edgefeatureextractionbasedondigitalimageprocessingtechniques-外文文献(编辑修改稿)

edgefeatureextractionbasedondigitalimageprocessingtechniques-外文文献(编辑修改稿)内容摘要：

22(/) (/)f xfy∂∂ +∂∂ . The vector with this direction and modulus is called as the gradient of the function f , that is, 39。 (, ) ( , )f ffxyxy∂∂∇=∂∂. So the gradient modulus operator is designed in the equation (2). 22[(,)] ( / ) ( / )Gfxy f x f y=∂∂ +∂∂ (2)For the digital image, the gradient template operator is designed as: 221/2[(,)] [ (,) (,)]xyGfij fij fij=Δ +Δ (3)Where ( , ) ( , ) ( 1, )xf ij fij fi jΔ=−−, (, ) (, ) (, 1)yfij fij fijΔ=−−. Differential operator mostly includes Roberts operator and Sobel operator. (1) Roberts operator Roberts operator is a kind of the most simple operator which makes use of partial difference operator to look for edge. Its effect is the best for the image with steep low noise. But the borderline of the extracted image is quite thick using the Roberts operator, so the edge location is not very accurate. Roberts operator is defined as: 221/2G[ ( , )] {[ ( 1, 1) ( , )][( 1,) (, 1)]}fxy fx y fxyfx y fxy=++− ++− + (4) But absolute deviation algorithm is usually used to predigest the equation (4) in practice. The following equations (5) and (6) are the process of reduction. [(,)] ( 1,) (,)(, 1) (, )Gf xy f x y f xyfxy fxy≈+−++− (5) [(,)] ( 1, 1) (,)(, 1) ( 1, )Gf xy f x y f xyfxy fx y≈++− ++− + (6) The template of the Roberts operator is shown in Fig. 3. Fig. 3 Roberts operator 2321 (2) Sobel and Prewitt operator To reduce the influence of noise when detecting edge, the Prewitt operator enlarges edge detection operator template from two by two to three by three to pute difference operator. Using the Prewitt operator can not only detect edge points, but also restrain the noise. The Sobel operator counts difference using weighted for 4 neighborhoods on the basis of the Prewitt operator. The Sobel operator has the similar function as the Prewitt operator, but the edge detected by the Sobel operator is wider. Suppose that the pixel number in the 3 3 subdomain of image is as follows: 0A1A 2A7A (, )f ij3A6A5A 4AWe order that012 654()()XAAA AAA=++−++ and 076 234()()Y AAA AAA=++−++. Then Prewitt operator is as follows: 221/2[(,)] ( )Gfij X Y=+ (7) Or [(,)]Gfij X Y=+ (8) Prewitt operator is said in in the form of the template. Fig. 4 Prewitt operator Sobel operator can process those images with lots of noises and gray gradient well. We order that 012 654(2 )(2 )XA AA A AA=++−++and076 234(2 )(2 )YA AA A AA=++−++. Then Sobel operator is as follows: 221/2[(,)] ( )Gfij X Y=+ (9) Or [(,)]Gfij X Y=+ (10)The template of the Sobel operator is shown in . Fig. 5 Sobel operator The original image of cable insulation layer and the edge detection drawing of Sobel operator gained using MatLab simulation are shown in Fig. 6 and Fig. 7. Fig. 6 the original image Fig. 7 the edge detection drawing of Sobel operator From the simulation drawing Fig. 7, we can know that the edge position is very accurate. And the effect of Sobel edge detection is very satisfying. In a word, the Sobel and Prewitt operators have a better effect for such images with grey level changing gradually and more noises. B. Log operator The Log operator is a linear and timeinvariant operator. It detects edge points through searching for spots which twoorder differential coefficient is zero in the image grey levels. For a continuous function ( , )f xy, the Log operator is defined as at pointK244。 x,yK245。 :22222f ffxy∂∂Δ= +∂∂ (11) The Log operator is the process of filtering and counting differential coefficient for the ima。