Robust point matching for two-dimensional nonrigid shapes

Recently, nonrigid shape matching has received more and more attention. For nonrigid shapes, most neighboring points cannot move independently under deformation due to physical constraints. Furthermore, the rough structure of a shape should be preserved under deformation, otherwise even people cannot match shapes reliably. Therefore, though the absolute distance between two points may change significantly, the neighborhood of a point is well preserved in general. Based on this observation, we formulate point matching as a graph matching problem. Each point is a node in the graph, and two nodes are connected by an edge if their Euclidean distance is less than a threshold. The optimal match between two graphs is the one that maximizes the number of matched edges. The shape context distance is used to initialize the graph matching, followed by relaxation labeling for refinement. Nonrigid deformation is overcome by bringing one shape closer to the other in each iteration using deformation parameters estimated from the current point correspondence. Experiments demonstrate the effectiveness of our approach: it outperforms the shape context and TPS-RPM algorithms under nonrigid deformation and noise on a public data set.