  Recently, enthusiastic studies have devoted to texture synthesis using deep
neural networks, because these networks excel at handling complex patterns in
images. In these models, second-order statistics, such as Gram matrix, are used
to describe textures. Despite the fact that these model have achieved promising
results, the structure of their parametric space is still unclear,
consequently, it is difficult to use them to mix textures. This paper addresses
the texture mixing problem by using a Gaussian scheme to interpolate deep
statistics computed from deep neural networks. More precisely, we first reveal
that the statistics used in existing deep models can be unified using a
stationary Gaussian scheme. We then present a novel algorithm to mix these
statistics by interpolating between Gaussian models using optimal transport. We
further apply our scheme to Neural Style Transfer, where we can create mixed
styles. The experiments demonstrate that our method can achieve
state-of-the-art results. Because all the computations are implemented in
closed forms, our mixing algorithm adds only negligible time to the original
texture synthesis procedure.
