} \label{fig:dunnock_sampled} }} normalised_convolution.tex @@ -13,7 +13,7 @@ those which are connected to it by triangulation edges. The geometric dual of the Delaunay triangulation, known as the Voronoi diagram, also has many useful properties. Its edges form cells around each -point, such that the area within each cell is closest to the point at its +point such that the area within each cell is closest to the point at its centre. Cells at the edges of Voronoi diagrams are unbounded. Voronoi edges are always perpendicular to Delaunay edges. \begin{figure}[ht!] @@ -24,9 +24,9 @@ centre. Cells at the edges of Voronoi diagrams are unbounded. Voronoi edges are \end{figure} Once a data-set has been triangulated, each point in the data-set will be -connected to several others by triangle vertices (See +connected to several others by triangle vertices (see Fig.~\ref{fig:delaunay}). Given the values of a triangle's nodes ($f_i$, where -$i = 1, 2, 3$), the interpolated value of any point within the triangle, can +$i = 1, 2, 3$), the interpolated value of any point within the triangle can be found using \begin{equation} \label{eqn:tri_interp} @@ -45,11 +45,11 @@ The coefficients $\mathbf{c} = (c_1, c_2, c_3)$ can then be found by solving $\m with the form $(x_i, y_i, 1)$, where $i$ is the row number. Higher (and lower) order basis functions can also be used, but require larger -numbers of input samples. Zero order triangulation-based interpolation is -known as nearest neighbour interpolation, and leads to regions of output -values in direct relation to Voronoi cells. Other commonly used schemes -include quadratic and cubic interpolation. This process can also be -generalised to higher-dimensions, and various implementations are readily +(or smaller) numbers of input samples. Zero order triangulation-based +interpolation is known as nearest neighbour interpolation, and leads to +regions of output values in direct relation to Voronoi cells. Other commonly +used schemes include quadratic and cubic interpolation. This process can also +be generalised to higher dimensions, and various implementations are readily available \citep{barber_quickhull_1996}. \section{Natural Neighbour Interpolation} @@ -82,13 +82,11 @@ value at any point can be determined using a weighted sum of the values at its neighbours. The way in which the weights are determined is best described in terms of Voronoi tessellations, the geometric dual of the Delaunay triangulation, see Fig.~\ref{fig:voronoi}. This method was first suggested by -\citet{sibson_brief_1981,sambridge_geophysical_1995,park_discrete_2006,fan_hardware_2005,watson_natural_1985}, -from the University of Bath, UK, and is sometimes known as Sibson -interpolation +\citet{sibson_brief_1981} from the University of Bath, UK, and is sometimes known as Sibson interpolation. Other useful references include \citet{sambridge_geophysical_1995,park_discrete_2006,fan_hardware_2005,watson_natural_1985}. For each point where a value is required: \begin{enumerate} - \item Assume the data are already tessellated + \item Assume the data are already tessellated. \item Re-tessellate the data to include the output point. This adds a new Voronoi cell which overlaps the cells of the natural neighbours of the output point. @@ -105,7 +103,7 @@ only neighbouring values are used in the interpolation. \label{sec:paper_rbf} \ac{RBF} interpolation approximates a field of data using a weighted sum of -radially symmetrical functions, known as basis +radially symmetrical functions known as basis functions~\citep[e.g.][]{carr_surface_1997}. One basis function is centred on each input sample, so that any given output point is composed of contributions from each input point. \ac{RBF} interpolation is therefore considered a global @@ -210,19 +208,19 @@ results which are indistinguishable to \ac{RBF} interpolation using \ac{TPS}. \ac{BSI} can be numerically unstable for large numbers of points and, like other cubic methods, has a tendency to drastically overshoot when points are close together. This problem occurs because of the imposed continuity in the -surface's derivatives, which makes smoothly varying curves preferable around -data points. Therefore, \ac{BSI} is better suited to the interpolation of -highly sparse data. The phenomenon of overshooting is discussed in more detail -in Chapter~\ref{cha:artefacts}. +derivatives of the surface, which makes smoothly varying curves preferable +around data points. Therefore, \ac{BSI} is better suited to the interpolation +of highly sparse data. The phenomenon of overshooting is discussed in more +detail in Chapter~\ref{cha:artefacts}. \section{Kriging} \label{sec:paper_kriging} Kriging was first suggested in the 1960s by D. G. Krige, a South African mining engineer. It was originally developed as a technique for estimating -yields of ore deposits from sparsely distributed core samples, but has now +yields of ore deposits from sparsely distributed core samples but has now been widely applied to many different fields and scenarios (for example, -mining, mathematics and classification \citet[e.g.][]{boucher_novel_2006}), as +mining, mathematics and classification \citep[e.g.][]{boucher_novel_2006}), as discussed in \citet{cressie_origins_1990}. One of the main attractions of kriging is its ability to provide a variance estimate for each output point. Kriging and all geostatistical methods operate under the assumption that a other_interp_methods.tex @@ -69,17 +69,17 @@ mapping. \citet{samardjiev_ionospheric_1993}, used the CCIR model to compare $f_0F_2$ results\footnote{The CCIR model is now part of the International Reference -Ionosphere (IRI) model.}). However, in many cases modelled data are far +Ionosphere (IRI) model.}. However, in many cases modelled data are far smoother than the actual phenomena being modelled, which leads to anomalous results. In particular, results tend to be biased towards favouring techniques which produce artificially smooth outputs. - - \item \textbf{Is there a data set for which the correct answers are known?} - - No standard set of real \ac{TEC} slant measurements with associated correct + + \item \textbf{Is there a data set for which the correct answers are known?