3D shapes are commonly modeled as manifolds. Lack of global parameterization makes the shape analysis tasks more challenging than processing signals and images in Euclidean domains. Geometric PDE based methods capture intrinsic manifolds structures and extract various invariant descriptor to characterize and understand shapes through solutions of differential equations on manifolds. In this tutorial, I will first discuss serval numerical methods for solving PDEs on manifolds based on different representations such as meshes, point clouds and inter-point distance. After that, I will discuss applications in shape analysis based on solutions of geometric PDEs on manifolds. The tutorial will also extend to build up well-defined geometric convolution on manifolds based on parallel transport and its applications to deep learning on 3D shapes.
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