Geometric feature learning for 3D surfaces is critical for many applications in computer graphics and 3D vision. However, deep learning currently lags in hierarchical modeling of 3D surfaces due to the lack of required operations and/or their efficient implementations. In this paper, we propose a series of modular operations for effective geometric feature learning from 3D triangle meshes. These operations include novel mesh convolutions, efficient mesh decimation and associated mesh (un)poolings. Our mesh convolutions exploit spherical harmonics as orthonormal bases to create continuous convolutional filters. The mesh decimation module is GPU-accelerated and able to process batched meshes on-the-fly, while the (un)pooling operations compute features for up/down-sampled meshes. We provide open-source implementation of these operations, collectively termed Picasso. Picasso supports heterogeneous mesh batching and processing. Leveraging its modular operations, we further contribute a novel hierarchical neural network for perceptual parsing of 3D surfaces, named PicassoNet++. It achieves highly competitive performance for shape analysis and scene segmentation on prominent 3D benchmarks. The code, data and trained models are available at https://github.com/EnyaHermite/Picasso.

翻译：三维表面的几何特征学习对于计算机图形学和三维视觉中的许多应用至关重要。然而，由于缺乏所需操作及其高效实现，深度学习目前在三维表面的分层建模方面仍相对滞后。本文提出了一系列模块化操作，用于从三维三角形网格中进行有效的几何特征学习。这些操作包括新型网格卷积、高效网格简化以及相关的网格（反）池化。我们的网格卷积利用球谐函数作为正交基来生成连续卷积滤波器。网格简化模块采用GPU加速，能够实时处理批量网格，而（反）池化操作用于计算上采样/下采样网格的特征。我们提供了这些操作的开源实现，统称为Picasso。Picasso支持异构网格的批处理与运算。借助其模块化操作，我们进一步提出了一种用于三维表面感知解析的新型分层神经网络，命名为PicassoNet++。该网络在主流三维基准测试中，在形状分析和场景分割任务上取得了极具竞争力的性能。代码、数据和训练模型可在 https://github.com/EnyaHermite/Picasso 获取。