Topology-Invariant Similarity of Nonrigid Shapes

摘要

This paper explores the problem of similarity cri_teria between nonrigid shapes. Broadly speaking, such crite_ria are divided into intrinsic and extrinsic, the first referring to the metric structure of the object and the latter to how it is laid out in the Euclidean space. Both criteria have their ad_vantages and disadvantages: extrinsic similarity is sensitive to nonrigid deformations, while intrinsic similarity is sen_sitive to topological noise. In this paper, we approach the problem from the perspective of metric geometry. We show that by unifying the extrinsic and intrinsic similarity criteria, it is possible to obtain a stronger topology-invariant similar_ity, suitable for comparing deformed shapes with different topology. We construct this new joint criterion as a tradeoff between the extrinsic and intrinsic similarity and use it as a set-valued distance. Numerical results demonstrate the effi_ciency of our approach in cases where using either extrinsic or intrinsic criteria alone would fail.