Joint prior models of Mumford-Shah regularization for blur identification and segmentation in video sequences

We study a regularized Mumford-Shah functional in the context of joint prior models for blur identification, blind image deconvolution and segmentation. For the ill-posed regularization problem, it is hard to find a good initial value for ensuring the soundness of the convergent value. A newly introduced prior solution space of point spread functions in a double regularized Bayesian estimation can satisfy such demands. The Mumford-Shah functional is formulated using Gamma-convergence approximation and is minimized by projecting iterations onto an alternating minimization within Neumann conditions. The pre-estimated priors support the Mumford-Shah functional to decrease of the complexity of computation and improve the restoration results simultaneously. Moreover, segmentation of blurred objects is more difficult. A graph-theoretic approach is used to group edges which driven from the Mumford-Shah functional. Blurred objects with lower gradients and objects with stronger gradients are grouped separately. Numerical experiments show that the proposed algorithm is robust and efficiency in that it can handle images that are formed in different environments with different types and amounts of blur and noise.