  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 $\phi$ on $X$, we establish a
condition so that
$\ell_{(X,\phi)=\ell_{(A,\phi|_A)}+\ell_{(B,\phi|_B)}-\ell_{(A\cap
B,\phi|_{A\cap B})}$. The main tool we use is the Mayer-Vietoris sequence of
\v{C}ech homology groups. This result allows us to prove that size functions
are able to detect partial matching between shapes by showing a common subset
of cornerpoints.
