We introduce a new general-purpose approach to deep learning on 3D surfaces, based on the insight that a simple diffusion layer is highly effective for spatial communication. The resulting networks are automatically robust to changes in resolution and sampling of a surface -- a basic property which is crucial for practical applications. Our networks can be discretized on various geometric representations such as triangle meshes or point clouds, and can even be trained on one representation then applied to another. We optimize the spatial support of diffusion as a continuous network parameter ranging from purely local to totally global, removing the burden of manually choosing neighborhood sizes. The only other ingredients in the method are a multi-layer perceptron applied independently at each point, and spatial gradient features to support directional filters. The resulting networks are simple, robust, and efficient. Here, we focus primarily on triangle mesh surfaces, and demonstrate state-of-the-art results for a variety of tasks including surface classification, segmentation, and non-rigid correspondence.
翻译:我们采用了一种新的通用方法来深入学习三维表面,其依据是,我们深知简单的扩散层对于空间通信非常有效。由此形成的网络对表面的分辨率和取样的变化具有自动的强大性 -- -- 一种对实用应用至关重要的基本属性。我们的网络可以分散在不同几何表象上,例如三角间距或点云,甚至可以就一个表示法进行再应用到另一个表示法的培训。我们优化了对传播的空间支持,将其作为一个从纯局部到完全全球的连续网络参数,消除了人工选择周边大小的负担。方法中的其他要素只有在每个点独立应用多层透视器,以及支持定向过滤的空间梯度特征。由此产生的网络简单、稳健、高效。在这里,我们主要侧重于三角网状表面,并展示各种任务的最新结果,包括地表分类、分解和非硬式通信。