We present a method for detecting correspondences between non-rigid shapes, that utilizes surface descriptors based on the eigenfunctions of the Laplace-Beltrami operator. We use clusters of probable matched descriptors to resolve the sign ambiguity in matching the eigenfunctions. We then define a matching cost that measures both the descriptor similarity, and the similarity between correspondi...

We consider the principal eigenvalue problem for Laplace-Beltrami operator on upper half of a topological torus under Dirichlet boundary condition. present construction that admits eigenfunction having exact numbers critical points. Furthermore, we manage to identify locations all points explicitly.

We present a new AFEM for the Laplace-Beltrami operator with arbitrary polynomial degree on parametric surfaces, which are globally W 1 ∞ and piecewise in a suitable Besov class embedded in C1,α with α ∈ (0, 1]. The idea is to have the surface sufficiently well resolved in W 1 ∞ relative to the current resolution of the PDE in H1. This gives rise to a conditional contraction property of the PDE...

The eigenfunctions and eigenvalues of the Laplace-Beltrami operator have proven to be a powerful tool for digital geometry processing, providing a description of geometry that is essentially independent of coordinates or the choice of discretization. However, since Laplace-Beltrami is purely intrinsic it struggles to capture important phenomena such as extrinsic bending, sharp edges, and fine s...