Cech homology for shape recognition in the presence of occlusions

Barbara Di Fabio; Claudia Landi

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arXiv · 0807.0796

Cech homology for shape recognition in the presence of occlusions

Barbara Di Fabio·Claudia Landi

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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 a shape changes when a portion of the shape is occluded by another shape. More precisely, considering a set $X=A\cup B$ and a measuring function $ϕ$ on $X$, we establish a condition so that $\ell_{(X,ϕ)=\ell_{(A,ϕ|_A)}+\ell_{(B,ϕ|_B)}-\ell_{(A\cap B,ϕ|_{A\cap B})}$. The main tool we use is the Mayer-Vietoris sequence of Čech 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.

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Barbara Di Fabio, Claudia Landi. 2008-07-04. Cech homology for shape recognition in the presence of occlusions. https://arxiv.org/abs/0807.0796

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