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Geometric Flows for Shape Segmentation

A number of active contour models have recently been proposed in the literature, which unify the curve evolution framework with classical energy minimization techniques for segmentation, such as snakes. The essential idea is to evolve a curve (in 2D) or a surface (in 3D) under constraints from image forces so that it clings to features of interest in an intensity image. Recently, the evolution equation has been derived from first principles as the gradient flow that minimizes a modified length functional, tailored to features such as edges. However, because the flow may be slow to converge in practice, a constant (hyperbolic) term is added to keep the curve/surface moving in the desired direction. We have derived a modification of this term based on the gradient flow derived from a weighted area functional, with image dependent weighting factor. When combined with the earlier modified length gradient flow, we obtain a PDE (partial differential equation) which offers a number of advantages, as illustrated by several examples of shape segmentation on medical images. In many cases the weighted area flow may be used on its own, with significant computational savings. A representative example is shown in Fig. 5.5.

K. Siddiqi, A. Tannenbaum (University of Minnesota), S. W. Zucker (Yale University)

Figure 5.5: The evolving front, overlayed in white, converges on the outline of the brain ventricle in an MR image.

Annual Report

Mon Jun 26 21:22:20 GMT 2000