The adaptive-rest condition spring system: an edge-preserving regularization technique

In the last decade, several authors have proposed edge preserving regularization (EPR) methods for solving ill posed problems in image processing and computer vision. These EPR techniques are based on the minimization of non-quadratic and in some cases non-convex energy functionals. We introduce a new EPR technique that corresponds to an adaptive-rest condition spring system, meaning that at those places where we want an homogeneous smoothing, the rest condition of the springs is close to zero (as a homogeneous spring system), whereas at edges, the rest condition is equal to the size of the corresponding jump.