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Informative and discriminative feature descriptors play a fundamental role indeformable shape analysis. For example, they have been successfully employed incorrespondence, registration, and retrieval tasks. In the recent years,significant attention has been devoted to descriptors obtained from thespectral decomposition of the Laplace-Beltrami operator associated with theshape. Notable examples in this family are the heat kernel signature (HKS) andthe wave kernel signature (WKS). Laplacian-based descriptors achievestate-of-the-art performance in numerous shape analysis tasks; they arecomputationally efficient, isometry-invariant by construction, and cangracefully cope with a variety of transformations. In this paper, we formulatea generic family of parametric spectral descriptors. We argue that in order tobe optimal for a specific task, the descriptor should take into account thestatistics of the corpus of shapes to which it is applied (the "signal") andthose of the class of transformations to which it is made insensitive (the"noise"). While such statistics are hard to model axiomatically, they can belearned from examples. Following the spirit of the Wiener filter in signalprocessing, we show a learning scheme for the construction of optimal spectraldescriptors and relate it to Mahalanobis metric learning. The superiority ofthe proposed approach is demonstrated on the SHREC'10 benchmark.

Spectral descriptors for deformable shapes