Generative modeling over natural images is one of the most fundamental
machine learning problems. However, few modern generative models, including
Wasserstein Generative Adversarial Nets (WGANs), are studied on manifold-valued
images that are frequently encountered in real-world applications. To fill the
gap, this paper first formulates the problem of generating manifold-valued
images and exploits three typical instances: hue-saturation-value (HSV) color
image generation, chromaticity-brightness (CB) color image generation, and
diffusion-tensor (DT) image generation. For the proposed generative modeling
problem, we then introduce a theorem of optimal transport to derive a new
Wasserstein distance of data distributions on complete manifolds, enabling us
to achieve a tractable objective under the WGAN framework. In addition, we
recommend three benchmark datasets that are CIFAR-10 HSV/CB color images,
ImageNet HSV/CB color images, UCL DT image datasets. On the three datasets, we
experimentally demonstrate the proposed manifold-aware WGAN model can generate
more plausible manifold-valued images than its competitors.

本文介绍了一种新的基于流型的生成模型，利用三个典型的例子：色相 - 饱和度 - 值（HSV）彩色图像生成、色度亮度（CB）彩色图像生成和扩散张量（DT）图像生成来生成流型值图像，并引入了一种最优输运定理，基于 WGAN 框架提出了一种新的 Wasserstein 距离度量，能够在三个基准数据集上生成比竞争对手更可信的流型值图像。