In this paper, we derive a novel optimal image transport algorithm over sparse dictionaries by taking advantage of Sparse Representation (SR) and Optimal Transport (OT). Concisely, we design a unified optimization framework in which the individual image features (color, textures, styles, etc.) are encoded using sparse representation compactly, and an optimal transport plan is then inferred between two learned dictionaries in accordance with the encoding process. This paradigm gives rise to a simple but effective way for simultaneous image representation and transformation, which is also empirically solvable because of the moderate size of sparse coding and optimal transport sub-problems. We demonstrate its versatility and many benefits to different image-to-image translation tasks, in particular image color transform and artistic style transfer, and show the plausible results for photo-realistic transferred effects.

翻译：本文利用稀疏表示与最优传输理论，提出了一种基于稀疏字典的创新型最优图像传输算法。具体而言，我们构建了一个统一的优化框架：首先通过稀疏表示对图像特征（颜色、纹理、风格等）进行紧凑编码，随后根据编码过程在两个学习到的字典之间推导出最优传输方案。该范式为同步实现图像表示与变换提供了一种简洁而有效的途径，且由于稀疏编码与最优传输子问题规模适中，该算法具备实证可解性。我们通过图像颜色变换和艺术风格迁移等多种图像到图像翻译任务，验证了该方法的普适性与显著优势，并展示了可生成照片级真实感迁移效果的合理结果。