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Variational models in connection with convex analysis, relaxation methods, problem decomposition and numerical optimization pervade current research activities in mathematical imaging and vision. This special issue contains a series of papers presenting corresponding progress. The intricate problem of jointly estimating stereo disparity and illumination variation is considered in the paper “A Parallel Proximal Splitting Method for Disparity Estimation from Multicomponent Images Under Illumination Variation” (doi:10.1007/s10851-012-0361-z). This initially non-convex problem is tackled by a first order Taylor approximation and solving a sequence of convex problems. Additionally, the paper demonstrates the application of an advanced decomposition technique that enables the parallel implementation of the numerical optimization algorithm on GPUs. Authors of the paper “A Variational Framework for Region-Based Segmentation Incorporating Physical Noise

Guest Editorial: Variational Models, Convex Analysis and Numerical Optimization in Mathematical Imaging