Energy minimization methods

Abstract

Energy minimization methods are a very popular tool in image and signal processing. This chapter deals with images defined on a discrete finite set. The energies under consideration can be differentiable or not or convex or not. Analytical results on the minimizers of different energies are provided that reveal salient features of the images recovered in this way, as a function of the shape of the energy itself. An intrinsic mutual relationship between energy minimization and modeling via the choice of the energy is thus established. Examples and illustrations corroborate the presented results. Applications that take benefit from these results are presented as well.