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weltenwort committed Oct 2, 2012
1 parent 4783b1a commit 217ad840160da78adaa9518267f80c9f907679e1
@@ -26,3 +26,6 @@ eval "$CMD\
eval "$CMD\
r_l_luma_canny_1_5_pmean_g8_3_hi_1000_itf_s4_a*.*.json\
> ${TARGET_DIR}/parameter_angles.csv"
+eval "$CMD\
+ r_l_luma_canny_1_5_pmean_g*_*_hi_*.json\
+ > ${TARGET_DIR}/parameter_grid.csv"
@@ -11,7 +11,9 @@ \section{Signature Extraction}\label{sec:solution_signature_extraction}
by Mandal et al.\ \autocite{mandal_curvelet_2009} and Guha and Wu
\autocite{guha_curvelet_????}. Furthermore, since the coarsest scale is
non-directional, as explained in section \ref{sec:background_cct}, it is
-ignored in further computations.
+ignored in further computations. Finally, since the curvelet coefficients can
+have positive or negative sign, only the absolute value of the coefficient is
+used in the calculations of the mean values.
The response image generated by the FDCT for each pair of scale and angle is
too large to be considered for the signature directly. Therefore the response
@@ -65,14 +67,14 @@ \section{Signature Extraction}\label{sec:solution_signature_extraction}
\label{fig:signature_examples}
\end{figure}
-\subsection{Global Features}
+\subsection{Global Features}\label{sec:solution_signature_extraction_global}
\paragraph{MEAN}
The global approach to signature extraction simply takes the family of matrices
$\bar{C}_{s, \theta}$ and concatenates them as the image signature.
-\subsection{Local Features}
+\subsection{Local Features}\label{sec:solution_signature_extraction_local}
The local feature extraction methods used here follow the bag-of-features
approach, that aims to represent an image using a set of local feature
@@ -85,14 +87,15 @@ \subsubsection{Sampling}
overlapping sampling of a grid of mean values. By using $m \times m$ windows,
the small-scale spatial relationship between features can be captured. The
overlap helps to avoid misinterpretation of features on grid boundaries that
-would occur with dense, non-overlapping sampling. Evaluations by Nowak et al.\
-\autocite{nowak_sampling_2006} have shown that random sampling, which dense
-sampling is a special case of, outperforms keypoint-based sampling for large
-enough numbers of samples. Dense sampling on grids has previously been
-successfully used by Lazebnik in \autocite{lazebnik_beyond_2006} and
-\autocite{lazebnik_spatial_2009}. The R-HOG descriptor
-\autocite{dalal_histograms_2005} also uses a dense grid for sampling with
-overlapping windows to improve matching performance.
+would occur with dense, non-overlapping sampling. Each window encodes the
+geometric relationships between cells within a neighborhood.
+Evaluations by Nowak et al.\ \autocite{nowak_sampling_2006} have shown that
+random sampling, which dense sampling is a special case of, outperforms
+keypoint-based sampling for large enough numbers of samples. Dense sampling on
+grids has previously been successfully used by Lazebnik in
+\autocite{lazebnik_beyond_2006} and \autocite{lazebnik_spatial_2009}. The R-HOG
+descriptor \autocite{dalal_histograms_2005} also uses a dense grid for sampling
+with overlapping windows to improve matching performance.
\paragraph{PMEAN}
@@ -28,15 +28,43 @@ \subsubsection{Curvelet Angles}
\begin{table}[h]
\centering
\pgfplotstableread[]{results/parameter_angles.csv}\resultsparameterangles
- \plottablexbars{scales,angles,cannysigma,metric}{\resultsparameterangles}
+ \plottablexbars{imagereader,features,scales,angles,metric}{\resultsparameterangles}
\caption[Angle Parameter Results]{
Influence of $N_{\theta}$ on the results of CANNY+PMEAN for $G=8$,
$P=3$ and $\sigma=1.5$.
}
- \label{tab:results_best_performers}
+ \label{tab:results_parameter_angles}
\end{table}
\FloatBarrier
+\subsubsection{Grid and Patch Sizes}
+
+All of the MEAN, PMEAN and PMEAN2 sampling methods use a regular grid to divide
+the curvelet coefficients into cells, in which the mean of the coefficients is
+calculated. Using a small number $G$ of subdivisions means that smaller
+features might vanish within a large grid cell, unable to influence the mean
+value. A finer subdivision allows for smaller features to be represented at the
+risk of cutting apart larger features that lie on the grid lines. In addition
+to $G$, the local sampling methods PMEAN and PMEAN2 are influenced by the
+number of grid cells that make up a patch. As explained in section
+\ref{sec:solution_signature_extraction_local}, a patch captures the geometric
+relationships within a $P \times P$ neighborhood of cells. It thus defines an
+upper limit on the size of a feature that can be represented atomically.
+
+\begin{table}[h]
+ \centering
+ \pgfplotstableread[]{results/parameter_grid.csv}\resultsparametergrid
+ \plottablexbars{imagereader,features,gridsize,patchsize,metric}{\resultsparametergrid}
+ \caption[Grid Size Parameter Results]{
+ Influence of grid parameters $P$ and $G$ on the results for $N_s=4$,
+ $N_{\theta}=12$ and $\sigma=1.5$.
+ }
+ \label{tab:results_parameter_grid}
+\end{table}
+
+\FloatBarrier
+\subsubsection{Canny Sigma}
+
%In an attempt to improve the
%result further, several sets of parameter values are examined: For the number
%of angles $N_{\theta} \in \{8, 12, 16\}$ the differences are small with

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