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3D models are commonly used in computer vision and graphics. With the wideravailability of mesh data, an efficient and intrinsic deep learning approach toprocessing 3D meshes is in great need. Unlike images, 3D meshes have irregularconnectivity, requiring careful design to capture relations in the data. Toutilize the topology information while staying robust under differenttriangulation, we propose to encode mesh connectivity using Laplacian spectralanalysis, along with Mesh Pooling Blocks (MPBs) that can split the surfacedomain into local pooling patches and aggregate global information among them.We build a mesh hierarchy from fine to coarse using Laplacian spectralclustering, which is flexible under isometric transformation. Inside the MPBsthere are pooling layers to collect local information and multi-layerperceptrons to compute vertex features with increasing complexity. To obtainthe relationships among different clusters, we introduce a Correlation Net tocompute a correlation matrix, which can aggregate the features globally bymatrix multiplication with cluster features. Our network architecture isflexible enough to be used on meshes with different numbers of vertices. Weconduct several experiments including shape segmentation and classification,and our LaplacianNet outperforms state-of-the-art algorithms for these tasks onShapeNet and COSEG datasets.

LaplacianNet: Learning on 3D Meshes with Laplacian Encoding and Pooling