This paper addresses the challenges of designing mesh convolution neural networks for 3D mesh dense prediction. While deep learning has achieved remarkable success in image dense prediction tasks, directly applying or extending these methods to irregular graph data, such as 3D surface meshes, is nontrivial due to the non-uniform element distribution and irregular connectivity in surface meshes which make it difficult to adapt downsampling, upsampling, and convolution operations. In addition, commonly used multiresolution networks require repeated high-to-low and then low-to-high processes to boost the performance of recovering rich, high-resolution representations. To address these challenges, this paper proposes a self-parameterization-based multi-resolution convolution network that extends existing image dense prediction architectures to 3D meshes. The novelty of our approach lies in two key aspects. First, we construct a multi-resolution mesh pyramid directly from the high-resolution input data and propose area-aware mesh downsampling/upsampling operations that use sequential bijective inter-surface mappings between different mesh resolutions. The inter-surface mapping redefines the mesh, rather than reshaping it, which thus avoids introducing unnecessary errors. Second, we maintain the high-resolution representation in the multi-resolution convolution network, enabling multi-scale fusions to exchange information across parallel multi-resolution subnetworks, rather than through connections of high-to-low resolution subnetworks in series. These features differentiate our approach from most existing mesh convolution networks and enable more accurate mesh dense predictions, which is confirmed in experiments.

本研究解决了3D网格密集预测中网格卷积神经网络设计的挑战，特别是如何处理不规则图数据的高低分辨率变换问题。提出的自参数化的多分辨率卷积网络，创新性地构建网格金字塔，并使用区域感知的网格下采样/上采样操作，从而提高了密集预测的准确性，实验结果证实了其有效性。

基于自参数化的多分辨率网格卷积网络