Joint intrinsic and extrinsic similarity for recognition of non-rigid shapes

This paper explores the problem of similarity criteria between nonrigid shapes. Broadly speaking, such criteria are divided into intrinsic and extrinsic, the first referring to the metric structure of the objects and the latter to the Euclidean coordinates of the points of which the objects comprises. Both criteria have their advantages and disadvantages; extrinsic similarity is sensitive to non-rigid deformations of the shapes, while intrinsic similarity is sensitive to topological noise. We present an approach unifying both criteria in a single measure. We consider the tradeoff between the extrinsic and intrinsic similarity and use it as a set-valued “distance” related to the notion of Pareto optimality in economics. Numerical results demonstrate the efficiency of our approach in cases where using solely extrinsic or intrinsic criteria would fail.