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.
It is worth noticing that not all texture models are able to mix textures. e.g. in the prominent work of Portilla and Simoncelli's @cite_3 , they mentioned that the parametric space of their model is not convex, because linear interpolation of statistics will result in poor quality (patchwise) results. Even the state-of-the-art texture model proposed by Gatys al @cite_0 suffered from the similar problem, as linear interpolation of Gram matrices only results in similar pathwise mixture @cite_44 .
@cite_0 @cite_44 @cite_3
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Here we introduce a new model of natural textures based on the feature spaces of convolutional neural networks optimised for object recognition. Samples from the model are of high perceptual quality demonstrating the generative power of neural networks trained in a purely discriminative fashion. Within the model, textures are represented by the correlations between feature maps in several layers of the network. We show that across layers the texture representations increasingly capture the statistical properties of natural images while making object information more and more explicit. The model provides a new tool to generate stimuli for neuroscience and might offer insights into the deep representations learned by convolutional neural networks. We present a universal statistical model for texture images in the context of an overcomplete complex wavelet transform. The model is parameterized by a set of statistics computed on pairs of coefficients corresponding to basis functions at adjacent spatial locations, orientations, and scales. We develop an efficient algorithm for synthesizing random images subject to these constraints, by iteratively projecting onto the set of images satisfying each constraint, and we use this to test the perceptual validity of the model. In particular, we demonstrate the necessity of subgroups of the parameter set by showing examples of texture synthesis that fail when those parameters are removed from the set. We also demonstrate the power of our model by successfully synthesizing examples drawn from a diverse collection of artificial and natural textures.