When shapes of objects are modeled as topological spaces endowed with functions, the shape comparison problem can be dealt with using persistent homology to provide shape descriptors, and the matching distance to measure dissimilarities. Motivated by the problem of dealing with incomplete or imprecise acquisition of data in computer vision and computer graphics, recent papers 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.
Ferri, M., Frosini, P., Landi, C. (2011). Stable shape comparison by persistent homology. ATTI DEL SEMINARIO MATEMATICO E FISICO DEL'UNIVERSITÀ DI MODENA E REGGIO EMILIA, 58, 143-162.
Stable shape comparison by persistent homology
FERRI, MASSIMO;FROSINI, PATRIZIO;LANDI, CLAUDIA
2011
Abstract
When shapes of objects are modeled as topological spaces endowed with functions, the shape comparison problem can be dealt with using persistent homology to provide shape descriptors, and the matching distance to measure dissimilarities. Motivated by the problem of dealing with incomplete or imprecise acquisition of data in computer vision and computer graphics, recent papers 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
