Local Geometry Inclusive Global Shape Representation
This work addresses shape analysis for applications like 3D modeling and computer vision, but it appears incremental as it builds on existing shape descriptor methods.
The paper tackles the problem of representing 3D shapes by introducing a local geometry-inclusive global descriptor based on quasi-geodesic paths, which preserves normal curvature and enables region-based correspondence and self-symmetry characterization without prior knowledge. The result includes experimental comparison showing performance against state-of-the-art 3D shape descriptors.
Knowledge of shape geometry plays a pivotal role in many shape analysis applications. In this paper we introduce a local geometry-inclusive global representation of 3D shapes based on computation of the shortest quasi-geodesic paths between all possible pairs of points on the 3D shape manifold. In the proposed representation, the normal curvature along the quasi-geodesic paths between any two points on the shape surface is preserved. We employ the eigenspectrum of the proposed global representation to address the problems of determination of region-based correspondence between isometric shapes and characterization of self-symmetry in the absence of prior knowledge in the form of user-defined correspondence maps. We further utilize the commutative property of the resulting shape descriptor to extract stable regions between isometric shapes that differ from one another by a high degree of isometry transformation. We also propose various shape characterization metrics in terms of the eigenvector decomposition of the shape descriptor spectrum to quantify the correspondence and self-symmetry of 3D shapes. The performance of the proposed 3D shape descriptor is experimentally compared with the performance of other relevant state-of-the-art 3D shape descriptors.