V. De Witte

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 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

A Fuzzy Noise Reduction Method for Color Images

A new fuzzy filter is presented for the reduction of additive noise for digital color images. The filter consists of two subfilters. The first subfilter computes fuzzy distances between the color components of the central pixel and its neighborhood. These distances determine in what degree each component should be corrected. All performed corrections preserve the color component distances. The goal of the second subfilter is to correct the pixels where the color components differences are corrupted so much that they appear as outliers in comparison to their environment. Experimental results show the feasibility of the proposed approach. We compare with other noise reduction methods by numerical measures and visual observations. We also illustrate the performance of the proposed method as preprocessing step for edge detection

Fuzzy Filters for Noise Reduction: The Case of Gaussian Noise

Noise reduction is a well-known problem in image processing. The reduction of noise in an image sometimes is as a goal itself, and sometimes is considered as a pre-processing step. Besides the classical filters for noise reduction, quite a lot of fuzzy inspired filters have been proposed during the past years. However, it is very difficult to judge the quality of this wide variety of filters. For which noise types are they designed? How do they perform for those noise types? How do they perform compared to each other? Can we select filters that clearly outperform the others? Is there a difference between numerical and visual results? In this paper, we answer these questions for images that are corrupted with Gaussian noise

A survey on the use and the construction of fuzzy similarity measures in image processing

Fuzzy techniques can be applied in several domains of image processing. In this paper we will give a survey on how fuzzy similarity measures can be used in establishing measures for image comparison. Objective quality measures or measures of comparison are of great importance in the field of image processing. These mea- sures serve as a tool to evaluate and to compare different algorithms designed to solve particular problems, such as noise reduction, de- blurring, compression, ... Consequently these measures serve as a basis on which one algorithm is preferred to another. Furthermore, it is well-known that classical quality measures, such as the RMSE (Root Mean Square Error) or the PSNR(Peak Signal to Noise Ra- tio), do not always correspond to visual observations.

Image similarity: from fuzzy sets to color image applications

Image similarity is an important topic in the field of image processing. The goal is to obtain objective measures that express the similarity between two images in a way that matches human evaluation. Such measures have both theoretical and practical applications. In this paper, we show how similarity measures for fuzzy sets have been modified in order to be applied in image processing. We also discuss a new application of these measures in the context of color image retrieval, indicating the potential of this class of similarity measures.

A New Fuzzy Filter for the Reduction of Randomly Valued Impulse Noise

In many current impulse noise models for images, corrupted pixels are replaced with values equal or near the maximum or minimum intensity values of the allowable dynamic range. In this paper, we present a new fuzzy filter for a more general noise model in which a noisy pixel has an arbitrary value in the dynamic range according to some underlying probability distribution. This filter consists of (1) a fuzzy detection method, where we investigate if a certain pixel position can be seen as noisy or not and (2) a fuzzy reduction method that reduces the noise while preserving the fine details (like edges and textures) of the image. Experimental results have shown that the proposed filter may be used for efficient removal of randomly valued impulse noise without distorting the useful information in the image.

Numerical Periodic Normalization for Codim 2 Bifurcations of Limit Cycles: Computational Formulas, Numerical Implementation, and Examples

Explicit computational formulas for the coefficients of the periodic normal forms for codimension 2 (codim 2) bifurcations of limit cycles in generic autonomous ODEs are derived. All cases (except the weak resonances) with no more than three Floquet multipliers on the unit circle are covered. The resulting formulas are independent of the dimension of the phase space and involve solutions of certain boundary-value problems on the interval (0 ,T ), where T is the period of the critical cycle, as well as multilinear functions from the Taylor expansion of the ODE right-hand side near the cycle. The formulas allow one to distinguish between various bifurcation scenarios near codim 2 bifurcations of limit cycles. Our formulation makes it possible to use robust numerical boundary- value algorithms based on orthogonal collocation, rather than shooting techniques, which greatly expands its applicability. The implementation is described in detail with numerical examples, where numerous codim 2 bifurcations of limit cycles are analyzed for the first time.

Colour Image Comparison Using Vector Operators

We constructed several new fuzzy similarity measures for greyscale images that outperform the classical measures of comparison, like root mean square error or peak signal to noise ratio, in the sense of image quality evaluation. In this paper we investigate the usefulness of similarity measures for the comparison of colour images. Instead of applying the similarity measures for greyscale images component-wise, we extend the similarity measures to colour images by applying vector morphological operators. We restrict ourselves to an investigation in the RGB colour space

Do fuzzy techniques offer an added value for noise reduction in images

In this paper we discuss an extensive comparative study of 38 different classical and fuzzy filters for noise reduction, both for impulse noise and gaussian noise. The goal of this study is twofold: (1) we want to select the filters that have a very good performance for a specific noise type of a specific strength; (2) we want to find out whether fuzzy filters offer an added value, i.e. whether fuzzy filters outperform classical filters. The first aspect is relevant since large comparative studies did not appear in the literature so far; the second aspect is relevant in the context of the use of fuzzy techniques in image processing in general.