Local Geometry Inclusive Global Shape Representation

A local geometry-inclusive global representation of 3D shapes based on the shortest quasi-geodesic paths between all possible pairs of points on the shape manifold is proposed. In the proposed representation, the normal curvature values along the quasi-geodesic paths are shown preserve the local shape geometry. The eigenspectrum of the proposed global representation is exploited to characterize the shape self-symmetry. The commutative property of the shape descriptor spectrum is exploited to address region-based correspondence determination between isometric 3D shapes without requiring prior correspondence maps and to extract stable regions between 3D shapes that differ from one another by a high degree of isometry transformation. Eigenspectrum-based characterization metrics are proposed to quantify the performance of the proposed 3D shape descriptor for correspondence determination and self-symmetry detection in comparison to its relevant state-of-the-art counterparts. The proposed shape descriptor spectrum and the optimization criterion based on spectral commutativity are observed to yield competitive performance compared to relevant state-of-the-art methods.