2.6
Summary and Conclusion
In this chapter, we reviewed some of the existing image segmentation approaches as well as the main computational methods which are relevant to the work in this thesis. The development of segmentation algorithms have gradually shifted over the years from global intensity-based meth- ods to those which use registration and spatially varying information. The shift in atlas-based methods from globally weighted to locally weighted methods have provided better accuracy and robustness. However, despite improvements in registration methods, the dependency on registration can still pose a problem as registrations errors still commonly occur and can ad- versely affect segmentation results. The recent developments in using patch-based methods have provided a starting point in reducing dependency on registration and improving robust- ness to registration errors, and it is from this point where the main contributions of this thesis are introduced.
In the next chapter, a novel kNN patch-based segmentation framework is presented which uses several of the methods reviewed here, in particular kNN data structures and patch-based seg- mentation based on nonlocal means. The conceptual idea is to extend patch-based methods and further reduce the dependency on registration whilst improving the robustness and accuracy.
Chapter 3
Spatially Aware Patch-based
Segmentation
This chapter is based on the following publication:
• Zehan Wang, Robin Wolz, Tong Tong, Daniel Rueckert. Spatially Aware Patch-based Segmentation (SAPS): An Alternative Patch-based Segmentation Framework. Second International MICCAI Workshop on Medical Computer Vision: Recognition Techniques and Applications in Medical Imaging (MCV 2012). LNCS Volume 7766, pages 93-103. Springer Heidelberg 2013.
3.1
Introduction
Patch-based segmentation methods compare patches in a local neighbourhood in order to de- termine the label for each voxel. The underlying assumption is that patches with similar intensities and from similar local neighbourhoods are likely to be the part of the same anatom- ical structure. Traditionally, this locality is enforced by a sliding search window of a fixed size (typically less than 113 voxels). Label fusion then determines spatially-varying weights for each
label according to the similarity of the corresponding patches within each voxel neighbourhood. 87
This neighbourhood, when defined as a fixed size search window, imposes a hard restriction on tolerance to any registration errors that occur. Increasing this search window increases the tol- erance to registration errors but also increases the computational requirements and may yield patches with similar appearance but from different anatomical structures. Using hierarchical frameworks [61], [191] partly addresses these restrictions, however these approaches still use a fixed search window size for patch selection and comparison.
As an alternative approach, the patch selection process is reformulated so that it is no longer constrained by a fixed search window size. Instead patches are considered from all plausible regions of the image, without fixing or limiting the size of the search volume. To reduce the computational burden, kNN data structures are used so that an exhaustive search of all patches is not necessary. To differentiate between similar patches from different structures, the use of spatial context is employed to augment the intensity information for each patch. This means that for each voxel x, a feature vector can be produced consisting of the intensity information for the patch centred on x in addition to the spatial information for x (see Figure 3.1). The local neighbourhood for patch comparison is then defined by the k nearest neighbours from each relevant label in the atlas library, in terms of both spatial distance and intensity distance, using the feature vector. This allows the search space of patches to be global whilst maintaining the sense of locality, thus removing the requirement for a fixed search window size to be set. Label fusion is performed by comparing the k nearest patches of each label to derive the final labelling.
For spatial context, the spatial coordinates of each voxel is used in this chapter, but other forms of spatial context will be discussed in later chapters.
3.1.1
Chapter Overview
This chapter introduces a novel patch-based segmentation framework which is used and ex- tended with new approaches for spatial context in subsequent chapters. We start with a re- formulation of an existing patch-based method [47] in a kNN framework which also includes spatial context as part of the label fusion process. This is followed by a proposal to use kNN
3.2. kNN Spatially Aware Label Fusion 89
Figure 3.1: The proposed patch-based segmentation framework uses both the intensities of the patch, extracted using a patch extraction operator P (x), and spatial information, provided by a spatial context function S(x). These are concatenated to produce a feature vector, enabling kNN with standard data structures. The spatial weight α controls the contribution and balance of the two components. In this chapter, S(x) is returns the image coordinates of voxel x, but in subsequent chapters, other functions for the spatial context will be explored.
data structures to enable the patch search process to occur without constraining the search window size. Finally, we end with the experiments performed using the proposed framework for hippocampus segmentation in brain MRI and a discussion of the results.