Universal style transfer tries to explicitly minimize the losses in feature space, thus it does not require training on any pre-defined styles. It usually uses different layers of VGG network as the encoders and trains several decoders to invert the features into images. Therefore, the effect of style transfer is achieved by feature transform. Although plenty of methods have been proposed, a theoretical analysis of feature transform is still missing. In this paper, we first propose a novel interpretation by treating it as the optimal transport problem. Then, we demonstrate the relations of our formulation with former works like Adaptive Instance Normalization (AdaIN) and Whitening and Coloring Transform (WCT). Finally, we derive a closed-form solution under our formulation by additionally considering the content loss of Gatys. Comparatively, our solution can preserve better structure and achieve visually pleasing results. It is simple yet effective and we demonstrate the advantages both quantitatively and qualitatively. Besides, we hope our theoretical analysis can inspire future works in neural style transfer.

通过将其视为最优输运问题（Optimal Transport Problem），我们提出了一种新颖的样式转移解释方法，并证明了与AdaIN和WCT之类的旧方法的关系，并在考虑了Gatys的内容损失后得出了闭合形式的最优样式转移（OST）解决方案。

通用风格转换的闭式解