NDLI: The staircasing effect in neighborhood filters and its solution

Content Provider	IEEE Xplore Digital Library
Author	Buades, A. Coll, B. Morel, J.-M.
Copyright Year	1992
Abstract	Many classical image denoising methods are based on a local averaging of the color, which increases the signal/noise ratio. One of the most used algorithms is the neighborhood filter by Yaroslavsky or sigma filter by Lee, also called in a variant "SUSAN" by Smith and Brady or "Bilateral filter" by Tomasi and Manduchi. These filters replace the actual value of the color at a point by an average of all values of points which are simultaneously close in space and in color. Unfortunately, these filters show a "staircase effect," that is, the creation in the image of flat regions separated by artifact boundaries. In this paper, we first explain the staircase effect by finding the subjacent partial differential equation (PDE) of the filter. We show that this ill-posed PDE is a variant of another famous image processing model, the Perona-Malik equation, which suffers the same artifacts. As we prove, a simple variant of the neighborhood filter solves the problem. We find the subjacent stable PDE of this variant. Finally, we apply the same correction to the recently introduced NL-means algorithm which had the same staircase effect, for the same reason.
Sponsorship	IEEE Signal Processing Society
Page Count	7
File Size	1632887
Starting Page	1499
Ending Page	1505
File Format	PDF
ISSN	10577149
Volume Number	15
Issue Number	6
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2006-06-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Image restoration Colored noise Low pass filters Nonlinear equations Image denoising Signal to noise ratio Image processing Filtering algorithms Digital filters Difference equations restoration Nonlinear filtering and enhancement
Content Type	Text
Resource Type	Article
Subject	Computer Graphics and Computer-Aided Design Software

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