} + + No standard set of real \ac{TEC} slant measurements with associated correct reconstructed outputs is available. \citet{meggs_simulations_2002} make -comparisons between slant \ac{TEC}, path measurements, simulated data. However -there are no data-sets for which ground truths are directly available. +comparisons between slant \ac{TEC}, path measurements, and simulated data. +However there are no data-sets for which ground truths are directly available. Simulated data may be sampled and then reconstructed. The reconstructions may then be compared with the original simulated data. This technique will be @@ -97,7 +97,7 @@ discussed in more detail in Section~\ref{sec:cross_val}. There are no specifically agreed `strawman' algorithms, although several of the most commonly used methods, such as linear and cubic triangulation based -interpolation would make obvious choices. Code implementing these and various +interpolation, would make obvious choices. Code implementing these and various other methods is readily available (see Chapter~\ref{cha:interpolation}). \item \textbf{What should we be measuring to quantify performance? What @@ -140,14 +140,14 @@ kinds of simulated field, designed with testing Kriging in mind. The first type may be produced by generating fields of normally-distributed random data (by using a random-number-generator), which can then filtered -using a pillbox or ball shaped kernel. The filtering process introduces -autocorrelation with a lag distance dependent on the filter radius. This data -has a multivariate Gaussian distribution which is considered ideal for +using a pillbox shaped kernel. The filtering process introduces +autocorrelation with a lag distance dependent on the filter radius. These data +have a multivariate Gaussian distribution which is considered ideal for ordinary kriging. The second method generates univariate data with an approximately log-normal distribution by filtering fields of uniformly distributed random data. -Multi-normality is then removed by examining $5 \times 5$ neighbourhoods, +Multi-normality is then removed by examining $5 \times 5$ neighbourhoods around each point, and randomly selecting from the ten highest values. Finally, the natural logarithm of the each data point is calculated. Histograms illustrating typical distributions generated by these two methods @@ -210,7 +210,7 @@ Cross-validation is a statistical technique designed to allow testing with the same data-set that is used for some process or methodology. Typically, cross validation is used for training classifiers, in which training data are divided into two classes, one of which is then used for training, and the -other testing the classifier. +other testing, the classifier. The use of cross-validation for interpolation is very similar, although the generation of many different data sparsities requires the data set to either @@ -234,15 +234,15 @@ with equal sizes. Then: \begin{enumerate} \item Interpolate the data in the first block, using the methods being tested. - \item Calculate the sparsity of the image to which this data gives rise (see Section~\ref{sec:sparsity}, page \pageref{sec:sparsity}). + \item Calculate the sparsity of the image to which these data gives rise (see Section~\ref{sec:sparsity}, page \pageref{sec:sparsity}). \item Difference the output data with the data in the remaining blocks and compute appropriate error measures (such as the \ac{RMSE}). \item Repeat this process using the first and second block, then the first, second and third block, etc. until the desired range of sparsities has been examined, or no blocks remain. \end{enumerate} -If multiple subsets of data are available, for example time slices, in the -case of \ac{TEC} data, this process can be repeated for each slice, and the +If multiple subsets of data are available, for example time slices in the +case of \ac{TEC} data, this process can be repeated for each slice and the results averaged by binning the sparsity values. Partitions could also be chosen randomly, or permuted to generate more results if necessary. However, it should be noted that using blocks for both simulation \emph{and} validation @@ -291,14 +291,14 @@ techniques requiring a distance metric. The techniques to be evaluated were applied to both simulated and real \ac{TEC} data. As simulated data provides ground truth values, it has the advantage of allowing analysis of residual errors to be calculated at every -point in the output field. In addition, parameters such as the of the input -sparsity can be carefully controlled. It should be noted, however, that the +point in the output field. In addition, parameters such as the input +sparsity can be carefully controlled. However, it should be noted, that the performance of any interpolation method can vary considerably with the statistics of the input data, and therefore the results gained through simulation are not necessarily indicative of the general performance. Therefore, the ultimate test of reconstruction techniques remains their application to real data. To this end, the interpolation methods are applied -to \ac{TEC} data from the much studied October 2003 ionospheric storm. +to \ac{TEC} data from the much-studied October 2003 ionospheric storm. \subsection{Simulated-Validation Results} \label{sec:simulation_validation_results} @@ -331,14 +331,14 @@ results. \begin{figure*}[tb] \centering \includegraphics[width=\textwidth]{sim_corr_radius} - \caption[Proportional RMSE from reconstructed simulated multivariate data]{Proportional \ac{RMSE} as a function of radius for simulated multivariate correlated data reconstruction.} + \caption[Proportional RMSE from reconstructed simulated multivariate data]{Proportional \ac{RMSE} as a function of filter radius (in pixels) for simulated multivariate correlated data reconstruction.} \label{fig:sim_corr_radius} \end{figure*} \begin{figure*}[tb] \centering \includegraphics[width=\textwidth]{sim_corr_uni_radius} - \caption[Proportional RMSE from reconstructed simulated univariate data]{Proportional \ac{RMSE} as a function of radius for simulated univariate correlated data reconstruction.} + \caption[Proportional RMSE from reconstructed simulated univariate data]{Proportional \ac{RMSE} as a function of filter radius (in pixels) for simulated univariate correlated data reconstruction.} \label{fig:sim_corr_uni_radius} \end{figure*} @@ -390,11 +390,11 @@ result of this type of analysis is shown in Fig.~\ref{fig:sim_val_hist}. \label{sec:paper_cross_validation} The sources of data used to test \ac{TEC} reconstruction are approximately 80 -\ac{GPS} measuring stations lying within 20--70\textdegree~N, and +\ac{GPS} measuring stations lying within 20--70\textdegree~N and 70--130\textdegree~W. This corresponds to a coverage of most of North America. Whilst more sites were available at that time, not all sites were used, as the main aim of this chapter is to examine interpolation during high sparsity -cases. The time period over which data were drawn