and thus match only the mean and variance (to obtain the statistical match) following by training a CNN to approximate the multivariate Gaussian CDF and do the inverse mapping.

Although it is faster, the CNN learning of the inverse CDF as in [@johnson2016; @ulyanov2016] dramatically limits the number of transferable styles, making the concept ineffective as domain adaptation method. The Gaussian matching [@huang2017], while being able to transfer an infinity of styles, still imposes two approximations that have an effect on the final image quality. Concluding, the original neural style transfer [@Gatys:2015] remains the most viable candidate for domain adaptation between the photographic image domain and the paintings domain.

Comparison Between Neural and Laplacian Transfers
-------------------------------------------------

While the Laplacian and Neural style transfer are built on different paradigms (neural vs. non-neural), we stress that the two methods share similar concepts. First, let us note that the pooling paradigm from the CNN is similar with the downsampling used in the Laplacian pyramid. Noting that the best results for the neural style transfer are achieved using a VGG-19 architecture, this implies an input image of $224\times 224$; the VGG-19 has 4 pooling layers between convolutional layers, thus offering a 5 level pyramidal 