A Thin Shell Approach to the Registration of Implicit Surfaces

Abstract

Frequently, one aims at the co-registration of geometries described implicitly by images as level sets. This paper proposes a novel shape sensitive approach for the matching of such implicit surfaces. Motivated by physical models of elastic shells a variational approach is proposed, which distinguishes two different types of energy contributions: a membrane energy measuring the rate of tangential distortion when deforming the reference surface into the template surface, and a bending energy reflecting the required amount of bending. The variational model is formulated via a narrow band approach. The built in tangential distortion energy leads to a suitable equidistribution of deformed length and area elements, under the optimal matching deformation, whereas the minimization of the bending energy fosters a proper matching of shape features such as crests, valleys or bumps. In the implementation, a spatial discretization via finite elements, a nonlinear conjugate gradient scheme with a Sobolev metric, and a cascadic multilevel optimization strategy are used. The features of the proposed method are discussed via applications both for synthetic and realistic examples.