Computational anatomy and implicit object representation: A level set approach

Abstract

In this paper, we look at the fundamental problem of object matching in computational anatomy. We present a new framework for warping pairs of overlapping and non-overlapping shapes, open curves, and landmarks based on the level set approach. When implemented in 3-D, the same framework could be used to warp 3-D objects with minimal modification. Our approach is to use the level set functions to represent the objects to be matched. Using this representation, the problem becomes an energy minimization problem. Cost functions for warping overlapping, non-overlapping, open curves, and landmarks are proposed. Euler-Lagrange equations are applied and gradient descent is used to solve the corresponding partial differential equations. Moreover, a general framework for linking the level set approach and the infinite dimensional group actions is discussed. © Springer-Verlag Berlin Heidelberg 2003.