3D shape representation and its processing have substantial effects on 3D shape recognition. The polygon mesh as a 3D shape representation has many advantages in computer graphics and geometry processing. However, there are still some challenges for the existing deep neural network (DNN)-based methods on polygon mesh representation, such as handling the variations in the degree and permutations of the vertices and their pairwise distances. To overcome these challenges, we propose a DNN-based method (PolyNet) and a specific polygon mesh representation (PolyShape) with a multi-resolution structure. PolyNet contains two operations; (1) a polynomial convolution (PolyConv) operation with learnable coefficients, which learns continuous distributions as the convolutional filters to share the weights across different vertices, and (2) a polygonal pooling (PolyPool) procedure by utilizing the multi-resolution structure of PolyShape to aggregate the features in a much lower dimension. Our experiments demonstrate the strength and the advantages of PolyNet on both 3D shape classification and retrieval tasks compared to existing polygon mesh-based methods and its superiority in classifying graph representations of images. The code is publicly available from https://myavartanoo.github.io/polynet/.

翻译：3D 形状代表及其处理对立体形状识别有重大影响。三维形状代表面作为三维形状代表面在计算机图形和几何处理方面有许多优势。然而,基于多边网代表面的现有深神经网络(DNN)方法仍然存在一些挑战,如处理脊椎程度和分布的变化及其对称距离等。为了克服这些挑战,我们建议采用基于DNN(PollyNet)的多分辨率方法(PollyShape)和具有多分辨率结构的特定的多边网网(PollyShape)代表面(PollyShape),它包含两个操作; (1) 多面网(Polly Convolution)(Polly Convolution)操作具有可学习的系数,它学习作为共振过滤器的连续分布,以分享不同脊椎的重量。 (2) 多边网(PollyPashape)的多分辨率结构(PollyNet)程序,以更低的维度汇总特征。我们的实验展示了3D形状分类和检索任务与现有多边网图像的强度和优势。在现有的多边网/Megramamamam 上,这是用于公共图解/smagravial的图解/smal。