Natural pseudodistance and optimal matching between reduced size functions
Abstract
This paper studies the properties of a new lower bound for the natural pseudodistance. The natural pseudodistance is a dissimilarity measure between shapes, where a shape is viewed as a topological space endowed with a realvalued continuous function. Measuring dissimilarity amounts to minimizing the change in the functions due to the application of homeomorphisms between topological spaces, with respect to the $L_\infty$norm. In order to obtain the lower bound, a suitable metric between size functions, called matching distance, is introduced. It compares size functions by solving an optimal matching problem between countable point sets. The matching distance is shown to be resistant to perturbations, implying that it is always smaller than the natural pseudodistance. We also prove that the lower bound so obtained is sharp and cannot be improved by any other distance between size functions.
 Publication:

arXiv eprints
 Pub Date:
 April 2008
 arXiv:
 arXiv:0804.3500
 Bibcode:
 2008arXiv0804.3500D
 Keywords:

 Computer Science  Computational Geometry;
 Computer Science  Computer Vision and Pattern Recognition