Cech homology for shape recognition in the presence of occlusions

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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.
32 pages, 12 figures

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Algebraic Topology, 55N05; 68U05

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http://salesiana.dossiersoluciones.com/handle/123456789/164298

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0807.0796
 http://arxiv.org/abs/0807.0796

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arXiv