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

Danny Barash

doi:10.1109/TPAMI.2002.1008390

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

Danny Barash

Research output: Contribution to journal › Article › peer-review

454 Scopus citations

Abstract

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 an inconsistent approximation to the nonlinear diffusion equation. We extend adaptive smoothing to make it consistent, thus enabling a unified viewpoint that relates between nonlinear digital image filters and the nonlinear diffusion equation.

Original language	English
Pages (from-to)	844-847
Number of pages	4
Journal	IEEE Transactions on Pattern Analysis and Machine Intelligence
Volume	24
Issue number	6
DOIs	https://doi.org/10.1109/TPAMI.2002.1008390
State	Published - 1 Jun 2002
Externally published	Yes

Keywords

Adaptive smoothing
Anisotropic diffusion
Bilateral filtering
Denoising

ASJC Scopus subject areas

Software
Computer Vision and Pattern Recognition
Computational Theory and Mathematics
Artificial Intelligence
Applied Mathematics

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10.1109/TPAMI.2002.1008390

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abstract = "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 an inconsistent approximation to the nonlinear diffusion equation. We extend adaptive smoothing to make it consistent, thus enabling a unified viewpoint that relates between nonlinear digital image filters and the nonlinear diffusion equation.",

keywords = "Adaptive smoothing, Anisotropic diffusion, Bilateral filtering, Denoising",

author = "Danny Barash",

note = "Funding Information: This research is jointly supported by the National Science and Technology Board and Ministry of Education, Singapore, under research grant R-252-000-071-112/303.",

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N2 - 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 an inconsistent approximation to the nonlinear diffusion equation. We extend adaptive smoothing to make it consistent, thus enabling a unified viewpoint that relates between nonlinear digital image filters and the nonlinear diffusion equation.

AB - 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 an inconsistent approximation to the nonlinear diffusion equation. We extend adaptive smoothing to make it consistent, thus enabling a unified viewpoint that relates between nonlinear digital image filters and the nonlinear diffusion equation.

KW - Adaptive smoothing

KW - Anisotropic diffusion

KW - Bilateral filtering

KW - Denoising

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

Abstract

Keywords

ASJC Scopus subject areas

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