# 3D Mesh Model Classification with a Capsule Network
## 1 Introduction
### Motivation and Contribution  
In order to overcome the above problems of CNN, [PERSON] et al. proposed a new algorithm called capsule network [16]. Routing replaces the maximum pooling down sampling in CNN, saves feature information of different dimensions, and reuses the output of some of these capsules to form a more stable high-order capsule representation [17], which better preserves the space of features information. At present, experiments have verified the advantages of capsule network compared with CNN in two-dimensional image classification [18]. In terms of application, [PERSON] et al. applied the capsule network based on binary classification to the detection of breast cancer [19]. [PERSON] et al. designed a capsule-based GAN [20]. [PERSON] et al. applied the capsule network to the text domain [21]. [PERSON] et al. applied the capsule network to digital media forensics [22].  
Recently, the capsule network has gradually been applied to the point cloud field to promote the development of computer graphics. Based on the combination of Euclidean, eigenvalues and geometrical space features, a dynamic capsule graph convolution network DCG-Net [23] was proposed. As the first method of using the capsule network architecture for point cloud edge detection, EDC-Net [24] is based on the extracted feature graph, by applying the attention module to the main capsule, and redesigning the loss function to obtain better results. Aiming at CNNs cannot sufficiently address the spatial relationship between features and require large amounts of data for training, the 3D point capsule networks [25] by [PERSON] and the method by [PERSON] [26] were proposed. They extended the capsule network to the three-dimensional field by 3D convolution and verified its effectiveness through experiments.  
These studies proved the effectiveness of the capsule network in many fields. However, due to the complex 3D mesh model data, no capsule network has been applied to 3D mesh processing, which prompted us to continue to develop a method for effective analysis of 3D mesh data.  
This paper proposes a three-dimensional mesh classification method based on capsule network, 3D Mesh Capsule Networks (MeshCaps), to expand the application field of capsule network. As the first method to apply capsule network to three-dimensional mesh structure, MeshCaps is similar to traditional multilayer neural networks can run directly on irregular grids, and can extract high-level features through a multilayer network structure.  
In MeshCaps, the mesh surface is convolved through the designed convolution template. Since the polynomial can effectively express a surface and the representation is more concise, the convolution kernel is designed as a high-order equation, and the polynomial fitting is used in the window. In the surface method, the high-order equation parameters are used as the local features of the window surface, which enables this method to deal with the complexity and irregular shape of the grid according to the surface unit.  
In addition, considering the inconsistency of the input size of the three-dimensional grid model, a capsule network that shares the weights of the pose matrix is introduced, and the concept of the capsule network is extended to the three-dimensional grid model. Based on these ideas, this paper designs a network structure in which is included a polynomial template convolution kernel used to learn feature descriptors of the patch unit and a capsule network used to aggregate and classify adjacent hidden layer features. Compared with the latest method MeshCNN based on edge folding for convolution pooling, it is expected that the improved capsule network will achieve better classification results under more expressive polynomial features.