Manifold-valued image generation with Wasserstein generative adversarial nets

• Main Authors: HUANG, Zhiwu, WU J., VAN, G. L.
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2019
• Subjects: Benchmark datasets; Complete manifold; Data distribution; Hue saturation values; Image generations; Machine learning problem; Optimal transport; Wasserstein distance; Artificial Intelligence and Robotics; OS and Networks
• Online Access: https://ink.library.smu.edu.sg/sis_research/6546; https://ink.library.smu.edu.sg/context/sis_research/article/7549/viewcontent/Manifold_valued_image_generation_with_Wasserstein_generative_adversarial_nets.pdf
• Institution: Singapore Management University

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.