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.

本论文通过利用稀疏表示和最优传输，推导出一种新颖的针对稀疏字典的最优图像传输算法。通过将图像特征编码为稀疏表示并根据编码过程在两个学习字典之间推测最优传输计划，得到了一种简单而有效的同时图像表示和转换方法，可广泛应用于图像转换任务。

稀疏字典上的最优图像传输