We propose DualConvMesh-Nets (DCM-Net) a family of deep hierarchical convolutional networks over 3D geometric data that combines two types of convolutions. The first type, geodesic convolutions, defines the kernel weights over mesh surfaces or graphs. That is, the convolutional kernel weights are mapped to the local surface of a given mesh. The second type, Euclidean convolutions, is independent of any underlying mesh structure. The convolutional kernel is applied on a neighborhood obtained from a local affinity representation based on the Euclidean distance between 3D points. Intuitively, geodesic convolutions can easily separate objects that are spatially close but have disconnected surfaces, while Euclidean convolutions can represent interactions between nearby objects better, as they are oblivious to object surfaces. To realize a multi-resolution architecture, we borrow well-established mesh simplification methods from the geometry processing domain and adapt them to define mesh-preserving pooling and unpooling operations. We experimentally show that combining both types of convolutions in our architecture leads to significant performance gains for 3D semantic segmentation, and we report competitive results on three scene segmentation benchmarks. Our models and code are publicly available.

提出了 DualConvMesh-Nets (DCM-Net) 模型，它是一种基于 3D 几何数据的深层分层卷积神经网络，结合了两种卷积类型：测地线卷积和欧几里得卷积，并且还采用了几何处理领域中的网格简化方法来定义网格池化和反池化运算。实验结果表明，我们提出的模型在 3D 语义分割任务上取得了显著的性能提升并在三个场景分割基准测试中获得了竞争性的结果。

DualConvMesh-Net: 3D 网格上的测地和欧几里得卷积联合