• International Journal of Fuzzy Logic and Intelligent Systems
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• v.3 no.1
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• pp.52-57
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• 2003

In this paper, we propose a Fuzzy Classifier System(FCS) to find a set of fuzzy rules which can carry out the edge detection. The classifier system of Holland can evaluate the usefulness of rules represented by classifiers with repeated learning. FCS makes the classifier system be able to carry out the mapping from continuous inputs to outputs. It is the FCS that applies the method of machine learning to the concept of fuzzy logic. It is that the antecedent and consequent of classifier is same as a fuzzy rule. In this paper, the FCS is the Michigan style. A single fuzzy if-then rule is coded as an individual. The average gray levels which each group of neighbor pixels has are represented into fuzzy set. Then a pixel is decided whether it is edge pixel or not using fuzzy if-then rules. Depending on the average of gray levels, a number of fuzzy rules can be activated, and each rules makes the output. These outputs are aggregated and defuzzified to take new gray value of the pixel. To evaluate this edge detection, we will compare the new gray level of a pixel with gray level obtained by the other edge detection method such as Sobel edge detection. This comparison provides a reinforcement signal for FCS which is reinforcement learning. Also the FCS employs the Genetic Algorithms to make new rules and modify rules when performance of the system needs to be improved.

• Journal of Information Processing Systems
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• v.9 no.4
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• pp.575-591
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• 2013

Most of the edge detection methods available in literature are gradient based, which further apply thresholding, to find the final edge map in an image. In this paper, we propose a novel method that is based on fuzzy logic for edge detection in gray images without using the gradient and thresholding. Fuzzy logic is a mathematical logic that attempts to solve problems by assigning values to an imprecise spectrum of data in order to arrive at the most accurate conclusion possible. Here, the fuzzy logic is used to conclude whether a pixel is an edge pixel or not. The proposed technique begins by fuzzifying the gray values of a pixel into two fuzzy variables, namely the black and the white. Fuzzy rules are defined to find the edge pixels in the fuzzified image. The resultant edge map may contain some extraneous edges, which are further removed from the edge map by separately examining the intermediate intensity range pixels. Finally, the edge map is improved by finding some left out edge pixels by defining a new membership function for the pixels that have their entire 8-neighbourhood pixels classified as white. We have compared our proposed method with some of the existing standard edge detector operators that are available in the literature on image processing. The quantitative analysis of the proposed method is given in terms of entropy value.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2001.12a
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• pp.283-286
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• 2001

Based on a fuzzy system representation of gray scale images, we derive an edge detection algorithm whose convolution kernel is different from the known kernels such as those of Roberts', Prewitt's or Sobel's gradient. Our fuzzy system representation is an exact representation of the bicubic spline function which represents the gray scale image approximately. Hence the fuzzy system is a continuous function and it provides a natural way to define the gradient and the Laplacian operator. We show that the gradient at grid points can be evaluated by taking the convolution of the image with a 3 3 kernel. We also show that our gradient coupled with the approximate value of the continuous function generates an edge detection method which creates edge images clearer than those by other methods. A few examples of applying our methods are included.

• Journal of the Korean Institute of Intelligent Systems
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• v.11 no.6
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• pp.454-458
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• 2001

Based on a fuzzy system representation of gray scale images, we derive and edge detection algorithm whose convolution kernel is different from the known kernels such as those of Robert's Prewitt's or Sobel's gradient. Our fuzzy system representation is an exact representation of the bicubic spline function which represents the gray scale image approximately. Hence the fuzzy system is a continuous function and it provides a natural way to define the gradient and the Laplacian operator. We show that the gradient at grid points can be evaluated by taking the convolution of the image with a 3$\times$3 kernel. We also that our gradient coupled with the approximate value of the continuous function generates an edge detection method which creates edge images clearer than those by other methods. A few examples of applying our methods are included.

