Biomedical Engineering Reference
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Figure 3. (a) Pre-compression; (b) post-compression (intermediate stage), and (c) post-
compression (final stage).
4. THEORY OF FRONT EVOLUTION FOR BOUNDARY ESTIMATION
OF LESION
The level set has dominated the field of imaging world for more than a decade.
It has features and characteristics that no other mathematical formulations offer.
In particular, the role of level sets in imaging and computer vision has been very
aggressively advancing, since this field deals with shape changes or morphing.
The ability of the level set to capture changes in morphology very well ties in
with the adaptation of shape variabilites. The application of the level set has been
gaining prominence since the early work by Sethian and colleagues [32, 33]. There
have since been few topics written on the application of level sets (e.g., Suri et
al. [34]). We will touch on the basics of the level set framework, which forms the
foundation for our proposed method.
4.1. Front Propagation
As a starting point and as motivation for the level set approach, consider a
closed curve moving in a plane. Let γ (0) be a smooth and closed initial curve in
Euclidean plane
2 , and let γ ( t ) be the family of curves that is generated by the
movement of initial curve γ (0) along the direction of its normal vector. Moreover,
we assume that the speed of this movement is a scalar function F of curvature κ ,
called F ( κ ).
The central idea of the level set approach [16,20,22,32] is to represent the front
γ ( t ) as the level set ψ =0of a function ψ . Thus, given a moving closed hyper-
surface γ ( t ), that is, γ ( t =0):[0 ,
N , we hope to produce a formulation
for the motion of the hypersurface propagating along its normal direction with
speed F , where F can be a function of various arguments, including the curvature,
)
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