Yavartanoo Mohsen ; Hung Shih-Hsuan ; Neshatavar Reyhaneh ; Zhang Yue ; Lee Kyoung Mu

Abstract

3D shape representation and its processing have substantial effects on 3Dshape recognition. The polygon mesh as a 3D shape representation has manyadvantages in computer graphics and geometry processing. However, there arestill some challenges for the existing deep neural network (DNN)-based methodson polygon mesh representation, such as handling the variations in the degreeand permutations of the vertices and their pairwise distances. To overcomethese challenges, we propose a DNN-based method (PolyNet) and a specificpolygon 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 asthe convolutional filters to share the weights across different vertices, and(2) a polygonal pooling (PolyPool) procedure by utilizing the multi-resolutionstructure of PolyShape to aggregate the features in a much lower dimension. Ourexperiments demonstrate the strength and the advantages of PolyNet on both 3Dshape classification and retrieval tasks compared to existing polygonmesh-based methods and its superiority in classifying graph representations ofimages. The code is publicly available fromhttps://myavartanoo.github.io/polynet/.