A Geometrical Active Contour Based Sobolev Metric

Abstract

Recently, a new reformulation of geometric active contour model is introduced by reformulating the gradient flow with Sobolev-type inner products. Classical inner product induces a pathological Riemannian metric on the space of smooth curves. However, there are also undesirable features associated with the gradient flow that this inner product induces. Sobolev metrics induce good regularity properties in gradient flow. The new formulation based Sobolev metric improved segmentation accuracy. We applied successfully the proposed model to synthetic and real MR images. The results drawn by the newer model are compared to expert segmentation and evaluated in term of F-measure.