Style transfer aims to render the content of a given image in the
graphical/artistic style of another image. The fundamental concept underlying
NeuralStyle Transfer (NST) is to interpret style as a distribution in the
feature space of a Convolutional Neural Network, such that a desired style can
be achieved by matching its feature distribution. We show that most current
implementations of that concept have important theoretical and practical
limitations, as they only partially align the feature distributions. We propose
a novel approach that matches the distributions more precisely, thus
reproducing the desired style more faithfully, while still being
computationally efficient. Specifically, we adapt the dual form of Central
Moment Discrepancy (CMD), as recently proposed for domain adaptation, to
minimize the difference between the target style and the feature distribution
of the output image. The dual interpretation of this metric explicitly matches
all higher-order centralized moments and is therefore a natural extension of
existing NST methods that only take into account the first and second moments.
Our experiments confirm that the strong theoretical properties also translate
to visually better style transfer, and better disentangle style from semantic
image content.

本文旨在提高图像风格迁移的实现效果，通过将卷积神经网络中的样式解释为分布，利用机器学习中的 Central Moment Discrepancy（CMD）方法来更精确地匹配目标样式和输出图像的特征分布，从而更加准确地还原所期望的风格，并改善样式与语义图像内容的区分效果。

基于特征分布：神经风格迁移的矩匹配方法

In the light of feature distributions: moment matching for Neural Style  Transfer

The learning of domain-invariant representations in the context of domain
adaptation with neural networks is considered. We propose a new regularization
method that minimizes the discrepancy between domain-specific latent feature
representations directly in the hidden activation space. Although some standard
distribution matching approaches exist that can be interpreted as the matching
of weighted sums of moments, e.g. Maximum Mean Discrepancy (MMD), an explicit
order-wise matching of higher order moments has not been considered before. We
propose to match the higher order central moments of probability distributions
by means of order-wise moment differences. Our model does not require
computationally expensive distance and kernel matrix computations. We utilize
the equivalent representation of probability distributions by moment sequences
to define a new distance function, called Central Moment Discrepancy (CMD). We
prove that CMD is a metric on the set of probability distributions on a compact
interval. We further prove that convergence of probability distributions on
compact intervals w.r.t. the new metric implies convergence in distribution of
the respective random variables. We test our approach on two different
benchmark data sets for object recognition (Office) and sentiment analysis of
product reviews (Amazon reviews). CMD achieves a new state-of-the-art
performance on most domain adaptation tasks of Office and outperforms networks
trained with MMD, Variational Fair Autoencoders and Domain Adversarial Neural
Networks on Amazon reviews. In addition, a post-hoc parameter sensitivity
analysis shows that the new approach is stable w.r.t. parameter changes in a
certain interval. The source code of the experiments is publicly available.

本研究提出了一种新的正则化方法，通过匹配概率分布的高阶中心矩的差异来学习域不变的特征表示，实现域自适应。结果表明，这种方法在两个不同的基准数据集上均取得了最新的性能，并显示出稳定性。