Herschel-Bulkley diffusion filtering: non-Newtonian fluid mechanics in image processing

摘要

We consider certain nonlinear diffusion filters of TV-type, which have a physical analogy as a visco-plastic fluid model. By separating timescales and spatial scales of the image and noise, we develop an energy inequality that governs the evolution of the noise on a local sub-domain of 4k(2) pixels. Subtracting the local mean of the noise we derive an inequality that bounds the decay of the L-2 norm of the noise, minus its local mean. We thus produce estimates for the decay of the noise to its local mean. We show that the noise decays to its local mean in a finite time and give an expression for this stopping time. We show that our stopping time estimate is valid for a range of filter parameters and show how to properly select filter parameters in a consistent way. Finally, we show how the noise decay can be improved by making our filter parameters locally defined, according to the underlying image. (c) 2006 WILEY-VCH Verlag GmbH & Co. MA, Weinheim