Abstract
We propose Gaussian optimal transport for Image style transfer in an Encoder/Decoder framework. Optimal transport for Gaussian measures has closed forms Monge mappings from source to target distributions. Moreover interpolates between a content and a style image can be seen as geodesics in the Wasserstein Geometry. Using this insight, we show how to mix different target styles , using Wasserstein barycenter of Gaussian measures. Since Gaussians are closed under Wasserstein barycenter, this allows us a simple style transfer and style mixing and interpolation. Moreover we show how mixing different styles can be achieved using other geodesic metrics between gaussians such as the Fisher Rao metric, while the transport of the content to the new interpolate style is still performed with Gaussian OT maps. Our simple methodology allows to generate new stylized content interpolating between many artistic styles. The metric used in the interpolation results in different stylizations.
Abstract (translated)
我们提出高斯最优传输的图像风格传输在编码器/解码器框架。高斯度量的最优传输具有从源到目标分布的封闭映射形式。此外，内容和样式图像之间的内插可以在华瑟斯坦几何中视为测地线。利用这一洞察，我们展示了如何混合不同的目标风格，使用高斯度量的瓦瑟斯坦重心。由于高斯人在瓦瑟斯坦重心下是封闭的，这使得我们可以进行简单的风格转换、风格混合和插值。此外，我们还展示了如何在高斯坐标系（如Fisher-Rao坐标系）之间使用其他测地测量来实现混合不同的样式，而将内容传输到新的插值样式仍然使用高斯OT图。我们的简单方法可以在多种艺术风格之间生成新的风格化内容。插值中使用的度量标准会导致不同的样式。
URL
https://arxiv.org/abs/1905.12828
