Continuous Geodesic Convolutions for Learning on 3D Shapes

The majority of descriptor-based methods for geometric processing of non-rigid shape rely on hand-crafted descriptors. Recently, learning-based techniques have been shown effective, achieving state-of-the-art results in a variety of tasks. Yet, even though these methods can in principle work directly on raw data, most methods still rely on hand-crafted descriptors at the input layer. In this work, we wish to challenge this practice and use a neural network to learn descriptors directly from the raw mesh. To this end, we introduce two modules into our neural architecture. The first is a local reference frame (LRF) used to explicitly make the features invariant to rigid transformations. The second is continuous convolution kernels that provide robustness to sampling. We show the efficacy of our proposed network in learning on raw meshes using two cornerstone tasks: shape matching, and human body parts segmentation. Our results show superior results over baseline methods that use hand-crafted descriptors.