1、1 A new fuzzy edge detection algorithm Sun Wei Xia Lianzheng ( Department of Automatic Control Engineering,SoutheastUniversity,Nanjing,210096,China) Abstract： Based upon the maximum entropy theorem of information theory, a novel fuzzy approach for edge detection is presented .Firstly, a definition o
2、f fuzzy partition entropy is proposed after introducing the concept of fuzzy probability and fuzzy partition, The relation of the probability partition and the fuzzy c-partition of the image gradient are used in the algorithm。Secondly, based on the conditional probabilities and the fury partition, t
3、he optimal thresholdingis searchedadaptively through the maximum fuzzy entropy principle, and then the edge image is obtained。 Lastly, an edge-enhancing procedure is executed on the edge image .The experimental results show that the proposed approach performs well。 Key words:edge detection ；fuzzy en
4、tropy ；image segmentation ；fuzzy partition Image segmentation is an important topic for image analysis, computer vision and patternrecognition .Until now, many classical edge detection algorithms have been put forward .In recent years, fuzzy set theory has been successfully applied to many areas, su
5、ch as automation control, image processing, pattern recognition and computer vision, etc .It is generally believed that image processing bears some fuzziness innature due to the following factors: Information loss while mapping 3-D objects into 2-D images； Ambiguity and vagueness in some definitions
6、 (such asedges, boundaries, regions, and textures, etc.)； Ambiguity and vagueness in interpreting low-level image processing results .Therefore, fuzzy techniqueshave frequently been used in image segmentation. Jin Lizuo .et a1. proposed a new definition of fuzzy partition entropy using the condition
7、al probability and conditional entropy, and designed a new thresholding selection algorithm based on the maximum fuzzy entropy .This paper extends the application of the work to the problem of the edge detection and presents a new fuzzy edge detection algorithm .In the algorithm, a gradient image is
8、 considered as being composed of an edge region and a smooth region .Based on the conditional probability and the fuzzy partition entropy, the optimal thresholding is searched adaptively through maximum fuzzy entropy principle .There are two major differences between the problems of the edge detecti
9、on and the image thresholding segmentation .First, theproblem is actually reduced to a two-level thresholding problem, where the purpose of thresholding is to 2 partition the image into two regions :an edge region anda smooth region .Second， in order to find the best compact representation of the im
10、age edges and contours, the gradient image is processed.The experimental results show the effectiveness of the algorithm. The rest of this paper is organized as follows .In section 1,we briefly outline the concept of fuzzy probability and fuzzy partition entropy .In section 2,we describe the fuzzy e
11、dge detection algorithm, In section 3,the experimental results and conclusions are presented. 2.4 Edge detection Let the edge image be ( , )exy ,then calculate it as 2 0 0 ( , )( , ) 0 ( , )i f g x y Te x y f g x y T (1) Spurious or weak edges(intensity discontinuities)may result in the image edge r
12、epresentation due tomany factorsamong them are noise and breaks in theboundary between two regions due to non uniform illumination .In this section, e introduce a simple yeteffective procedure for removing spurious or weakedges .The procedure is as follows: 1)Run a 33 pixel window on the edge image
13、.where the center of the window imposed on each location (x, y)； 2)Sum the number of points which have beenclassified as edge in the window, if the number isgreater than four, leave these edge points, else theyrepresent weak or spurious edges. 3) Experimental Results and conclusions In this section,
14、 the experiments on various kinds of images have been carried out with proposed method .The three original images areselected andshown in Figs.2 4.Fig.2 is an airplane image .The size of which is 212200 pixe1.The membershipfunction parameters set(a,b)= (5,157)and theimage thresholding is 81.Fig.3 is
15、 a baboon image, thesize of which is 202200 pixe1.The membershipfunctions parameter set(a, b) = (6,164)and theimage thresholding is 85.Fig.4 is a Lena image, thesize of which is 212208 pixe1.The membershipfunction parameters set(a, b)= (3,147)and theimage thresholding is 75. 3 In this paper, we comb
16、ine conditional probabilitywith fuzzy maximum entropy to introduce a new fuzzyedge detection algorithm. The experimental resu1tsshow that this algorithm performs well. It is verified that segmentationmethods, which combine fuzzystatistics. are suitable fortheoryfurther research. 作者： 孙伟 夏良正 国籍： 中国 出处：东南大学学报 (英文版 ).第二期 .卷 20.2003.
