HybridSegmentationMethods.tex

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\subsection{Introduction}
\label{sec:HybridSegmentationIntroduction}
This section introduces the use of hybrid methods for segmentation of image
data. Typically we are dealing with radiological patient and the Visible
Human data. The hybrid segmentation approach integrates boundary-based and
region-based segmentation methods that amplify the strength but reduce the
weakness of both techniques. The advantage of this approach comes from
combining region-based segmentation methods like the fuzzy connectedness and
Voronoi diagram classification with boundary-based deformable model
segmentation. The synergy between fundamentally different methodologies tends
to result in robustness and higher segmentation quality.  A hybrid
segmentation engine can be built, as illustrated in
Figure~\ref{fig:ComponentsofaHybridSegmentationApproach}. It consists of
modules representing segmentation methods and implemented as ITK filters. We
can derive a variety of hybrid segmentation methods by exchanging the filter
used in each module. It should be noted that under the fuzzy connectedness
and deformable models modules, there are several different filters that can
be used as components. Below, we describe two examples of hybrid segmentation
methods, derived from the hybrid segmentation engine: integration of fuzzy
connectedness and Voronoi diagram classification (hybrid method 1), and
integration of Gibbs prior and deformable models (hybrid method 2).  Details
regarding the concepts behind these methods have been discussed in the
literature
\cite{Angelini2002,Udupa2002,Jin2002,Imielinska2001,Imielinska2000a,Imielinska2000b}.


%REMOVED PATENTED: \subsection{Fuzzy Connectedness and Confidence Connectedness }
%REMOVED PATENTED:
%REMOVED PATENTED: Probably the simplest combination of hybrid filters is the pair formed by the
%REMOVED PATENTED: \doxygen{ConfidenceConnectednessImageFilter} and
%REMOVED PATENTED: \doxygen{SimpleFuzzyConnectednessScalarImageFilter}. In this combination the
%REMOVED PATENTED: confidence connectedness filter is used to produce a rough segmentation of an
%REMOVED PATENTED: anatomical structure and to compute and estimation of the mean and variance of
%REMOVED PATENTED: gray values in such structure. The values of mean and variance are then passed
%REMOVED PATENTED: to the Simple Fuzzy Connectedness image filter in order to compute an affinity map.
%REMOVED PATENTED:
%REMOVED PATENTED: \input{FuzzyConnectednessImageFilter.tex}


\subsection{Fuzzy Connectedness and Voronoi Classification}
\label{sec:HybridMethod1}
In this section we present a hybrid segmentation method that requires
minimal manual initialization by integrating the fuzzy connectedness and
Voronoi diagram classification segmentation algorithms. We start with a fuzzy
connectedness filter to generate a sample of tissue from a region to be
segmented. From the sample, we automatically derive image statistics that
constitute the homogeneity operator to be used in the next stage of the
method. The output of the fuzzy connectedness filter is used as a prior to
the Voronoi diagram classification filter. This filter performs iterative
subdivision and classification of the segmented image resulting in an
estimation of the boundary. The output of this filter is a 3D binary image
that can be used to display the 3D result of the segmentation, or passed to
another filter (e.g. deformable model) for further improvement of the final
segmentation. Details describing the concepts behind these methods have been
published in
\cite{Angelini2002,Udupa2002,Jin2002,Imielinska2001,Imielinska2000a,Imielinska2000b}

In Figure~\ref{fig:UMLClassDiagramoftherFuzzyConnectednessFilter}, we
describe the base class for simple fuzzy connectedness segmentation. This
method is non-scale based and non-iterative, and requires only one seed to
initialize it. We define affinity between two nearby elements in a image
(e.g. pixels, voxels) via a degree of adjacency, similarity in their
intensity values, and their similarity to the estimated object.  The closer
the elements and the more similar their intensities, the greater the affinity
between them. We compute the strength of a path and fuzzy connectedness
between each two pixels (voxels) in the segmented image from the fuzzy
affinity.  Computation of the fuzzy connectedness value of each pixel (voxel)
is implemented by selecting a seed point and using dynamic programming. The
result constitutes the fuzzy map. Thresholding of the fuzzy map gives a
segmented object that is strongly connected to the seed point (for more
details, see \cite{Udupa1996}). Two fuzzy connectedness filters are available
in the toolkit:

\begin{itemize}
\item The \doxygen{SimpleFuzzyConnectednessScalarImageFilter}, an implementation of the
fuzzy connectedness segmentation of single-channel (grayscale) image.
\item The \doxygen{SimpleFuzzyConnectednessRGBImageFilter}, an implementation
of fuzzy connectedness segmentation of a three-channel (RGB) image.
\end{itemize}

New classes can be derived from the base class by defining other affinity
functions and targeting multi-channel images with an arbitrary number of
channels. Note that the simple fuzzy connectedness filter can be used as a
stand-alone segmentation method and does not necessarily need to be combined
with other methods as indicated by
Figure~\ref{fig:UMLCollaborationDiagramoftheFuzzyConnectednessFilter}.

