Dense shape correspondences using spectral high-order graph matching

This paper addresses the problem of establishing point correspondences between two object instances using spectral high-order graph matching. Therefore, 3D objects are intrinsically represented by weighted high-order adjacency tensors. These are, depending on the weighting scheme, invariant for structure-preserving, equi-areal, conformal or volume-preserving object deformations. Higher-order spectral decomposition transforms the NP-hard assignment problem into a linear assignment problem by canonical embedding. This allows to extract dense correspondence information with reasonable computational complexity, making the method faster than any other previously published method imposing higher-order constraints to shape matching. Robustness against missing data and resampling is measured and compared with a baseline spectral graph matching method.