Texture Repairing by Unified Low Rank Optimization

In this paper, we show how to harness both low-rank and sparse structures in regular or near-regular textures for image completion. Our method is based on a unified formulation for both random and contiguous corruption. In addition to the low rank property of texture, the algorithm also uses the sparse assumption of the natural image: because the natural image is piecewise smooth, it is sparse in certain transformed domain (such as Fourier or wavelet transform). We combine low-rank and sparsity properties of the texture image together in the proposed algorithm. Our algorithm based on convex optimization can automatically and correctly repair the global structure of a corrupted texture, even without precise information about the regions to be completed. This algorithm integrates texture rectification and repairing into one optimization problem. Through extensive simulations, we show our method can complete and repair textures corrupted by errors with both random and contiguous supports better than existing low-rank matrix recovery methods. Our method demonstrates significant advantage over local patch based texture synthesis techniques in dealing with large corruption, non-uniform texture, and large perspective deformation.