Non-negative Sparse Modeling of Textures

This paper presents a statistical model for textures that uses a non-negative decomposition on a set of local atoms learned from an exemplar. This model is described by the variances and kurtosis of the marginals of the decomposition of patches in the learned dictionary. A fast sampling algorithm allows to draw a typical image from this model. The resulting texture synthesis captures the geometric features of the original exemplar. To speed up synthesis and generate structures of various sizes, a multi-scale process is used. Applications to texture synthesis, image inpainting and texture segmentation are presented. 1 Statistical Models for Texture Synthesis The characterization of textures is a central topic in computer vision and graphics, mainly approached from a probabilistic point of view. Spatial domain modeling. The works of both Efros and Leung [1] and Wei and Levoy [2] pioneered a whole area of greedy approaches to texture synthesis. These methods copy pixels one by one, enforcing locally the consistence of the synthesized image with the exemplar. Recent approaches such as the method of Lefebvre and Hoppe [3] are fast, multiscale and give impressive results. Transformed domain modeling. Julesz [4] stated simple axioms about the probabilistic characterization of textures. A texture is described as a realization of a random process characterized by the marginals of responses to a set of linear filters. Zhu, Wu and Mumford [5] setup a Gibbs energy to learn both the filters and the marginals. They use a Gibbs sampler to draw textures from this model. A fast synthesis can be obtained by fixing the analyzing filters to be steerable wavelets as done by Heeger and Bergen [6]. The resulting textures are similar to those obtained by Perlin [7]. They exhibit isotropic cloud-like structures and fail to reproduce long range anisotropic features. This is because wavelets decompositions represent sparsely point wise singularities but do not compress enough long edge features. Higher order statistics such as local correlations are used by Portilla and Simoncelli [8] to synthesize high quality textures. Sparse image decompositions. Representing a complex image with few meaningful elements is at the core of the visual processing made by the human cortex. Atteneave [9] and Barlow [10] first stated that efficient high level computations should be performed over a representation of reduced complexity. This biological processing suggests a sparse description of a patches y ∈ R of N pixels extracted from a natural image as