Efficient deformable shape correspondence via multiscale spectral manifold wavelets preservation

The functional map framework has proven to be extremely effective for representing dense correspondences between deformable shapes. A key step in this framework is to formulate suitable preservation constraints to encode the geometric information that must be preserved by the unknown map. For this issue, we construct novel and powerful constraints to determine the functional map, where multiscale spectral manifold wavelets are required to be preserved at each scale correspondingly. Such constraints allow us to extract significantly more information than previous methods, especially those based on descriptor preservation constraints, and strongly ensure the isometric property of the map. In addition, we also propose a remarkable efficient iterative method to alternatively update the functional maps and pointwise maps. Moreover, when we use the tight wavelet frames in iterations, the computation of the functional maps boils down to a simple filtering procedure with low-pass and various band-pass filters, which avoids time-consuming solving large systems of linear equations commonly presented in functional maps. We demonstrate on a wide variety of experiments with different datasets that our approach achieves significant improvements both in the shape correspondence quality and the computing efficiency.