Principal Curvature Guided Surface Geometry Aware Global Shape Representation

A surface principal curvature preserving local geometry aware global shape representation for 3D shapes is proposed. The shape representation computes the shortest quasi-geodesic path between all possible pairs of points on the shape manifold that enforces minimal variation of geodesic curvature along the path. The normal component of the principal curvature along the quasi-geodesic paths is dominant and shown to preserve the local shape geometry. The eigenspectrum of the proposed representation is exploited to characterize self-symmetry. The commutative property between shape spectra is exploited to compute region-based correspondence between isometric 3D shapes without requiring an initial correspondence map to be specified a priori. The results of the region-based correspondence are extended to characterize the compatibility of the commutative eigen-spectrum in order to address the problem of shape deformation transfer. Eigenspectrum-based characterization metrics are proposed to quantify the performance of the proposed 3D shape descriptor for self-symmetry detection and correspondence determination. The proposed shape descriptor spectrum-based optimization criterion is observed to yield competitive performance compared to relevant state-of-the-art correspondence determination techniques.