We present an extended Mumford-Shah regularization for blind image deconvolution and segmentation in the context of Bayesian estimation for blurred, noisy images or video sequences. The Mumford-Shah functional is extended to have cost terms for the estimation of blur kernels via a newly introduced prior solution space. This functional is minimized using Γ-convergence approximation in an embedded alternating minimization within Neumann conditions. Accurate blur identification is the basis of edge-preserving image restoration in the extended Mumford-Shah regularization. One output of the finite set of curves and object boundaries are grouped and partitioned via a graph theoretical approach for the segmentation of blurred objects. The chosen regularization parameters using the L-curve method is presented.
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