Convolutional neural networks (CNNs) have been pivotal in various 2D image analysis tasks, including computer vision, image indexing and retrieval or semantic classification. Extending CNNs to 3D data such as point clouds and 3D meshes raises significant challenges since the very basic convolution and pooling operators need to be completely re-visited and re-defined in an appropriate manner to tackle irregular connectivity issues. In this paper, we introduce MeshConv3D, a 3D mesh-dedicated methodology integrating specialized convolution and face collapse-based pooling operators. MeshConv3D operates directly on meshes of arbitrary topology, without any need of prior re-meshing/conversion techniques. In order to validate our approach, we have considered a semantic classification task. The experimental results obtained on three distinct benchmark datasets show that the proposed approach makes it possible to achieve equivalent or superior classification results, while minimizing the related memory footprint and computational load.

本研究解决了在处理三维数据（如点云和3D网格）时卷积神经网络（CNN）所面临的挑战，特别是如何重新定义卷积和池化算子以应对不规则连接性问题。我们提出了MeshConv3D，这是一种专为3D网格设计的方法，采用专门的卷积和基于面合并的池化算子，能够直接在任意拓扑的网格上操作。实验结果表明，该方法在语义分类任务上实现了等效或更优的分类结果，同时减少了内存占用和计算负担。

MeshConv3D：用于三角形 3D 网格的高效卷积和池化算子