Fuzzy Peer Groups for Reducing Mixed Gaussian-Impulse Noise From Color Images

Abstract

The peer group of an image pixel is a pixel similarity-based concept which has been successfully used to devise image denoising methods. However, since it is difficult to define the pixel similarity in a crisp way, we propose to represent this similarity in fuzzy terms. In this paper, we introduce the fuzzy peer group concept, which extends the peer group concept in the fuzzy setting. A fuzzy peer group will be defined as a fuzzy set that takes a peer group as support set and where the membership degree of each peer group member will be given by its fuzzy similarity with respect to the pixel under processing. The fuzzy peer group of each image pixel will be determined by means of a novel fuzzy logic-based procedure. We use the fuzzy peer group concept to design a two-step color image filter cascading a fuzzy rule-based switching impulse noise filter by a fuzzy average filtering over the fuzzy peer group. Both steps use the same fuzzy peer group, which leads to computational savings. The proposed filter is able to efficiently suppress both Gaussian noise and impulse noise, as well as mixed Gaussian-impulse noise. Experimental results are provided to show that the proposed filter achieves a promising performance.

Robust local similarity filter for the reduction of mixed Gaussian and impulsive noise in color digital images

“…f Vector median filter [1] Very often the mixed noise is being suppressed by applying first a filter suitable for the removal of impulsive and then the one intended for the reduction of Gaussian noise. However, such a scheme is not effective, as the consecutive application of two filters leads to significant image distortions and substantial increase in the computational burden [27].…”

“…Another approach to the problem of mixed noise reduction is based on the switching filtering [10,18,27], which detects the impulses and removes them using a suitable technique replacing the remaining samples with a filter designed for the Gaussian noise. Such procedure can be effective when the contamination is not severe; otherwise, the detection module fails to detect the impulses which are masked by the Gaussian noise.…”

“…An efficient family of filters is utilizing the concept of a peer group introduced in [5,11,41,42] and its fuzzy extensions [27,28], in which a combination of impulsive noise detection and a replacement scheme based on averaging is performed. Another group of filters relies on the concept of geodesic digital paths [8,25,26,51], which determines the connection cost between pixels belonging to the processing window used as weights in the averaging process.…”

A note on local bases and convergence in fuzzy metric spaces

“…An interesting aspect in this type of fuzzy metric is that it includes in its definition a parameter t. This feature has been successfully used in engineering applications such color image filtering [7,14,15] and perceptual color differences [5,13]. From the mathematical point of view it allows to introduce novel (fuzzy metric) concepts that only have natural sense in the fuzzy metric setting.…”

Adaptive rank weighted switching filter for impulsive noise removal in color images

“…In order to alleviate the problems caused by the blurring properties of the VMF and other filters utilizing the ordering scheme, a filtering method using the concept of a peer group was introduced in [71,72] and extensively used in various filtering designs [49,57,66,[73][74][75][76][77][78]. The peer group associated with the central pixel x i of a filtering window W i denotes the set of close pixels, whose distance to x i is not exceeding a given threshold.…”