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Herschel‐Bulkley diffusion filtering: non‐Newtonian fluid mechanics in image processing
Author(s) -
Frigaard I.A.,
Scherzer O.
Publication year - 2006
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200510256
Subject(s) - herschel–bulkley fluid , fluid mechanics , non newtonian fluid , mechanics , newtonian fluid , diffusion , geology , physics , classical mechanics , thermodynamics
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 4 k 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.