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

Cech homology for shape recognition in the presence of occlusions