Special issue on "Heat Diffusion Equation and Optimal Transport in Geometry Processing and Computer Graphics"

In geometry processing and shape analysis, several problems and applications have been addressed through the prop-erties of the solution to the heat diffusion equation and to the optimal transport. For instance, diffusion kernels allow us to define diffusion distances, shape descriptors and clustering methods, to approximate geodesics and optimal transport distances, to deform 3D shapes, to smooth and approximate signals in a multi-scale fashion. Optimal transport has been successfully applied to volume parameterization, surface registration, inter-surface mapping, shape matching and compari-son. Furthermore, the heat diffusion equation and the optimal transport are intrinsically correlated and central in different research fields, such as Computer Graphics, Geometry, Manifold Learning, and Differential Equations. This Special Issue of the CAGD Journal covers a range of topics on the properties, discretization, computation, and ap-plications of the heat equation and the optimal transport in the context of Computer Graphics, Computer-Aided Geometric Design, and related research fields. The topics range from geometry processing to high-level understanding of 3D shapes, and more generally n-dimensional data, including feature extraction, segmentation, and matching. The CAGD Special Issue received a total of 10 paper submissions, and 5 papers have been accepted for publication. Each paper received from three to five reviews from experts and underwent a two-stage review process. The topics of the accepted papers cover a wide range of topics, which include theoretical results on the p-Laplace diffusion and optimal transport [1, 2], and applications to path planning, video despeckling, and shape segmentation [3, 4, 5].