# The staircasing effect in neighborhood filters and its solution

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 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.
Type de document :
Article dans une revue
IEEE Transactions on Image Processing, Institute of Electrical and Electronics Engineers, 2006, 15 (6), pp.1499-1505
Domaine :

https://hal.archives-ouvertes.fr/hal-00271143
Soumis le : jeudi 21 janvier 2010 - 13:30:26
Dernière modification le : jeudi 9 février 2017 - 15:34:38
Document(s) archivé(s) le : vendredi 21 mai 2010 - 01:29:05

### Fichier

double_revised.pdf
Fichiers produits par l'(les) auteur(s)

### Identifiants

• HAL Id : hal-00271143, version 1

### Citation

Antoni Buades, Bartomeu Coll, Jean-Michel Morel. The staircasing effect in neighborhood filters and its solution. IEEE Transactions on Image Processing, Institute of Electrical and Electronics Engineers, 2006, 15 (6), pp.1499-1505. <hal-00271143>

Consultations de
la notice

## 251

Téléchargements du document