1 research outputs found
Local Geometry Inclusive Global Shape Representation
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.Comment: 11 pages, 5 figure