A unified definition and computation of Laplacian spectral distances
作者：
Highlights：
• Definition of spectral distances through a filtering of the Laplacian eigenpairs and as a generalization of the heat diffusion, wave, bi-harmonic, and commute-time distances for specific filters.
• Novel definition of Laplacian distances and kernels, whose approximation requires the solution of a set of differential equations involving only the Laplace-Beltrami operator.
• The computation of the discrete spectral distances is equivalent to the solution of a set of sparse linear systems, which are efficiently solved with iterative methods.
• The approach is free of user-defined parameters, overcomes the evaluation of the Laplacian spectrum, and guarantees a higher approximation accuracy than previous work.
摘要
•Definition of spectral distances through a filtering of the Laplacian eigenpairs and as a generalization of the heat diffusion, wave, bi-harmonic, and commute-time distances for specific filters.•Novel definition of Laplacian distances and kernels, whose approximation requires the solution of a set of differential equations involving only the Laplace-Beltrami operator.•The computation of the discrete spectral distances is equivalent to the solution of a set of sparse linear systems, which are efficiently solved with iterative methods.•The approach is free of user-defined parameters, overcomes the evaluation of the Laplacian spectrum, and guarantees a higher approximation accuracy than previous work.
论文关键词：Laplacian spectrum,Spectral distances,Spectral kernels,Heat kernel,Diffusion distances and geometry,Shape and graph analysis
论文评审过程：Received 23 June 2016, Revised 31 March 2019, Accepted 6 April 2019, Available online 13 April 2019, Version of Record 17 April 2019.
论文官网地址：https://doi.org/10.1016/j.patcog.2019.04.004
