Biomedical Engineering Reference
In-Depth Information
Whilst geometric or geodesic snakes go a long way in improving on paramet-
ric snakes, they still suffer from two significant shortcomings. First, they allow
leakage into neighboring image regions when confronted with weak edges; here-
after we refer to this as the weak-edge leakage problem. Second, they may rest
at local maxima in noisy image regions. In this chapter, both of these problems
are dealt with by introducing diffused region forces into the standard geometric
snake formulation. The proposed method is referred to as the region-aided geo-
metric snake or RAGS. It integrates gradient flows with a diffused region vector
flow. The gradient flow forces supplant the snake with local object boundary
information, while the region vector flow force gives the snake a global view of
object boundaries. The diffused region vector flow is derived from the region
segmentation map which in turn can be generated from any image segmentation
technique. This chapter demonstrates that RAGS can indeed act as a refinement
of the results of the initial region segmentation. It also illustrates RAGS' weak
edge leakage improvements and tolerance to noise through various examples.
Using color edge gradients, RAGS will be shown to naturally extend to object de-
tection in color images. The partial differential equations (PDEs) resulting from
the proposed method will be implemented numerically using level set theory,
which enables topological changes to be dealt with automatically.
In Section 10.2 we review the geometric snake model, encompassing its
strength and its shortcomings. Section 10.3 provides a brief overview of the
geometric GGVF snake, also outlining its shortcomings. The former section is
essential as RAGS' theory is built upon it, and the latter is necessary since we
shall make performance comparisons to it. Section 10.4 presents the deriva-
tion of the RAGS snake including its level set representation. Then, in Section
10.5, the numerical solutions for obtaining the diffused region force and level
set implementation of RAGS are introduced. Section 10.6 describes the exten-
sion of RAGS to vector-valued images, again showing the equivalent level set
numerical representation. Since RAGS is independent of any particular region
segmentation method, its description so far is not affected by the fact that no
discussion of region segmentation has yet taken place! This happens next in
Section 10.7 where the mean shift algorithm is employed as a typical, suitable
method for obtaining a region segmentation map for use with RAGS. Follow-
ing a brief summary of the RAGS algorithm in Section 10.8, examples and re-
sults illustrating the improvements obtained on noisy images and images with
weak edges are presented in Section 10.9. This includes an application with
