TY - JOUR
T1 - Partial Shape Matching Without Point-Wise Correspondence
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 1
SP - 223
EP - 244
PY - 2013
DA - 2013/06
SN - 6
DO - http://doi.org/10.4208/nmtma.2013.mssvm12
UR - https://global-sci.org/intro/article_detail/nmtma/5901.html
KW - Deformable shapes, partial matching, partial correspondence, partial similarity, diffusion geometry, Laplace-Beltrami operator, shape descriptors, heat kernel signature, Mumford-Shah regularization.
AB - <p style="text-align: justify;">Partial similarity of shapes is a challenging problem arising in many important applications in computer vision, shape analysis, and graphics, e.g. when one has to deal with partial information and acquisition artifacts.
The problem is especially hard when the underlying shapes are non-rigid and are given up to a deformation.
Partial matching is usually approached by computing local descriptors on a pair of shapes and then establishing a point-wise non-bijective correspondence between the two, taking into account possibly different parts.
In this paper, we introduce an alternative correspondence-less approach to matching fragments to an entire shape undergoing a non-rigid deformation. We use region-wise local descriptors and optimize over the integration domains on which the integral descriptors of the two
parts match. The problem is regularized using the Mumford-Shah functional. We show an efficient discretization based on the Ambrosio-Tortorelli approximation generalized to triangular point clouds and meshes, and present experiments demonstrating the success of the proposed method.</p>