Hierarchical Matching of Non-rigid Shapes

Detecting similarity between non-rigid shapes is one of the fundamental problems in computer vision. While rigid alignment can be parameterized using a small number of unknowns representing rotations, reflections and translations, non-rigid alignment does not have this advantage. The majority of the methods addressing this problem boil down to a minimization of a distortion measure. The complexity of a matching process is exponential by nature, but it can be heuristically reduced to a quadratic or even linear for shapes which are smooth two-manifolds. Here we model shapes using both local and global structures, and provide a hierarchical framework for the quadratic matching problem.