Mathematics – Algebraic Topology
Scientific paper
2008-07-04
Mathematics
Algebraic Topology
32 pages, 12 figures
Scientific paper
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.
Fabio Barbara Di
Landi Claudia
No associations
LandOfFree
Cech homology for shape recognition in the presence of occlusions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Cech homology for shape recognition in the presence of occlusions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Cech homology for shape recognition in the presence of occlusions will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-598207