caa a22 4500 445331631 CHVBK 20180317142739.0 cr unu---uuuuu 170323e20111001xx s 000 0 eng 10.1007/s10208-011-9100-x doi (NATIONALLICENCE)springer-10.1007/s10208-011-9100-x A Mayer-Vietoris Formula for Persistent Homology with an Application to Shape Recognition in the Presence of Occlusions [Elektronische Daten] [Barbara Di Fabio, Claudia Landi] In algebraic topology it is well known that, using the Mayer-Vietoris sequence, the homology of a space X can be studied by splitting X into subspaces A and B and computing the homology of A, B, and A∩B. A natural question is: To what extent does persistent homology benefit from a similar property? In this paper we show that persistent homology has a Mayer-Vietoris sequence that is generally not exact but only of order 2. However, we obtain a Mayer-Vietoris formula involving the ranks of the persistent homology groups of X, A, B, and A∩B plus three extra terms. This implies that persistent homological features of A and B can be found either as persistent homological features of X or of A∩B. As an application of this result, we show that persistence diagrams are able to recognize an occluded shape by showing a common subset of points. SFoCM, 2011 Čech homology nationallicence Mayer-Vietoris sequence nationallicence Persistence diagram nationallicence Partial matching nationallicence Shape occlusion nationallicence Di Fabio Barbara ARCES, Università di Bologna, Bologna, Italy aut Landi Claudia Dipartimento di Scienze e Metodi dell'Ingegneria, Università di Modena e Reggio Emilia, Reggio Emilia, Italy aut Foundations of Computational Mathematics Springer-Verlag 11/5(2011-10-01), 499-527 1615-3375 11:5<499 2011 11 10208 https://doi.org/10.1007/s10208-011-9100-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10208-011-9100-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Di Fabio Barbara ARCES, Università di Bologna, Bologna, Italy aut NATIONALLICENCE 700 1- Landi Claudia Dipartimento di Scienze e Metodi dell'Ingegneria, Università di Modena e Reggio Emilia, Reggio Emilia, Italy aut NATIONALLICENCE 773 0- Foundations of Computational Mathematics Springer-Verlag 11/5(2011-10-01), 499-527 1615-3375 11:5<499 2011 11 10208 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer