  Arbitrary style transfer (AST) and domain generalization (DG) are important
yet challenging visual learning tasks, which can be cast as a feature
distribution matching problem. With the assumption of Gaussian feature
distribution, conventional feature distribution matching methods usually match
the mean and standard deviation of features. However, the feature distributions
of real-world data are usually much more complicated than Gaussian, which
cannot be accurately matched by using only the first-order and second-order
statistics, while it is computationally prohibitive to use high-order
statistics for distribution matching. In this work, we, for the first time to
our best knowledge, propose to perform Exact Feature Distribution Matching
(EFDM) by exactly matching the empirical Cumulative Distribution Functions
(eCDFs) of image features, which could be implemented by applying the Exact
Histogram Matching (EHM) in the image feature space. Particularly, a fast EHM
algorithm, named Sort-Matching, is employed to perform EFDM in a plug-and-play
manner with minimal cost. The effectiveness of our proposed EFDM method is
verified on a variety of AST and DG tasks, demonstrating new state-of-the-art
results. Codes are available at https://github.com/YBZh/EFDM.
