We introduce a new approach to deep learning on 3D surfaces such as meshes or point clouds. Our key insight is that a simple learned diffusion layer can spatially share data in a principled manner, replacing operations like convolution and pooling which are complicated and expensive on surfaces. The only other ingredients in our network are a spatial gradient operation, which uses dot-products of derivatives to encode tangent-invariant filters, and a multi-layer perceptron applied independently at each point. The resulting architecture, which we call DiffusionNet, is remarkably simple, efficient, and scalable. Continuously optimizing for spatial support avoids the need to pick neighborhood sizes or filter widths a priori, or worry about their impact on network size/training time. Furthermore, the principled, geometric nature of these networks makes them agnostic to the underlying representation and insensitive to discretization. In practice, this means significant robustness to mesh sampling, and even the ability to train on a mesh and evaluate on a point cloud. Our experiments demonstrate that these networks achieve state-of-the-art results for a variety of tasks on both meshes and point clouds, including surface classification, segmentation, and non-rigid correspondence.
翻译:我们引入了对三维表面,如梅shes或点云进行深层学习的新方法。 我们的关键洞察力是,一个简单的学习到的传播层可以有原则地共享数据,以空间方式共享数据,取代在表面复杂和昂贵的卷叠和集合等操作。我们网络中唯一的其它成份是空间梯度操作,使用衍生物的点产品来编码正对异差过滤器,并在每个点独立应用一个多层透视器。由此产生的结构(我们称之为DiflutionNet)非常简单、高效和可缩放。对空间支持的持续优化避免了对周围大小或过滤宽度的偏移,或者担心其对网络规模/培训时间的影响。此外,这些网络的有原则性和几何性质使得它们对基本代表面和离散反应不敏感。在实践中,这意味着对网格取样的高度坚固性,甚至对网点云的训练和评价能力都是非常简单、高效和可缩放的。我们的实验表明,这些网络在地面和地面的分类上,包括不精密的云层和对等点上,都实现了。