Edge-preserving image denoising and estimation of discontinuous surfaces

Abstract

In this paper, we are interested in the problem of estimating a discontinuous surface from noisy data. A novel procedure for this problem is proposed based on local linear kernel smoothing, in which local neighborhoods are adapted to the local smoothness of the surface measured by the observed data. The procedure can therefore remove noise correctly in continuity regions of the surface and preserve discontinuities at the same time. Since an image can be regarded as a surface of the image intensity function and such a surface has discontinuities at the outlines of objects, this procedure can be applied directly to image denoising. Numerical studies show that it works well in applications, compared to some existing procedures.

An adaptive window mechanism for image smoothing

“…Since only pixels adjacent to the center pixel are considered in averaging, iterations are needed to include larger neighborhoods in smoothing. Methods to find the weighted average of intensities within sliding windows while changing the weights according to differential [22,59] and statistical [32] measures have been proposed as well.…”

“…Qiu [46] estimates jump surfaces by local piecewise linear smoothing. Gijbels et al [22] uses a similar method but adapts the neighborhoods based on image gradients. Other discontinuity-preserving smoothing methods that are based on surface estimation are described by Stevenson and Delp [55] and Yi and Chelberg [63].…”

Smoothing and preservation of irregularities using local linear fitting

“…The estimation procedure is quite appealing due to its simplicity and its theoretical foundations. A generalization of the method to the case of estimation of non-smooth regression surfaces is given in Gijbels et al [11].…”

Computer-Aided Diagnosis for Acute Stroke in CT Images

“…The APMF has a characteristic: noise can be reduced without degrading signal, i.e., edge. In the field of image processing, various image filtering techniques for noise reduction have been reported (Russ, 1995;Tukey, 1971;Davis & Rosenfeld, 1978;Wu et al, 1992;Ehrich, 1978;Lev et al, 1977;Wang et al, 1981;Nagao & Matuyama, 1978;Zamperoni, 1990;Xu et al, 2004;Kuan et al 1985;Centeno & Haertel, 1997;Fischl & Shwarts, 1999;Westin et al, 2000;Schilham et al, 2006;Gijbels et al, 2006), and almost of them were edge-preserving smoothing techniques. The novel denoising technique, namely APMF, was compared to 14 conventional smoothing techniques by criterion-referenced performance study.…”