Neural texture synthesis and style transfer are both powered by the Gram matrix as a means to measure deep feature statistics. Despite its ubiquity, this second-order feature descriptor has several shortcomings resulting in visual artifacts, ill-defined interpolation, or inability to capture spatial constraints. Many previous works acknowledge these shortcomings but do not really explain why they occur. Fixing them is thus usually approached by adding new losses, which require parameter tuning and make the problem even more ill-defined, or architecturing complex and/or adversarial networks. In this paper, we propose a comprehensive study of these problems in the light of the multi-dimensional histograms of deep features. With the insights gained from our analysis, we show how to compute a well-defined and efficient textural loss based on histogram transformations. Our textural loss outperforms the Gram matrix in terms of quality, robustness, spatial control, and interpolation. It does not require additional learning or parameter tuning, and can be implemented in a few lines of code.

摘自一篇研究论文，介绍了使用卷积神经网络中的特征激活统计数据来计算文本损失的问题，Gram矩阵损失虽然是常见的这类问题的近似替代方法，但是有一些缺陷，提出了Sliced Wasserstein Distance作为一种优秀的替代方案，其具有理论证明、实用性、易于实现和对纹理合成及生成神经网络训练等方面有较好的效果。

神经材质合成的分割瓦瑟斯坦损失