Nonlocal Convex Functionals for Image Regularization

G. Gilboa, J. Darbon, S. Osher and T. Chan, Nonlocal Convex Functionals for Image Regularization. UCLA CAM Report 06-57


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 L1 energy of this type can be viewed as a nonlocal extension of total-variation. Thus we obtain non-local 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.