Modified Fuzzy Linear Discriminant Analysis for Threshold Selection
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Modified Fuzzy Linear Discriminant Analysis for Threshold Selection Yinggan Tang · Weiwei Mu · Xiumei Zhang · Yixian Yang
Received: 2 February 2012 / Revised: 31 July 2012 / Published online: 21 August 2012 © Springer Science+Business Media, LLC 2012
Abstract Otsu’s thresholding method is a popular and efficient method for image segmentation. However, its performance is greatly affected by noise and the population size of object and background. In this paper, a novel thresholding method is proposed based on modified fuzzy linear discriminant analysis (MFLDA). MFLDA is an extension of linear discriminant analysis to fuzzy domain, where the between-class variance is modified as the distance between the centers of background and object. The optimal threshold is selected such that the MFLDA criterion is maximized. Some images are used to test the performance of the proposed thresholding method and results reveal that the proposed method is less affected by noise, the population size of objects and background, and better segmentation results are obtained than Otsu’s method and other classical thresholding methods. Keywords Image segmentation · Thresholding · Linear discriminant analysis · Fuzzy Y. Tang () · W. Mu Institute of Electrical Engineering, Yanshan University, Qinhuangdao, Hebei 066004, China e-mail: [email protected] W. Mu e-mail: [email protected] Y. Tang National Engineering Research Center for Equipment and Technology of Cold Strip Rolling, Qinhuangdao, Hebei 066004, China X. Zhang Qian’An College, Hebei United University, Tangshan, Hebei 064400, China e-mail: [email protected] Y. Yang Information Security Center, Beijing University of Posts and Telecommunications, Beijing 100876, China e-mail: [email protected]
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Circuits Syst Signal Process (2013) 32:711–726
1 Introduction The main purpose of image segmentation is to extract interested objects from original image according to certain similarity criterion. It is not only an important step in image processing but also the foundation of the lower computer vision. Image segmentation finds many applications in various image-processing applications such as object tracking [22], character recognition [17], document analysis [20], visual inspection of defects [19, 24], etc.. Thresholding is a popular tool for image segmentation due to its simpleness. It separates an image into several classes through comparing the value of gray level of the image with selected threshold. The pixel is classified into the first class if its value of gray level is smaller than the selected threshold, otherwise, it is classified into the second class. For the purpose of selecting a good threshold, thresholding methods make two assumptions [11]. One is that the objects can be parted from the background according to the value of gray level. The other is that the histogram of an image has two obvious peaks and a deep steep valley among the peaks. If an appropriate threshold is selected, good segmentation results can be obtained; otherwise, poor results are obtained. In the pas
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