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The heat diffusion distance and kernel have gained a central role in geometry processing and shape analysis. This paper addresses a novel discretization and spectrum-free computation of the diffusion kernel and distance on a 3D shape P represented as a triangle mesh or a point set. After rewriting different discretizations of the Laplace–Beltrami operator in a unified way and using an intrinsic scalar...
Recent results in geometry processing have shown that shape segmentation, comparison, and analysis can be successfully addressed through the spectral properties of the Laplace–Beltrami operator, which is involved in the harmonic equation, the Laplacian eigenproblem, the heat diffusion equation, and the definition of spectral distances, such as the bi-harmonic, commute time, and diffusion distances...
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