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.

在编码器 / 解码器框架下，我们提出了用于图像风格迁移的高斯最优输运方法。通过高斯测量的最优输运，可以从源分布到目标分布闭合形成 Monge 映射。此外，风格与内容图像的插值可以被视为 Wasserstein 几何中的测地线。使用这样的洞察力，我们展示了如何使用高斯测度的 Wasserstein barycenter 来混合不同的目标样式。我们的简单方法允许插入许多艺术风格之间的新样式化内容的生成。