彩色图像边缘检测Color Edge Detection in Presence of Gaussian Noise.docx

1、彩色图像边缘检测Color Edge Detection in Presence of Gaussian Noise Color Edge Detection in Presence of Gaussian Noise Using Nonlinear Pre-filtering Abstract: A new way for edge detection in color images disturbed by Gaussian noise ispresented. This paper proposed a method which uses a multi-pass processing

2、methodthat reduces the noise in the color image. The main idea for this paper is that adopt twodifferent pre-filtering that aim at avoiding false edges produced by noise and atpreserving the image details during noise removal. After doing that we need design analgorithm for edge detection which aims

3、 at decreasing the sensitivity to noise of theoverall method so that we can successfully accurate edge maps even encounter highlycorrupted data. According to the simulation and data, we can find the proposed methodfor noise images are quite good.Key Word: edge detection, fuzzy systems, Gaussian nois

4、e, image processing, nonlinearfilters.INTRODUCTIONEdge detection is a measure which plays a very important role in the realization of acomplete image understanding system (Like image segmentation and object recognitionare all depends on the quality of the edge detection). Compared with gray scale pi

5、cture,color image has richer measurement information that can improve the quality of theimage and extend its range. However, edge detection will encounter some trouble whenimage has some noise like Gaussian. There are some methods focuse on monochromepictures like Sobel technique to the three image

6、channels. Actually Sobels edge point inthe color image could be estimated by evaluating the maximum of the gradientcomponents sum so that it can yield an accurate edge map. Some methods like Differencevector (DV) method using gradient-based algorithms which is very sensitive to noise hasa good perfo

7、rmance to the edge detection. But these methods are limited, especially whenthe image data are highly corrupted, the result will become very annoying so we neednew method to solve this problem. New method which uses multi-pass processing aims atreducing noise before extracting the image edges. Combi

8、ning pre-filtering scheme withalgorithm for edge detection which not only improve the increase the accuracy of theedge detection but also consider the noise smoothing and spatial resolution. So thefollows will show the methodology and the result. MethodologyPre-filtering for edge detectionFirst we n

9、eed know pre-filtering for edge detection is based on the different kinds ofnoisy pixels:Type A pixels: pixels corrupted by noise with amplitude not too different from that of theneighbors.Type B pixels: pixels corrupted by noise with amplitude much larger than that of theneighbors.Fig1 Block diagra

10、m of the multi-pass processing( p)We deal with digitized multichannel RGB images. x denote the Multi-channel image atthe pass, and the x denotes the input noisy image, xk means where the R (red), G(0)(green), and B (blue) channels are respectively, denoted by k=1,k=2, k=3. Put themtogether which con

11、struct this diagram. In this method, we use 24-bit color image. So wehave L=256.Fig 2 color division Here we need mention that here we use type A pre-filtering twice which aims to increasethe effectiveness of the smoothing action.The proposed multi-pass processing involves the following operations:T

12、ype A Pre-filtering:Differences between the pixel to be deal with and its neighbors as below:Small differences are supposed noise to be reduced; large differences are supposed edgesto be preserved.The procedure is defined by the following relationship:181811 x(1)k(i, j) = xk(0)(i, j)+(i, j)+(1)(xkk(

13、0)(i + m, j + n), xk(0)(i, j)(i, j)m=-1 n=-111 x(2)k(i, j) = xk(1)(2)(xkk(1)(i + m, j + n), xk(1)m=-1 n=-1Where k is a parameterized nonlinear function. Let k( p)(i, j) be a constant pixel( p)xvalue, 0 xk (i, j) L -1 at location i , j.( p)This formula means we put the noise image into the type A pre

14、-filtering and Let x(n) bethe pixel luminance at location n=n1, n2 and the pixels processed combine with itsneighbor construct 3*3 window. With this model which shows below we can useparameterized nonlinear function to achieve the smoothing action and excludes the valuesthat are very different from

15、the central element, in order to avoid detail blur during noisecancellation.Fig 3 3*3 windowThe ( p)kparameterized nonlinear function procedure shows as follow:k( p)(u,v) = u-v|u-v | a( p)kWhere u represents the neighbor and v denoted the central pixel. With this value which means the neighbor are q

16、uite close to the central pixel. So the filterperforms the arithmetic mean of the pixel luminance in the neighborhood, thusrealizing the maximum smoothing action.k( p)(u,v) = 0|u -v | 3a( p)kIn this form which means the neighbor is quite difference with the central pixel the filterbehaves as the ide

