@article{di_fabio_mayervietoris_2011,
abstract = {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.},
author = {Di Fabio, Barbara and Landi, Claudia},
date = {2011-09-07},
doi = {10.1007/s10208-011-9100-x},
issn = {1615-3383},
journaltitle = {Foundations of Computational Mathematics},
keywords = {1 - Occlusion, 1 - Shape recognition, 2 - Mayer-Vietoris, 2 - Persistent homology, 3 - images:2d},
langid = {english},
number = {5},
pages = {499},
shortjournal = {Found Comput Math},
title = {A Mayer–Vietoris Formula for Persistent Homology with an Application to Shape Recognition in the Presence of Occlusions},
url = {https://doi.org/10.1007/s10208-011-9100-x},
urldate = {2021-04-11},
volume = {11}
}