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CHAPTER 5 EDGE DETECTION
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Exercises
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51 What is an edge How does it relate to the boundary of an object How does it relate to the boundary of a region 52 How can an edge be modeled in an image Which is the most commonly used model in edge detection Why 53 What is an isotropic edge detector How can you implement it 54 What is a directional edge detector How can you implement it Where will you use a directional edge detector Give edge detector masks for detecting edges oriented at 45 and -450 55 Name all the steps required in edge detection Can you implement an edge detector by skipping one or more of these steps How 56 Why is the Laplacian not a good edge operator 57 Describe the Laplacian of Gaussian edge detector Considering different steps in edge detection, show how the Laplacian is not a good edge operator, but the Laplacian of Gaussian is 58 How can you select the correct size of the operator in the LoG operators What factors should you consider in selecting the proper size of the operator Can you have an automatic selection algorithm 59 What is the facet model of an image How can you use it for edge detection Can you use this model for region growing also 510 Compare the Gaussian edge detector with the Laplacian of Gaussian Use all steps in edge detection and compare what the two operators do at these steps Where is the difference Do you think that their performances will differ significantly Explain clearly the difference and the effect of the difference in edge detection 511 Can edges be located at subpixel resolution How Is there any particular approach that will be more suitable for this Consider subpixel edge location estimation for the gradient, Laplacian, and facet models Compare the different estimation problems
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512 To select a particular edge detector in a machine vision application, we should know the comparative performance of edge detectors in the type of application that we are faced with How can we compare performance of various edge detectors in an objective manner List all important factors in edge detection and then define a performance measure that can be effectively evaluated 513 What is edge tracking What factors must be considered in edge tracking 514 The equation for the sloped planar facet model is obtained by setting all terms above k3 to zero, yielding
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The error in this approximation is given by
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= i=-l j=-l (k3i + k2j + k1- g[i,jJ)2 L L
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For the case 1 = 1, estimate the parameters k1, k2, and k3 for the sloped facet model that best approximates the gray levels in the 3 x 3 neighborhood given below
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-1 0 1
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5 7 9 3 7 7 j~1 1 3 5 What is the magnitude of the gradient 515 Suppose that an image is smoothed with an n x n Gaussian filter During smoothing, the square filter window is moved across the image The pixel at position [i,j] in the upper left corner of the window is replaced by the smoothed value After smoothing, the gradient magnitude is computed using the approximations in Section 51 As the 2 x 2 operators are moved across the smoothed image, the pixel at position [i,j]
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CHAPTER
5 EDGE DETECTION
in the upper left corner of the window is replaced by the gradient magnitude After edge detection, the edge location (Xij, Yij) for each edge pixel is computed to subpixel resolution Where is the edge location in the coordinate system of the original (unsmoothed) image
Computer
Projects
51 Implement the Roberts, Sobel, and Prewitt operators Apply these to various images Do you get edges where you expect them Manually identify several edge segments and note their locations Compare the locations of edge segments given by your program with manually marked edges Are you satisfied Can you improve your program to do better Change the threshold values for your detection step and see the results 52 Generate a synthetic image that contains one or more known objects with clear, known intensity discontinuities You should know the locations of these discontinuities precisely The rest of the image should be without edges Use any graphics technique or cut and paste using image processing programs Use this image to do systematic experiments with different edge detectors Apply the edge detector to the image and obtain all edges Define a measure to evaluate the performance of an edge detector and use that in all experiments What factors would you consider in defining the performance measure Repeat your experiment by adding noise You can systematically add random noise using a random number generator You may also want to systematically change the intensity values of the objects and background Change the threshold values for your detection step and see the results 53 Develop a test-bed to generate or acquire images for evaluating the performance measure that you defined in the above exercise Apply each edge detector that you studied in this chapter, and plot the performance of various edge detectors by varying the parameters controlling the quality of images These curves represent performance characteristics of edge detectors and may be useful in selecting a suitable edge detector for your application
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