17、ntity filter, thus performing the maximum detail preservation.(u,v) = (3ak( p)-u + v)sgm(u - v)( p)kak( p) u - v | 3ak( p)|2Intermediate situations are processed as a compromise between these opposite effects.( p)According to the formula, we find that the behavior depends on the value of ak . In ord

18、erto get the optimal value, we use the automatic parameter tuning to get the best value.Fig 4 Automatic parameter tuning. ( p)Here we use P instead of ak , and the k is equal to the initial p value. Here p is from 2 toL/4, each image has its own p value, using this tuning procedure we can get the va

19、lue. Whywe choose MSE? Because it is conceptually simple and widely used, follow the steps everytime, through different k1 and k2 we can get the optimal value and do the second tuningprocedure. After getting the p value we can use it to do the smoothing action.This is the result for type A pre-filte

20、ring:Fig. 5 Gaussian noise image and noise image with type A pre-filteringAccording to the image, we can find that the noise image with type A pre-filteringmake the image more smoothing and leave the outlier for type B pre-filtering to dealwith. Type B pre-filtering:Actually type B pre-filtering foc

21、us on the outlier, we know outlier present in the data as aneffect of the tail of Gaussian distribution the effect can become very annoying Type B pre-filtering considers the differences between the pixel to be processed and its neighbors in adifferent way: if all these differences are very large, t

22、he pixel is an outlier to be cancelled. Itis briefly summarized as follows.LA(u,v) denotes the membership function that describes the fuzzy relation: “ u is muchlarger than v ” and the formula shows below:Using these three formulas can achieve the goal which outlier can be removed by this way.We can

23、 see the result shows below:Fig 6 image after filter A and image after filter B If we add pepper and salt noise to original image and see how type B works.Because pepper and salt noise belong to type B noise, type B filter should have a very goodperformance.Fig 7 pepper and salt filteringAccording t

24、o the Fig 6 and 7 we can find that use the type B pre-filtering which can removethe outlier successfully but actually it still not noise free. However we can still declare thismethod is quite good. Noise-protected edge detectorEven though the nonlinear pre-filtering significantly reduces the Gaussia

25、n noise, accordingto the image which shows before the image data are not noise-free. Thus, an edge detectorwith very low sensitivity to noise is necessary. We use the follow relationship to do thedetection:y(i, j) = (L-1)1- MINSM (B1),SM (B2)Suitable choices are:S1 =x(3)(i -1, j -1), x(i -1, j -1),

26、x(i, j), x (i, j +1), x (i +1, j), A1, A2(3)(3)(i -1, j), x (i -1, j +1)(3)S2 =x(3)(3)(3)(i, j -1), x (i +1, j -1)S1 =x(3)(3)SMis the membership function of fuzzy set “small,” symbol |denotes the Euclideandistance, Sh is the set of NhWhere b1 and b2 are integer parameters. Smaller values perform a s

27、tronger activation of theoperator in the presence of image edges at the price of an increase of the sensitivity tonoise, so the choosing of this two values also need to be considered in our experiment.Typically b1=5, 30 b2 60, in this experiment I choose b1 =5, b2 =40.The edge detection procedure ai

28、ms at representing object contours as bright lines in theresulting edge map. Conversely, uniform regions are represented as dark areas.It is known that accurate detection of edges in noisy data should satisfied two requirements:(1) The edge detection process should avoid false edges produced by nois

29、e(2) Ensure that actual edges are correctly detected.We will do summation by gray and color image to show how our edge detector worksWe can see the result shows below: Fig 8 Summation by gray imageFig 9 Summation by color image Fig 10 Summation by lena imageAccording to the Fig 8, 9 and 10 we can fi

30、nd that by using multichannel, color image has abetter pre-filtering and edge detection result, because that color image has 3 channels butgray image only has 1 channel, so that type A filter will have a better performance whendeal with color image. We can declare our method is quite good.We will al

31、so show the edge detection result when image id corrupted by pepper and saltnoise. The result shows below:Fig 11 ED of pepper and salt noisy image According to the figure 11, we can get a very good edge detection result by using type Bfilter, it almost remove all superimposing impulse noise (salt and pepper noise). The threemain parts of our method: multichannel, type A filter, type B f