Constrained sparse texture synthesis

This paper presents a novel texture synthesis algorithm that performs a sparse expansion of the patches of the image in a dictionary learned from an input exemplar. The synthesized texture is computed through the minimization of a non-convex energy that takes into account several constraints. Our first contribution is the computation of a sparse expansion of the patches imposing that the dictionary atoms are used in the same proportions as in the exemplar. This is crucial to enable a fair representation of the features of the input image during the synthesis process. Our second contribution is the use of additional penalty terms in the variational formulation to maintain the histogram and the low frequency content of the input. Lastly we introduce a non-linear reconstruction process that stitches together patches without introducing blur. Numerical results illustrate the importance of each of these contributions to achieve state of the art texture synthesis.