Spectral feature selection for shape characterization and classification

This paper proposes a framework for selecting the Laplacian eigenvalues of 3D shapes that are more relevant for shape characterization and classification. We demonstrate the redundancy of the information coded by the shape spectrum and discuss the shape characterization capability of the selected eigenvalues. The feature selection methods used to demonstrate our claim are the AdaBoost algorithm and Support Vector Machine. The efficacy of the selection is shown by comparing the results of the selected eigenvalues on shape characterization and classification with those related to the first k eigenvalues, by varying k over the cardinality of the spectrum. Our experiments, which have been performed on 3D objects represented either as triangle meshes or point clouds, show that working directly with point clouds provides classification results that are comparable with respect to those related to surface-based representations. Finally, we discuss the stability of the computation of the Laplacian spectrum to matrix perturbations.