Regularized partial matching of rigid shapes

Matching of rigid shapes is an important problem in numerous applications across the boundary of computer vision, pattern recognition and computer graphics communities. A particularly challenging setting of this problem is partial matching, where the two shapes are dissimilar in general, but have significant similar parts. In this paper, we show a rigorous approach allowing to find matching parts of rigid shapes with controllable size and regularity. The regularity term we use is similar to the spirit of the Mumford-Shah functional, extended to non-Euclidean spaces. Numerical experiments show that the regularized partial matching produces better results compared to the non-regularized one.