Variational pairing of image segmentation and blind restoration

Segmentation and blind restoration are both classical problems, that are known to be difficult and have attracted major research efforts. This paper shows that the two problems are tightly coupled and can be successfully solved, together. Mutual support of the segmentation and blind restoration processes within a joint variational framework is theoretically motivated, and validated by successful experimental results. The proposed variational method integrates Mumford-Shah segmentation with parametric blur-kernel recovery and image deconvolution. The functional is formulated using the Γ-convergence approximation and is iteratively optimized via the alternate minimization method. While the major novelty of this work is in the unified solution of the segmentation and blind restoration problems, the important special case of known blur is also considered and promising results are obtained.