Title :
The staircasing effect in neighborhood filters and its solution
Author :
Buades, Antoni ; Coll, Bartomeu ; Morel, Jean-Michel
Author_Institution :
Univ. de les Illes Baleares, Palma de Mallorca, Spain
fDate :
6/1/2006 12:00:00 AM
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.
Keywords :
filtering theory; image denoising; partial differential equations; Perona-Malik equation; bilateral filter; image denoising method; image processing model; neighborhood filters; partial differential equation; sigma filter; staircasing effect; Colored noise; Difference equations; Digital filters; Filtering algorithms; Image denoising; Image processing; Image restoration; Low pass filters; Nonlinear equations; Signal to noise ratio; Nonlinear filtering and enhancement; restoration; Algorithms; Artifacts; Artificial Intelligence; Filtration; Image Enhancement; Image Interpretation, Computer-Assisted; Imaging, Three-Dimensional; Information Storage and Retrieval; Reproducibility of Results; Sensitivity and Specificity; Signal Processing, Computer-Assisted;
Journal_Title :
Image Processing, IEEE Transactions on
DOI :
10.1109/TIP.2006.871137