Manifold-valued Image Generation with Wasserstein Generative Adversarial Nets
This work addresses a gap in generative modeling for manifold-valued images, which is important for applications like medical imaging and color processing, but it is incremental as it extends existing WGAN methods to new data types.
The paper tackles the problem of generating manifold-valued images, which are common in real-world applications but underexplored in generative modeling, by formulating the problem for instances like HSV, CB, and DT images and deriving a new Wasserstein distance for complete manifolds, resulting in a model that generates more plausible images than competitors on benchmark datasets.
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.