In many unpaired image domain translation problems, e.g., style transfer or super-resolution, it is important to keep the translated image similar to its respective input image. We propose the extremal transport (ET) which is a mathematical formalization of the theoretically best possible unpaired translation between a pair of domains w.r.t. the given similarity function. Inspired by the recent advances in neural optimal transport (OT), we propose a scalable algorithm to approximate ET maps as a limit of partial OT maps. We test our algorithm on toy examples and on the unpaired image-to-image translation task. The code is publicly available at https://github.com/milenagazdieva/ExtremalNeuralOptimalTransport

翻译：在许多无配对图像域翻译问题（例如风格迁移或超分辨率）中，保持翻译后的图像与相应输入图像相似至关重要。我们提出了极端传输（Extremal Transport, ET），这是对给定相似函数下理论上最优的无配对域间翻译的数学形式化。受神经最优传输（Neural Optimal Transport, OT）最新进展的启发，我们提出了一种可扩展的算法，通过部分最优传输映射的极限来近似极端传输映射。我们在玩具示例和无配对图像到图像翻译任务上测试了该算法。代码已公开在 https://github.com/milenagazdieva/ExtremalNeuralOptimalTransport