Matching distance functions: A shape-to-area variational approach for global-to-local registration

Abstract

This paper deals with the matching of geometric shapes. Our primary contribution is the use of a simple, robust, rich and efficient way to represent shapes, the level set representations according to singed distance transforms. Based on these representations we propose a variational framework for global as well as local shape registration that can be extended to deal with structures of higher dimension. The optimization criterion is invariant to rotation, translation and scale and combines efficiently a global motion model with local pixel-wise deformations. Promising results are obtained on examples showing small and large global deformations as well as arbitrary topological changes.