Adaptive Rest Condition Potentials: First and Second Order Edge-Preserving Regularization

A new regularization formulation for inverse problems in computer vision and image processing is introduced, which allows one to reconstruct second order piecewise smooth images, that is, images consisting of an assembly of regions with almost constant value, almost constant slope, or almost constant curvature. This formulation is based on the idea of using potential functions that correspond to springs or thin plates with an adaptive rest condition. Efficient algorithms for computing the solution and examples illustrating the performance of this scheme, compared with other known regularization schemes, are presented as well.