Symmetry-Aware Nonrigid Matching of Incomplete 3D Surfaces

We present a nonrigid shape matching technique for es-tablishing correspondences of incomplete 3D surfaces that exhibit intrinsic reflectional symmetry. The key for solving the symmetry ambiguity problem is to use a point-wise lo-cal mesh descriptor that has orientation and is thus sensi-tive to local reflectional symmetry, e.g. discriminating the left hand and the right hand. We devise a way to com-pute the descriptor orientation by taking the gradients of a scalar field called the average diffusion distance (ADD). Because ADD is smoothly defined on a surface, invariant under isometry/scale and robust to topological errors, the robustness of the descriptor to non-rigid deformations is improved. In addition, we propose a graph matching al-gorithm called iterative spectral relaxation which combines spectral embedding and spectral graph matching. This for-mulation allows us to define pairwise constraints in a scale-invariant manner from k-nearest neighbor local pairs such that non-isometric deformations can be robustly handled. Experimental results show that our method can match chal-lenging surfaces with global intrinsic symmetry, data in-completeness and non-isometric deformations. 1