Applying convolution methods to domains that lack regular underlying structures is a challenging task for 3D vision. Existing methods require the manual design of feature representations suitable for the task or full-voxel-level analysis, which is memory intensive. In this paper, we propose a novel feature extraction method to facilitate 3D nonrigid shape analysis. Our approach, called 3D-MConv, extends convolution operations from regular grids to irregular mesh sets by parametrizing a series of convolutional templates and adopts a novel local perspective to ensure that the algorithm is more invariant against global isometric deformation and articulation. We carefully design the convolutional template as a polynomial function that flexibly represents the local shape. An unsupervised learning method is adopted to learn the convolutional template function. By using the convolution operation and the movement of the template on the model surface, we can obtain the distribution of the typical template shapes. We combine this distribution feature with the spatial co-occurrence information of typical template shapes modelled by Markov chains to form a high-level descriptor of a 3D model. The support vector machine method is used to classify the nonrigid 3D objects. Experiments on SHREC10 and SHREC15 demonstrate that 3D-MConv achieves state-of-the-art accuracy on standard benchmarks.

With the widespread success of deep learning in the two-dimensional field, how to apply deep learning methods from two-dimensional to three-dimensional field has become a current research hotspot. Among them, the polygon mesh structure in the three-dimensional representation as a complex data structure provides an effective shape approximate representation for the three-dimensional object. Although the traditional method can extract the characteristics of the three-dimensional object through the graphical method, it cannot be applied to more complex objects. However, due to the complexity and irregularity of the mesh data, it is difficult to directly apply convolutional neural networks to 3D mesh data processing. Considering this problem, we propose a deep learning method based on a capsule network to effectively classify mesh data. We first design a polynomial convolution template. Through a sliding operation similar to a two-dimensional image convolution window, we directly sample on the grid surface, and use the window sampling surface as the minimum unit of calculation. Because a high-order polynomial can effectively represent a surface, we fit the approximate shape of the surface through the polynomial, use the polynomial parameter as the shape feature of the surface, and add the center point coordinates and normal vector of the surface as the pose feature of the surface. The feature is used as the feature vector of the surface. At the same time, to solve the problem of the introduction of a large number of pooling layers in traditional convolutional neural networks, the capsule network is introduced. For the problem of nonuniform size of the input grid model, the capsule network attitude parameter learning method is improved by sharing the weight of the attitude matrix. The amount of model parameters is reduced, and the training efficiency of the 3D mesh model is further improved. The experiment is compared with the traditional method and the latest two methods on the SHREC15 data set. Compared with the MeshNet and MeshCNN, the average recognition accuracy in the original test set is improved by 3.4% and 2.1%, and the average after fusion of features the accuracy reaches 93.8%. At the same time, under the premise of short training time, this method can also achieve considerable recognition results through experimental verification. The three-dimensional mesh classification method proposed in this paper combines the advantages of graphics and deep learning methods, and effectively improves the classification effect of 3D mesh model.

Learning the relationship between the part and whole of an object, such as humans recognizing objects, is a challenging task. In this paper, we specifically design a novel neural network to explore the local-to-global cognition of 3D models and the aggregation of structural contextual features in 3D space, inspired by the recent success of Transformer in natural language processing (NLP) and impressive strides in image analysis tasks such as image classification and object detection. We build a 3D shape Transformer based on local shape representation, which provides relation learning between local patches on 3D mesh models. Similar to token (word) states in NLP, we propose local shape tokens to encode local geometric information. On this basis, we design a shape-Transformer-based capsule routing algorithm. By applying an iterative capsule routing algorithm, local shape information can be further aggregated into high-level capsules containing deeper contextual information so as to realize the cognition from the local to the whole. We performed classification tasks on the deformable 3D object data sets SHREC10 and SHREC15 and the large data set ModelNet40, and obtained profound results, which shows that our model has excellent performance in complex 3D model recognition and big data feature learning.

Multi-manifold clustering is among the most fundamental tasks in signal processing and machine learning. Although the existing multi-manifold clustering methods are quite powerful, learning the cluster number automatically from data is still a challenge. In this paper, a novel unsupervised generative clustering approach within the Bayesian nonparametric framework has been proposed. Specifically, our manifold method automatically selects the cluster number with a Dirichlet Process (DP) prior. Then, a DP-based mixture model with constrained Mixture of Gaussians (MoG) is constructed to handle the manifold data. Finally, we integrate our model with the k-nearest neighbor graph to capture the manifold geometric information. An efficient optimization algorithm has also been derived to do the model inference and optimization. Experimental results on synthetic datasets and real-world benchmark datasets exhibit the effectiveness of this new DP-based manifold method.