# 3D Mesh Model Classification with a Capsule Network
## 1 Introduction
### Problem Description and Existing Work  
At present, the data formats of three-dimensional model recognition methods mainly include the voxel form, the point cloud form and the three-dimensional grid representation. For voxel representation, 3 DShapeNets [2] proposed by [PERSON] et al. and VoxNet [3] proposed by [PERSON] and [PERSON] et al. both directly learn on voxels and divide the space into regular cubes. However, due to the sparseness of voxel data, it introduces additional computational cost, which limits the method from being applied to complex datasets. FPNN [4] proposed by [PERSON] et al., Vote3D [5] proposed by [PERSON] and [PERSON] et al. and the Octtree-based convolutional neural network (OCNN) [6] proposed by [PERSON] et al. solve the problem of the sparseness of voxel data. Compared with two-dimensional convolution, the use of three-dimensional convolution adds a spatial dimension, the memory requirements become too large, and the entire method is limited by the size of the input data. For point cloud representation, due to the disorder of the point cloud data, the usual network framework is not suitable for a direct application of the point cloud data. [PERSON] et al. proposed PointNet [7] in 2017, which solved the problem through a symmetric function, but it ignored the point cloud local information. [PERSON] and others later proposed PointNet++ [8], an improved version of PointNet, which added an aggregation operation with neighbors to solve this problem. Because the point cloud data structure is too simple, for two compact nonconnected surfaces, the local surface cannot be distinguished simply by the Euclidean distance, so it cannot represent a complex model well. The mesh representation is a collection of points, faces, and edges, which are topologically combined through triangular patches, which can accurately express the neighborhood information of the points and has the natural advantage of expressing the complex surface of the object. However, the grid data are more complicated and the ordinary convolution operation cannot be directly applied to the mesh model, and there are currently few deep learning methods based on the mesh model. [PERSON], [PERSON] et al. proposed MeshCNN [9] in 2019 to define the convolution with an edge as the center of two triangles. The ratio of the dihedral angle, the inner angle, and the height of the triangle to the bottom edge is used as a five-dimensional feature vector, which is pooled by edge folding to apply the convolution network to the grid structure. [PERSON] et al. proposed Mesh-Net (2019) [10], taking triangular patches as the smallest unit; extracting its center point coordinates, normal vectors, neighborhood polygon index and other features; designing a convolutional neural network for classification; and achieving a recognition rate of 91.9% for the ModelNet40 data set. [PERSON] et al. proposed a mesh grid-based convolution framework PFCNN [11], which constructed a new translation structure by using multiple directions of parallel frame field to encode plane connections on the surface to ensure the translation of convolution. Degeneration is more accurate than surface-based CNN in terms of fine-scale feature learning. In 2020, [PERSON] et al. proposed the first method of grid pose conversion through style conversion [12], through spatial adaptive instance normalization (SPAdaIN) To simulate image pixels and mesh vertices. Learn the pose characteristics of each vertex in the source mesh and use the affine transformation learned from the target mesh vertices to transform it, thereby effectively transferring the pose of the source mesh to the target mesh [PERSON] et al.