Fundamental relationship between bilateral filtering, adaptive smoothing, and the nonlinear diffusion equation

In this paper, the relationship between bilateral filtering and anisotropic diffusion is examined. The bilateral filtering approach represents a large class of nonlinear digital image filters. We first explore the connection between anisotropic diffusion and adaptive smoothing, and then the connecti...

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Bibliographic Details
Published in:IEEE transactions on pattern analysis and machine intelligence 2002-06, Vol.24 (6), p.844-847
Main Author: Barash, D.
Format: Article
Language:English
Subjects:
Adaptive filters
Anisotropic magnetoresistance
Convolution
Diffusion
Digital
Digital filters
Digital images
Filtering
Filtration
Joints
Low pass filters
Mathematical analysis
Noise reduction
Nonlinear equations
Nonlinearity
Smoothing
Smoothing methods
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Summary:In this paper, the relationship between bilateral filtering and anisotropic diffusion is examined. The bilateral filtering approach represents a large class of nonlinear digital image filters. We first explore the connection between anisotropic diffusion and adaptive smoothing, and then the connection between adaptive smoothing and bilateral filtering. Previously, adaptive smoothing was considered to be an inconsistent approximation to the nonlinear diffusion equation. We extend adaptive smoothing to make it consistent, thus enabling a unified viewpoint that relates nonlinear digital image filters and the nonlinear diffusion equation.
ISSN:0162-8828
1939-3539
DOI:10.1109/TPAMI.2002.1008390