Dietrich Van der Weken

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.

An overview of similarity measures for images

Fuzzy techniques can be applied in several domains of image processing. In this paper we will show how notions of fuzzy set theory are used in establishing measures for image quality evaluation. Objective quality measures or measures of comparison are of great importance in the field of image processing. Such measures are necessary for the evaluation and the comparison of different algorithms that are designed to solve a similar problem, and consequently they serve as a basis on which algorithm is preferred to the other. In this paper, we will show how similarity measures originally introduced to compare two fuzzy sets can be applied successfully in the domain of image processing.

Histogram-based fuzzy colour filter for image restoration

A new impulse noise reduction method for colour images, called histogram-based fuzzy colour filter (HFC), is presented in this paper. The HFC filter is particularly effective for reducing high-impulse noise in digital images while preserving edge sharpness. Colour images that are corrupted with noise are generally filtered by applying a greyscale algorithm on each colour component separately. This approach causes artefacts especially on edge or texture pixels. Vector-based filtering methods were successfully introduced to overcome this problem. In this paper, we discuss an alternative technique so that no artefacts are introduced. The main difference between the new proposed method and the classical vector-based methods is the usage of colour component differences for the detection of impulse noise and the preservation of the colour component differences. The construction of the HFC filter involves three steps: (1) the estimation of the original histogram of the colour component differences, (2) the construction of suitable fuzzy sets for representing the linguistic values of these differences and (3) the construction of fuzzy rules that determine the output. Extensive simulation results show that the proposed filter outperforms many well-known filters (including vector-based approaches).

Using similarity measures for histogram comparison

Objective quality measures or measures of comparison are of great importance in the field of image processing. Such measures are needed for the evaluation and the comparison of different algorithms that are designed to solve a similar problem, and consequently they serve as a basis on which one algorithm is preferred above the other. Similarity measures, originally introduced to compare two fuzzy sets, can be applied in different ways to images. In [2] we gave an overview of similarity measures which can be applied straightforward to images. In this paper, we will show how some similarity measures can be applied to normalized histograms of images.

Perceived image quality measurement of state-of-the-art noise reduction schemes

In this paper we compare the overall image quality of 7 state-of-the-art denoising schemes, based on human visual perception. A psycho-visual experiment was set up in which 37 subjects were asked to score and compare denoised images. A perceptual space is constructed from this experiment through multidimensional scaling (MDS) techniques using the perceived dissimilarity and quality preference between the images and the scaled perceptual attributes bluriness and artefacts. We found that a two-dimensional perceptual space adequately represents the processed images used in the experiment, and that the perceptual spaces obtained for all scenes are very similar. The interpretation of this space leads to a ranking of the filters in perceived overall image quality. We can show that the impairment vector, whose direction is opposite to that of the quality vector, lies between the attribute vectors for bluriness and artefacts, which on their account form an angle of about 35 degrees meaning they do interact. A follow-up experiment allowed us to determine even further why subjects preferred one filter over the other.

Vector morphological operators for colour images

In this paper we extend the basic morphological operators dilation and erosion for grey-scale images based on the threshold approach, umbra approach and fuzzy set theory to colour images. This is realised by treating colours as vectors and defining a new vector ordering so that new colour morphological operators are presented. Here we only discuss colours represented in the RGB colour space. The colour space RGB becomes together with the new ordering and associated minimum and maximum operators a complete chain. All this can be extended to the colour spaces HSV and L*a*b*. Experimental results show that our method provides an improvement on the component-based approach of morphological operators applied to colour images. The colours in the colour images are preserved, that is, no new colours are introduced.

Fuzzy Impulse Noise Reduction Methods for Color Images

The reduction or removal of noise in a color image is an essential part of image processing, whether the final information is used for human perception or for an automatic inspection and analysis. In addition to all the classical based filters for noise reduction, many fuzzy inspired filters have been developed during the past years [3–26]. However, it is very difficult to judge the quality of all these different filters. For which noise types are they designed? How do they perform compared to each other? Are there some filters that clearly outperform the others? Do the numerical results correspond with the visual results? In this paper we answer these questions for color images that are corrupted with impulse noise. We also have developed a Java Applet (http://www.fuzzy.ugent.be/Dortmund.html). The Java Applet is used to compare all the mentioned filters with each other. It illustrates the numerical and visual performance of all these filters. Users have the possibility to load and corrupt an image from a predefined list.

A New Similarity Measure for Image Processing

Objective quality measures or measures of comparison are of great importance in the field of image processing. These measures serve as a tool to evaluate and to compare different algorithms designed to solve problems, such as noise reduction, deblurring, compression ... Consequently these measures serve as a basis on which one algorithm is preferred to another. It is well-known that classical quality measures, such as the MSE (mean square error) or the PSNR (peak signal to noise ratio), not always correspond to visual observations. Therefore, several researchers are and have been looking for new quality measures, better adapted to human perception. The existing similarity measures are all pixel-based, and have therefore not always satisfactory results. To cope with this drawback, we propose a similarity measure based on a neigbourhood, so that the relevant structures of the images are observed very well. The new similarity measure is designed especially for the use in image processing.

Fuzzy Relational Images in Computer Science

Relations appear in many fields of mathematics and computer science. In classical mathematics these relations are usually crisp, i.e. two objects are related or they are not. However, many relations in real-world applications are intrinsically fuzzy, i.e. objects can be related to each other to a certain degree.With each fuzzy relation, different kinds of fuzzy relational images can be associated, all with a very practical interpretation in a wide range of application areas. In this paper we will explicite the formal link between well known direct and inverse images of fuzzy sets under fuzzy relations on one hand, and different kinds of compositions of fuzzy relations on the other. Continuing from this point of view we are also able to define a new scale of so-called double images. The wide applicability in mathematics and computer science of all these fuzzy relational images is illustrated with several examples.

Evaluation of the perceptual performance of fuzzy image quality measures

In this paper we present a comparison of fuzzy instrumental image quality measures versus experimental psycho-visual data. A psycho-visual experiment we recently performed at our departments was used to collect data on human visual perception. The Multi-Dimensional Scaling (MDS) framework was applied in order to test which of our fuzzy image similarity measures correlates best to this human visual perception. Based on Spearmans Rank Order Correlation coefficient we will show that the M