We propose an algorithm for efficiently minimizing the piecewise smooth Mumford-Shah functional. The algorithm is based on an extension of a recent primal-dual algorithm from convex to non-convex optimization problems. The key idea is to rewrite the proximal operator in the primal-dual algorithm using Moreau's identity. The resulting algorithm computes piecewise smooth approximations of color images at 15-20 frames per second at VGA resolution using GPU acceleration. Compared to convex relaxation approaches, it is orders of magnitude faster and does not require a discretization of color values. In contrast to the popular Ambrosio-Tortorelli approach, it naturally combines piecewise smooth and piecewise constant approximations, it does not require an epsilon approximation and it is not based on an alternation scheme. The achieved energies are in practice at most $5\%$ off the optimal value for one-dimensional problems. Numerous experiments demonstrate that the proposed algorithm is well-suited to perform discontinuity-preserving smoothing and real-time video cartooning.     «

We propose an algorithm for efficiently minimizing the piecewise smooth Mumford-Shah functional. The algorithm is based on an extension of a recent primal-dual algorithm from convex to non-convex optimization problems. The key idea is to rewrite the proximal operator in the primal-dual algorithm using Moreau's identity. The resulting algorithm computes piecewise smooth approximations of color images at 15-20 frames per second at VGA resolution using GPU acceleration. Compared to convex relaxatio...     »