Nonlocal Convex Functionals for Image Regularization

. We examine weighted nonlocal convex functionals. The weights determine the affinities between different regions in the image and are computed according to image features. The L 1 energy of this type can be viewed as a nonlocal extension of total-variation. Thus we obtain nonlocal versions of ROF, TV-flow, Bregman iterations and inverse-scale-space (based on nonlocal ROF). Constructing the weights using patch distances, similarly to the nonlocal-means of Buades-Coll-Morel results in very robust and powerful regularizations. The flows and minimizations are computed efficiently by extending some recently proposed graph-cuts techniques. Numerical results which illustrate the performance of such models are presented.

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