A single 3D shape wavelet-based generative model

3D shape generation, vital in fields including computer graphics, industrial design, and robotics, has seen a significant growth due to deep learning advancements. Nevertheless, a prevailing challenge in this area lies in its heavy reliance on extensive data for training. Consequently, the ability to generate 3D shapes with a limited quantity of training samples emerges as a desirable objective. The aim of this research is to design deep generative models capable of learning from a single reference 3D shape, thereby eliminating the requirement for sizeable datasets. Drawing inspiration from contemporary Generative Adversarial Networks (GANs) that operate on individual 3D shapes in a coarse-to-fine manner hierarchically, we propose a novel wavelet-based framework for single 3D shape generation, which preserves the global shape structure whilst inducing local variability. Our key observation is that, through wavelet decomposition, the low-frequency components of two inputs, where one input is a corrupted version of the other, are very similar. This similarity enables reconstruction of the uncorrupted input by leveraging the low-frequency components of the corrupted version. This observation motivates us to propose the wavelet decomposition of the 2D tri-plane feature maps of a given 3D shape, followed by the synthesis of new tri-plane feature maps for shape generation. To the best of our knowledge, this work represents the first endeavor to incorporate wavelet analysis into a deep generative model for the purpose of generating novel 3D shapes with a single example. Furthermore, we adapt data augmentation and Coulomb adversarial generative loss to facilitate training and generation procedures. We demonstrate the effectiveness of our approach by generating diverse 3D shapes and conducting quantitative comparisons with established baseline methods. Our implementation is available at https://github.com/hhuang-code/SinWavelet.