In Figure~\ref{fig:UMLVoronoiSegmentationClassFilter} we present the base
class for Voronoi diagram classification. We initialize the method with a
number of random seed points and compute the Voronoi diagram over the
segmented 2D image. Each Voronoi region in the subdivision is classified as
internal or external, based on the homogeneity operator derived from the
fuzzy connectedness algorithm.  We define boundary regions as the external
regions that are adjacent to the internal regions.  We further subdivide the
boundary regions by adding seed points to them. We converge to the final
segmentation using simple stopping criteria (for details, see
\cite{Imielinska2001}). Two Voronoi-based segmentation methods are available in ITK: the \doxygen{VoronoiSegmentationImageFilter} for processing single-channel
(grayscale) images, and the \doxygen{VoronoiSegmentationRGBImageFilter}, for
segmenting three-channel (RGB) images. New classes can be derived from the
base class by defining other homogeneity measurements and targeting
multichannel images with an arbitrary number of channels.  The other classes
that are used for computing a 2D Voronoi diagram are shown in
Figure~\ref{fig:UMLClassesforImplementationofVoronoiDiagramFilter}. Note that
the Voronoi diagram filter can be used as a stand-alone segmentation method,
as depicted in
Figure~\ref{fig:UMLCollaborationDiagramoftheVoronoiSegmentationFilter}.

Figures~\ref{fig:UMLHybridMethodDiagram1} and
\ref{fig:UMLHybridMethodDiagram2} illustrate hybrid segmentation methods
that integrate fuzzy connectedness with Voronoi diagrams, and fuzzy
connectedness, Voronoi diagrams and deformable models, respectively.


\begin{figure}
\centering
\includegraphics[width=0.8\textwidth]{HybridSegmentationEngine1.eps}
\itkcaption[Hybrid Segmentation Engine]{The hybrid segmentation engine.}
\label{fig:ComponentsofaHybridSegmentationApproach}
\end{figure}


\begin{figure}
\centering
\includegraphics[width=0.8\textwidth]{FuzzyConnectednessClassDiagram1.eps}
\itkcaption[FuzzyConectedness Filter Diagram]{Inheritance diagram for the fuzzy connectedness filter.}
\label{fig:UMLClassDiagramoftherFuzzyConnectednessFilter}
\end{figure}


\begin{figure}
\centering
\includegraphics[width=0.8\textwidth]{FuzzyConnectednessCollaborationDiagram1.eps}
\itkcaption[Fuzzy Connectedness Segmentation Diagram]{Inputs and outputs to
FuzzyConnectednessImageFilter segmentation algorithm.}
\label{fig:UMLCollaborationDiagramoftheFuzzyConnectednessFilter}
\end{figure}

\begin{figure}
\centering
\includegraphics[width=0.8\textwidth]{VoronoiSegmentationClassDiagram1.eps}
\itkcaption[Voronoi Filter class diagram]{Inheritance diagram for the Voronoi
segmentation filters.}
\label{fig:UMLVoronoiSegmentationClassFilter}
\end{figure}

\begin{figure}
\centering
\includegraphics[width=0.8\textwidth]{VoronoiSegmentationCollaborationDiagram1.eps}
\itkcaption[Voronoi Diagram Filter classes]{Classes used by the Voronoi
segmentation filters.}
\label{fig:UMLClassesforImplementationofVoronoiDiagramFilter}
\end{figure}


\begin{figure}
\centering
\includegraphics[width=0.8\textwidth]{VoronoiSegmentationCollaborationDiagram2.eps}
\itkcaption[Voronoi Diagram Segmentation]{Input and output to the
VoronoiSegmentationImageFilter.}
\label{fig:UMLCollaborationDiagramoftheVoronoiSegmentationFilter}
\end{figure}


\begin{figure}
\centering
\includegraphics[width=0.8\textwidth]{FuzzyVoronoiCollaborationDiagram1.eps}
\itkcaption[Fuzzy Connectedness and Voronoi Diagram Classification]{Integration
 of the fuzzy connectedness and Voronoi segmentation filters.}
\label{fig:UMLHybridMethodDiagram1}
\end{figure}

\begin{figure}
\centering
\includegraphics[width=0.8\textwidth]{FuzzyVoronoiDeformableCollaborationDiagram1.eps}
\itkcaption[Fuzzy Connectedness, Voronoi diagram, and Deformable
Models]{Integration of the fuzzy connectedness, Voronoi, and
deformable model segmentation methods.}
\label{fig:UMLHybridMethodDiagram2}
\end{figure}


\subsubsection{Example of a Hybrid Segmentation Method}
\label{sec:HybridMethod1:Example}
\input{HybridSegmentationFuzzyVoronoi.tex}


\subsection{Deformable Models and Gibbs Prior}

Another combination that can be used in a hybrid segmentation method is the
set of Gibbs prior filters with deformable models.

\subsubsection{Deformable Model}
\input{DeformableModel1.tex}


\subsubsection{Gibbs Prior Image Filter}
\input{GibbsPriorImageFilter1.tex}