Noise Reduction by Fuzzy Image Filtering
Dimitri Van De Ville, Member, IEEE, Mike Nachtegael, Dietrich Van der Weken, Etienne E. Kerre, Wilfried Philips, Member, IEEE, and Ignace Lemahieu, Senior Member, IEEE
Abstract—A new fuzzy filter is presented for the noise reduction of images corrupted with additive noise. The filter consists of two stages. The first stage computes a fuzzy derivative for eight different directions. The second stage uses these fuzzy derivatives to perform fuzzy smoothing by weighting the contributions of neighboring pixel values. Both stages are based on fuzzy rules which make use of membership functions. The filter can be applied iteratively to effectively reduce heavy noise. In particular, the shape of the membership functions is adapted according to the remaining noise level after each iteration, making use of the distribution of the homogeneity in the image. A statistical model for the noise distribution can be incorporated to relate the homogeneity to the adaptation scheme of the membership functions. Experimental results are obtained to show the feasibility of the proposed approach. These results are also compared to other filters by numerical measures and visual inspection. Index Terms—Additive noise, edge preserving filtering, fuzzy image filtering, noise reduction.
I. INTRODUCTION HE application of fuzzy techniques in image processing is a promising research field . Fuzzy techniques have already been applied in several domains of image processing (e.g., filtering, interpolation , and morphology , ), and have numerous practical applications (e.g., in industrial and medical image processing , ). In this paper, we will focus on fuzzy techniques for image filtering. Already several fuzzy filters for noise reduction have been developed, e.g., the well-known FIRE-filter from –, the weighted fuzzy mean filter from  and , and the iterative fuzzy control based filter from . Most fuzzy techniques in image noise reduction mainly deal with fat-tailed noise like impulse noise. These fuzzy filters are able to outperform rank-order filter schemes (such as the median filter). Nevertheless, most fuzzy techniques are not specifically designed for Gaussian(-like) noise or do not produce convincing results when applied to handle this type of noise.
Therefore, this paper presents a new technique for filtering narrow-tailed and medium narrow-tailed noise by a fuzzy filter. Two important features are presented: first, the filter estimates a “fuzzy derivative” in order to be less sensitive to local variations due to image structures such as edges; second, the membership functions are adapted accordingly to the noise level to perform “fuzzy smoothing.” The construction of the fuzzy filter is explained in Section II. For each pixel that is processed, the first stage computes a fuzzy derivative. Second, a set of 16 fuzzy rules is fired to determine a correction term. These rules make use of the fuzzy derivative as input. Fuzzy sets are employed to represent the properties , , and . While the membership funcand are fixed, the membership tions for is adapted after each iteration. The adaptafunction for tion scheme is extensively explained in Section III and can be combined with a statistical model for the noise. In Section IV, we present several experimental results. These results are discussed in detail, and are compared to those obtained by other filters. Some final conclusions are drawn in Section V. II. FUZZY FILTER The general idea behind the filter is to average a pixel using other pixel values from its neighborhood, but simultaneously to take care of important image structures such as edges.1 The main concern of the proposed filter is to distinguish between local variations due to noise and due to image structure. In order to accomplish this, for each pixel we derive a value that expresses...