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Geometric feature learning for 3D surfaces is critical for many applicationsin computer graphics and 3D vision. However, deep learning currently lags inhierarchical modeling of 3D surfaces due to the lack of required operationsand/or their efficient implementations. In this paper, we propose a series ofmodular operations for effective geometric feature learning from 3D trianglemeshes. These operations include novel mesh convolutions, efficient meshdecimation and associated mesh (un)poolings. Our mesh convolutions exploitspherical harmonics as orthonormal bases to create continuous convolutionalfilters. The mesh decimation module is GPU-accelerated and able to processbatched meshes on-the-fly, while the (un)pooling operations compute featuresfor up/down-sampled meshes. We provide open-source implementation of theseoperations, collectively termed Picasso. Picasso supports heterogeneous meshbatching and processing. Leveraging its modular operations, we furthercontribute a novel hierarchical neural network for perceptual parsing of 3Dsurfaces, named PicassoNet++. It achieves highly competitive performance forshape analysis and scene segmentation on prominent 3D benchmarks. The code,data and trained models are available athttps://github.com/EnyaHermite/Picasso.

Mesh Convolution with Continuous Filters for 3D Surface Parsing