On Robust Estimation and smoothing with Spatial and Tonal Kernels
P. Mräzek, Joachim Weickert, Andrés Bruhn · Kluwer Academic Publishers eBooks · 2006
This paper deals with establishing relations between a number of widely-used nonlinear filters for digital image processing. We cover robust statistical estimation with (local) M-estimators, local mode filtering in image or histogram space, bilateral filtering, nonlinear diffusion, and regularisation approaches. Although these methods originate in different mathematical theories, we show that their implementation reveals a highly similar structure. We demonstrate that all these methods can be cast into a unified framework of functional minimisation combining nonlocal data and nonlocal smoothness terms. This unification contributes to a better understanding of the individual methods, and it opens the way to new techniques combining the advantages of known filters. Keywords: image analysis, M-estimators, mode filtering, nonlinear diffusion, bilateral filter, regularisation