Noise Reduction by Fuzzy Image Filtering
IEEE TRANSACTIONS ON FUZZY SYSTEMS, VOL. 11, NO. 4, AUGUST 2003
429
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 [1]. Fuzzy techniques have already been applied in several domains of image processing (e.g., filtering, interpolation [2], and morphology [3], [4]), and have numerous practical applications (e.g., in industrial and medical image processing [5], [6]). 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 [7]–[9], the weighted fuzzy mean filter from [10] and [11], and the
429
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 [1]. Fuzzy techniques have already been applied in several domains of image processing (e.g., filtering, interpolation [2], and morphology [3], [4]), and have numerous practical applications (e.g., in industrial and medical image processing [5], [6]). 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 [7]–[9], the weighted fuzzy mean filter from [10] and [11], and the