2008/04/22 by Michele D’Amico, M. d'Amico, d'Amico, M. +6 · 3 citations
Computer Science · #Advanced Image and Video Retrieval Techniques #Computational Geometry (cs.CG) #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #Image Retrieval and Classification Techniques #Machine Learning and Algorithms #cs.CG #cs.CV
paper · pdf · doi:10.48550/arxiv.0804.3500
arxiv created 2008/04/22 · openalex publication_date 2008/04/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper studies the properties of a new lower bound for the natural pseudo-distance. The natural pseudo-distance is a dissimilarity measure between shapes, where a shape is viewed as a topological space endowed with a real-valued 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_∞-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 pseudo-distance. We also prove that the lower bound so obtained is sharp and cannot be improved by any other distance between size functions.