The staircasing effect in neighborhood filters and its solution

被引:164
|
作者
Buades, Antoni [1 ]
Coll, Bartomeu
Morel, Jean-Michel
机构
[1] Univ Balearic Isl, Palma de Mallorca 07122, Spain
[2] Ecole Normale Super, F-94235 Cachan, France
关键词
nonlinear filtering and enhancement; restoration;
D O I
10.1109/TIP.2006.871137
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
Many classical image denoising methods are based on a local averaging of the color, which increases the signat/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 differntial 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. 9 correction to the recently introduced NL-means algorithm which had the same staircase effect. for the same reason.
引用
收藏
页码:1499 / 1505
页数:7
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