Evolutionary Fronts for Topology-Independent Shape Modeling and Recoveery

Abstract

This paper presents a novel framework for shape modeling and shape recovery based on ideas developed by Osher & Sethian for interface motion. In this framework, shapes are represented by propagating fronts, whose motion is governed by a “Hamilton-Jacobi” type equation. This equation is written for a function in which the interface is a particular level set. Unknown shapes are modeled by making the front adhere to the object boundary of interest under the influence of a synthesized halting criterion. The resulting equation of motion is solved using a narrow-band algorithm designed for rapid front advancement. Our techniques can be applied to model arbitrarily complex shapes, which include shapes with significant protrusions, and to situations where no a priori assumption about the object's topology can be made. We demonstrate the scheme via examples of shape recovery in 2D and 3D from synthetic and low contrast medical image data.