Symmetry-Aware Nonrigid Matching of Incomplete 3D Surfaces

We present a nonrigid shape matching technique for establishing correspondences of incomplete 3D surfaces that exhibit intrinsic reflectional symmetry. The key for solving the symmetry ambiguity problem is to use a point-wise local mesh descriptor that has orientation and is thus sensitive to local reflectional symmetry, e.g. discriminating the left hand and the right hand. We devise a way to compute 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 algorithm called iterative spectral relaxation which combines spectral embedding and spectral graph matching. This formulation 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 challenging surfaces with global intrinsic symmetry, data incompleteness and non-isometric deformations.