This article introduces a new model for patch-based texture synthesis that controls the distribution of patches in the synthesized texture. The proposed approach relies on an optimal assignment of patches over decimated pixel grids. This assignment problem formulates the synthesis as the minimization of a discrepancy measure between input's and output's patches through their optimal permutation. The resulting non-convex optimization problem is addressed with an iterative algorithm alternating between a patch assignment step and a patch aggregation step. We show that this model statistically constrains the output texture content , while inheriting the structure-preserving property of patch-based methods. We also propose a relaxed patch assignment extension that increases the robustness to non-stationnary textures.
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