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.
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