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

Author

Barash, Danny

Author_Institution

Dept. of Chem. & the Courant Inst. of Math. Sci., New York Univ., NY, USA

Volume

24

Issue

6

fYear

2002

fDate

6/1/2002 12:00:00 AM

Firstpage

844

Lastpage

847

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 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

Keywords

adaptive signal processing; diffusion; digital filters; filtering theory; nonlinear equations; nonlinear filters; smoothing methods; spatial filters; adaptive smoothing; anisotropic diffusion; bilateral filtering; consistent approximation; denoising; nonlinear diffusion equation; nonlinear digital image filters; unified viewpoint; Adaptive filters; Anisotropic magnetoresistance; Convolution; Digital filters; Digital images; Filtering; Low pass filters; Noise reduction; Nonlinear equations; Smoothing methods;

fLanguage

English

Journal_Title

Pattern Analysis and Machine Intelligence, IEEE Transactions on

Publisher

ieee

ISSN

0162-8828

Type

jour

DOI

10.1109/TPAMI.2002.1008390

Filename

1008390