# Size functions for shape recognition in the presence of occlusions

Di Fabio, Barbara ; Landi, Claudia (2009) Size functions for shape recognition in the presence of occlusions. p. 30. DOI 10.6092/unibo/amsacta/2624.
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## Abstract

In Computer Vision the ability to recognize objects in the presence of occlusions is a necessary requirement for any shape representation method. In this paper we investigate how the size function of an object shape changes when a portion of the object is occluded by another object. More precisely, considering a set $X=A\cup B$ and a measuring function $\varphi$ on $X$, we establish a condition so that $\ell_{(X,\varphi)}=\ell_{(A,\varphi|_A)}+\ell_{(B,\varphi|_B)}-\ell_{(A\cap B,\varphi|_{A\cap B})}$. The main tool we use is the Mayer-Vietoris sequence of \v{C}ech homology groups. This result allows us to prove that size functions are able to detect partial matching between shapes by showing a common subset of cornerpoints.

Abstract
Document type
Monograph (Technical Report)
Creators
CreatorsAffiliationORCID
Di Fabio, Barbara
Landi, Claudia
MSC (2000): 55N05, 68U05
Keywords
\v{C}ech homology, Mayer-Vietoris sequence, persistent homology, shape occlusion
Subjects
DOI
Deposit date
22 Sep 2009 07:44
16 May 2011 12:11
URI