We propose a novel integral probability metric-based generative adversarial network (GAN), called SphereGAN. In the proposed scheme, the distance between two probability distributions (i.e., true and fake distributions) is measured on a hypersphere. Given that its hypersphere-based objective function computes the upper bound of the distance as a half arc, SphereGAN can be stably trained and can achieve a high convergence rate. In sphereGAN, higher-order information of data is processed using multiple geometric moments, thus improving the accuracy of the distance measurement and producing more realistic outcomes. Several properties of the proposed distance metric on the hypersphere are mathematically derived. The effectiveness of the proposed SphereGAN is demonstrated through quantitative and qualitative experiments for unsupervised image generation and 3D point cloud generation, demonstrating its superiority over state-of-the-art GANs with respect to accuracy and convergence on the CIFAR-10, STL-10, LSUN bedroom, and ShapeNet datasets.

中文翻译：

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SphereGAN：基于几何矩匹配的球面生成对抗网络及其应用

我们提出了一种新颖的基于积分概率度量的生成对抗网络 (GAN)，称为 SphereGAN。在所提出的方案中，两个概率分布（即真分布和假分布）之间的距离是在超球面上测量的。鉴于其基于超球面的目标函数将距离的上限计算为半圆弧，SphereGAN 可以稳定地训练并且可以实现较高的收敛速度。在 sphereGAN 中，使用多个几何矩处理数据的高阶信息，从而提高距离测量的准确性并产生更真实的结果。在超球面上提出的距离度量的几个属性是数学推导的。