A common viewpoint on broad kernel filtering and nonlinear diffusion

Using a consistent adaptive smoothing formulation we show that both nonlinear diffusion and adaptive smoothing can be extended to an arbitrary window, a process called broad kernel filtering. Based on this idea, this paper presents a unified treatment of a number of well known nonlinear techniques for filtering. We show that bilateral filtering represents a particular choice of weights in the extended diffusion process, that is obtained from geometrical considerations. We then show that kernel density estimation applied in the joint spatial-range domain yields a powerful processing paradigm - the mean shift procedure, related to bilateral filtering but having additional flexibility. This establishes an attractive relationship between the theory of statistics and that of diffusion and energy minimization. We experimentally compare the discussed methods and give insights on their performance.