When shapes of objects are modeled as topologicalspaces endowed with functions, the shape comparison problem canbe dealt with using persistent homology to provide shape descriptors,and the matching distance to measure dissimilarities. Motivatedby the problem of dealing with incomplete or imprecise acquisitionof data in computer vision and computer graphics, recentpapers have studied stability properties of persistent Betti numbers with respect to perturbations both in the topological space and in the function. This paper reports on progress in this area of research.
Stable Shape Comparison by Persistent Homology / M., Ferri; P., Frosini; Landi, Claudia. - In: ATTI DEL SEMINARIO MATEMATICO E FISICO DEL'UNIVERSITÀ DI MODENA E REGGIO EMILIA. - ISSN 1825-1269. - STAMPA. - 58:(2011), pp. 143-162.
Stable Shape Comparison by Persistent Homology
LANDI, Claudia
2011
Abstract
When shapes of objects are modeled as topologicalspaces endowed with functions, the shape comparison problem canbe dealt with using persistent homology to provide shape descriptors,and the matching distance to measure dissimilarities. Motivatedby the problem of dealing with incomplete or imprecise acquisitionof data in computer vision and computer graphics, recentpapers have studied stability properties of persistent Betti numbers with respect to perturbations both in the topological space and in the function. This paper reports on progress in this area of research.
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