• Journal of the Korean Institute of Intelligent Systems
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• v.10 no.3
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• pp.252-259
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• 2000

In this paper, we propose a Fuzzy Classifier System(FCS) to find a set of fuzzy rules which can carry out the edge detection of a image. The FCS is based on the fuzzy logic system combined with machine learning. Therefore the antecedent and consequent of a classifier in FCS are the same as those of a fuzzy rule. There are two different approaches, Michigan and Pittsburgh approaches, to acquire appropriate fuzzy rules by evolutionary computation. In this paper, we use the Michigan style in which a single fuzzy if-then rule is coded as an individual. Also the FCS employs the Genetic Algorithms to generate new rules and modify rules when performance of the system needs to be improved. The proposed method is evaluated by applying it to the edge detection of a gray-level image that is a pre-processing step of the computer vision. the differences of average gray-level of the each vertical/horizontal arrays of neighborhood pixels are represented into fuzzy sets, and then the center pixel is decided whether it is edge pixel or not using fuzzy if-then rules. We compare the resulting image with a conventional edge image obtained by the other edge detection method such as Sobel edge detection.

• IEIE Transactions on Smart Processing and Computing
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• v.3 no.6
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• pp.345-352
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• 2014

Edge detection considers the important technical details of digital image processing. Many edge detection operators already perform edge detection in digital color imaging. In this study, the edge of many real color images that represent the type of digital image was detected using a new operator in the least square approximation method, which is a type of numerical method. The Linear Fitting algorithm is computationally more expensive compared to the Canny, LoG, Sobel, Prewitt, HIS, Fuzzy, Parametric, Synthetic and Vector methods, and Robert' operators. The results showed that the new method can detect an edge in a digital color image with high efficiency compared to standard methods used for edge detection. In addition, the suggested operator is very useful for detecting the edge in a digital color image.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.31B no.6
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• pp.71-80
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• 1994

The purpose of this paper is to explore the use of fuzzy set theory for image processing and analysis. As an application example, the fuzzy method of edge detection is proposed to extract the edges of raised characters on tires.In general, Sobel, Prewitt, Robert and LoG filters are used to detect the edge, but it is difficult to detect the edge because of ambiguity of representations, noise and general problems in the interpretation of tire image. Therefore, in his paper, the fuzzy property plane has been extracted from the spatial domain using the ramp-mapping function. And then the ideas of fuzzy MIN and MAX are applied in removing noise and enhancement of the image simultaneously. From the result of MIN and MAX procedure a new fuzzy singleton is generated by extracting the difference between adjacent membership function values. And the edges are extracted by applying fuzzy $\alpha$-cut set to the fuzzy singletion, Finally, these ideas are applied to the tire images.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.7 no.3
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• pp.506-512
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• 2003

The edge detection has been so far under a lot of studies on its methods, as a very important part of image recognition. Never the less the correct detection of the edge has been yet a difficult problem because of the various scopes of detection according to the applied field. One of those problems to be solved is the edge detection in images with noise. This paper presents an efficient method which removes noise and detect edge in the same framework based on fuzzy logic. The method consists of two steps. First, an efficient filtering is applied to eliminate the noise from original image. The filtering is performed by utilizing fuzzy MIN-MAX operator in three directions such as vertical, horizontal and diagonal angle of 3${\times}$3 mask. Second, edges are detected by using extended fuzzy Shanon Function.

• The Transactions of the Korea Information Processing Society
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• v.5 no.9
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• pp.2447-2456
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• 1998

Edge detection in the presence of noise is a well-known problem. this pper atempts to implement edge detection algorithms using fuzzy reasoning of fuzzy membership models. It examines an application-motived approach for solving the problem. Our approach is divided into three stages; fitering, segmentation and tracing. Filtering removes the noise from the original image and segmentation determines the edges and deects them. Finally, tracing assembles the edges into the related structure. Proposed method can be used effectively on these procedures by using fuzzy reasoning based on fuzzy models. In is compared with the previous edge detectio algorithms with fvorable results. Simulation results of the research are presented and discussed.

• 제어로봇시스템학회:학술대회논문집
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• 2004.08a
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• pp.1315-1318
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• 2004

Based on fuzzy 2-mean classification and template matching method, we propose a new algorithm to detect the edges of an image. In the algorithm, fuzzy 2-mean classification can classify all pixels in the mask into two clusters whatever the mask in the dark or light region; and template matching not only determines the edge's direction, but also thins the detected edge by a set of inference rules and, by the way, reduces the impulse noises.