Point clouds are fundamental in the representation of 3D objects. However, they can also be highly unstructured and irregular. This makes it difficult to directly extend 2D generative models to three-dimensional space. In this article, we cast the problem of point cloud generation as a topological representation learning problem. In order to capture the representative features of 3D shapes in the latent space, we propose a hierarchical mixture model that integrates self-attention with an inference tree structure for constructing a point cloud generator. Based on this, we design a novel Generative Adversarial Network (GAN) architecture that is capable of generating recognizable point clouds in an unsupervised manner. The proposed adversarial framework (SG-GAN) relies on self-attention mechanism and Graph Convolution Network (GCN) to hierarchically infer the latent topology of 3D shapes. Embedding and transferring the global topology information in a tree framework allows our model to capture and enhance the structural connectivity. Furthermore, the proposed architecture endows our model with partially generating 3D structures. Finally, we propose two gradient penalty methods to stabilize the training of SG-GAN and overcome the possible mode collapse of GAN networks. To demonstrate the performance of our model, we present both quantitative and qualitative evaluations and show that SG-GAN is more efficient in training and it exceeds the state-of-the-art in 3D point cloud generation.

中文翻译：

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SG-GAN：用于点云拓扑零件生成的对抗性自注意力 GCN

点云是表示 3D 对象的基础。然而，它们也可以是高度非结构化和不规则的。这使得将 2D 生成模型直接扩展到 3D 空间变得困难。在本文中，我们将点云生成问题视为拓扑表示学习问题。为了捕捉潜在空间中 3D 形状的代表性特征，我们提出了一种分层混合模型，该模型将自注意力与推理树结构相结合，用于构建点云生成器。基于此，我们设计了一部小说生成对抗网络 (GAN) 架构，能够以无监督的方式生成可识别的点云。提出的对抗框架（SG-GAN）依赖于自我注意机制和图卷积网络 (GCN) 分层推断 3D 形状的潜在拓扑。在树形框架中嵌入和传输全局拓扑信息使我们的模型能够捕获和增强结构连接性。此外，所提出的架构使我们的模型能够部分生成 3D 结构。最后，我们提出了两种梯度惩罚方法来稳定 SG-GAN 的训练并克服 GAN 网络可能的模式崩溃。为了展示我们模型的性能，我们提出了定量和定性评估，并表明 SG-GAN 在训练中更有效，并且超过了 3D 点云生成的最新技术。