The generation of 3D meshes is critical in numerous applications, evidenced by the growing popularity and attention towards interactive generative models. Although diffusion models currently stand out as powerful interactive generative models, they are confined to the 2D domain. Performing direct diffusion and denoising on complex 3D meshes with dense vertices and faces is impractical, time-consuming, and resource-intensive. In this work, we discretize the 3D space and incorporate the intricate 3D mesh topology within the Truncated-Signed Distance Fields (T-SDFs) of each discrete cell vertex and propose an efficient discrete index graph diffusion model for T-SDFs. We further divide T-SDFs into multiple local shapes and encode the complete object as a discretized 3D grid based on codebook indices, with each index labeled for its position to preserve its discretization while reducing the input dimensionality. A graph neural network is trained on these latent spaces to jointly denoise the diffusion process on continuous coordinates and discrete codebook indices to incorporate local and global information. As we delete the most frequently repeated codebook indices in the 3D grid, the input size of the diffusion model becomes variable. We employ diverse conditional embeddings from task-specific autoencoders to estimate the quantity of codebook indices in various 3D grids and achieve interactive conditional synthesis by utilizing classifier-free guidance to sample from diverse normal distributions. Our model exhibits exceptional generative performance, supported by experimental results showcasing its effectiveness in various generative tasks, including shape completion, single-view 3D generation, and text-driven generation.

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.

The principle of generative adversarial net is to fit the given data distribution by combining a generative model and discriminative model. There are two major challenges to conventional systems – they are difficult to train and they easily fall into ‘mode collapse’. To improve it, this study describes a novel network structure with dual generators. A ‘cooperation’ mechanism is introduced to help the generators work together. During training, generators not only learn from discriminative feedback but also from each other (like a study group). Compared with a single‐generator network, a dual‐generator network could capture many more ‘modes’ and eventually reduce the impact of ‘mode collapse.’ Dual networks also require extra computational resources. However, our experiment shows that even with network parameters of similar size, dual networks still achieved better results. Additionally, a dual‐generator structure could be extended to multiple generators. The proposed network structure is also very robust and flexible. It can be adapted to various application scenarios, such as high‐resolution image generation, domain adaptation and 3D model generation. The experimental results showed that with the same computing resources, multiple generators can generate better quality synthetic data, including 2D images, 3D objects, style transferring etc.

Spectral clustering is a popular tool in many unsupervised computer vision and machine learning tasks. Recently, due to the encouraging performance of deep neural networks, many conventional spectral clustering methods have been extended to the deep framework. Although these deep spectral clustering methods are quite powerful and effective, learning the cluster number from data is still a challenge. In this paper, we aim to tackle this problem by integrating the spectral clustering, generative adversarial network and low rank model within a unified Bayesian framework. First, we adapt the low rank method to the cluster number estimation problem. Then, an adversarial-learning-based deep clustering method is proposed and incorporated. When introducing the spectral clustering method into our model clustering procedure, a hidden space structure preservation term is proposed. Via a Bayesian framework, the structure preservation term is embedded into the generative process, which can then be used to deduce a spectral clustering in the optimization procedure. Finally, we derive a variational-inference-based method and embed it into the network optimization and learning procedure. Experiments on different datasets prove that our model has the cluster number estimation capability and show that our method can outperform many similar graph clustering methods.