Partial matching is probably one of the most challenging problems in shape analysis.
The problem consists of matching similar parts of shapes that are dissimilar on the whole.
Conceptually, two shapes can be considered partially matching if they have significant similar parts,
with the simplest definition of significance being the size of the parts. Thus, partial matching can be
defined as a multcriterion optimization problem trying to simultaneously maximize the similarity and the
significance of these parts.
In previous works, we used straightforward definition of significance as the area of the part. It appears that in some cases, the resulting partial matching is semantically incorrect. To cope with this problem, we proposed adding a regularity term similar to the spirit of the Mumford-Shah functional, which allows controlling the “quality” of the selected parts.
In this talk, we will address two settings of shape similarity: rigid and non-rigid shapes. In the first case, the proposed approach can be regarded as an extension of the classical iterative closest point (ICP) method. The second case requires similarity invariant to deformations that the shapes can undergo. We will show that both settings can be treated using the same framework.
*joint work with Alexander Bronstein