Mike Nachtegael

Noise reduction by fuzzy image filtering

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.

Fuzzy techniques in image processing

Vision in general and images in particular have always played an important and essential role in human life. Today, image processing is a very active research area with many applications. In order to cope with the wide variety of image processing problems, several techniques have been introduced and developed, quite often with great success. Among the different techniques that are currently in use, we also encounter fuzzy techniques. The use of fuzzy techniques in image processing is one of the main topics of the Fuzziness and Uncertainty Modelling Research Group of Prof. Kerre. In this paper, we briefly summarize some achievements of the past years.

A fuzzy impulse noise detection and reduction method

Removing or reducing impulse noise is a very active research area in image processing. In this paper we describe a new algorithm that is especially developed for reducing all kinds of impulse noise: fuzzy impulse noise detection and reduction method (FIDRM). It can also be applied to images having a mixture of impulse noise and other types of noise. The result is an image quasi without (or with very little) impulse noise so that other filters can be used afterwards. This nonlinear filtering technique contains two separated steps: an impulse noise detection step and a reduction step that preserves edge sharpness. Based on the concept of fuzzy gradient values, our detection method constructs a fuzzy set impulse noise. This fuzzy set is represented by a membership function that will be used by the filtering method, which is a fuzzy averaging of neighboring pixels. Experimental results show that FIDRM provides a significant improvement on other existing filters. FIDRM is not only very fast, but also very effective for reducing little as well as very high impulse noise.

Fuzzy random impulse noise reduction method

A new two-step fuzzy filter that adopts a fuzzy logic approach for the enhancement of images corrupted with impulse noise is presented in this paper. The filtering method (entitled as Fuzzy Random Impulse Noise Reduction method (FRINR)) consists of a fuzzy detection mechanism and a fuzzy filtering method to remove (random-valued) impulse noise from corrupted images. Based on the criteria of peak-signal-to-noise-ratio (PSNR) and subjective evaluations we have found experimentally, that the proposed method provides a significant improvement on other state-of-the-art methods.

Fuzzy Two-Step Filter for Impulse Noise Reduction From Color Images

A new framework for reducing impulse noise from digital color images is presented, in which a fuzzy detection phase is followed by an iterative fuzzy filtering technique. We call this filter the fuzzy two-step color filter. The fuzzy detection method is mainly based on the calculation of fuzzy gradient values and on fuzzy reasoning. This phase determines three separate membership functions that are passed to the filtering step. These membership functions will be used as a representation of the fuzzy set impulse noise (one function for each color component). Our proposed new fuzzy method is especially developed for reducing impulse noise from color images while preserving details and texture. Experiments show that the proposed filter can be used for efficient removal of impulse noise from color images without distorting the useful information in the image

Fuzzy Filters for Image Processing

1. Fuzzy Filters for Noise Removal.- 2. Fuzzy Filters for Noise Reduction in Images.- 3. Real-time Image Noise Cancellation Based on Fuzzy Similarity.- 4. Fuzzy Rule-Based Color Filtering Using Statistical Indices.- 5. Fuzzy Based Image Segmentation.- 6. Fuzzy Thresholding and Histogram Analysis.- 7. Color Image Segmentation by Analysis of 3D Histogram with Fuzzy Morphological Filters.- 8. Fast and Robust Fuzzy Edge Detection.- 9. Fuzzy Data Fusion for Multiple Cue Image and Video Segmentation.- 10. Fuzzy Image Enhancement in the Framework of Logarithmic Models.- 11. Observer-Dependent Image Enhancement.- 12. Fuzzy Techniques in Digital Image Processing and Shape Analysis.- 13. Adaptive Fuzzy Filters and Their Application to Online Maneuvering Target Tracking.- 14. Lossy Image Compression and Reconstruction Based on Fuzzy Relational Equation.- 15. Avoidance of Highlights through ILFOs in Automated Visual Inspection.- Appendix Color Images.

Connections between binary, gray-scale and fuzzy mathematical morphologies

Fuzzy mathematical morphology is an extension of binary morphology to gray-scale morphology, using techniques from fuzzy set theory. In this paper we will discuss several known and new approaches towards fuzzy morphology and show how they are connected, not only to each other, but also to binary and classical gray-scale morphology.

Classical and Fuzzy Approaches towards Mathematical Morphology

Fuzzy mathematical morphology is an alternative extension of binary morphology to gray-scale morphology, using techniques from fuzzy set theory. In this chapter we first review the basic definitions and properties of binary and classical gray-scale mathematical morphology. Next we present a general logical framework for fuzzy morphology. Finally, we give an extensive overview of other recent fuzzy approaches towards mathematical morphology, and show how they all fit into the general logical framework.

Fuzzy Random Impulse Noise Removal From Color Image Sequences

In this paper, a new fuzzy filter for the removal of random impulse noise in color video is presented. By working with different successive filtering steps, a very good tradeoff between detail preservation and noise removal is obtained. One strong filtering step that should remove all noise at once would inevitably also remove a considerable amount of detail. Therefore, the noise is filtered step by step. In each step, noisy pixels are detected by the help of fuzzy rules, which are very useful for the processing of human knowledge where linguistic variables are used. Pixels that are detected as noisy are filtered, the others remain unchanged. Filtering of detected pixels is done by blockmatching based on a noise adaptive mean absolute difference. The experiments show that the proposed method outperforms other state-of-the-art filters both visually and in terms of objective quality measures such as the mean absolute error (MAE), the peak-signal-to-noise ratio (PSNR) and the normalized color difference (NCD).

On the role of complete lattices in mathematical morphology: From tool to uncertainty model

Mathematical morphology has a rich history. Originally introduced for binary images, it was quite soon extended to grayscale images, leading to grayscale morphology with the threshold approach and the umbra approach. Later on, different models based on fuzzy set theory were introduced. These models were based on the observation that, from a formal point of view, grayscale images and fuzzy sets are modeled in the same way. Consequently, techniques from fuzzy set theory could be applied in the context of mathematical morphology, and fuzzy mathematical morphology was born. In that framework, fuzzy set theory was only a tool to construct morphological models, and was not employed to model any fuzziness or uncertainty. Quite recently however, new extensions have led to the construction of fuzzy interval-valued and fuzzy intuitionistic mathematical morphologies. Here, extensions of fuzzy set theory actually take into account the uncertainty that comes along with image capture, specifically regarding the grayscale values, which in some cases is also related to the uncertainty regarding the spatial position of an object in an image. In this framework, (extended) fuzzy set theory not only serves as a tool to deal with grayscale images, but also as a model for uncertainty. This paper sketches this evolution of fuzzy set theory in the field of mathematical morphology, and also points out some directions for future research.