1. 240-373: Chapter 8: Edge Detection 1 Montri Karnjanadecha montri@coe.psu.ac.th http://fivedots.coe.psu. ac.th/~montri 240-373 Image Processing

2. 240-373: Chapter 8: Edge Detection 2 Chapter 8 Edge Detection

3. 240-373: Chapter 8: Edge Detection 3 Basic Edge Detection Edge detection, ideally, identifies all the lines that outline the objects in an image. Template for edge detection: Y_difference(x,y) = value(x,y) - value(x,y+1) This is equivalent to convolving with image with a 2x1 template 1

4. 240-373: Chapter 8: Edge Detection 4 Basic Edge Detection X_difference(x,y) = value(x,y) - value(x-1,y) use the template -1 1 –Once X_difference and Y_difference are computed to create the single measurement of “gradient magnitude” (strength of the edge)

5. 240-373: Chapter 8: Edge Detection 5 Basic Edge Detection –It is also useful to divide Y_difference by X_difference and identify a gradient direction (the angle of the edge between the regions)

6. 240-373: Chapter 8: Edge Detection 6 Example Image X_difference Y_difference Gradient Direction 1 1 1 1 1 0 0 0 0 * 0 0 0 0 0 * * * * * 1 1 1 1 1 0 0 0 0 * 0 0 0 1 1 * * * 1 1 1 0 0 0 0 -1 0 * 0 0 1 0 0 * * * * 1 1 0 0 0 0 -1 0 0 * 0 0 0 0 0 * * * * 1 1 0 0 0 0 -1 0 0 * * * * * * * * * *

7. 240-373: Chapter 8: Edge Detection 7 Example Technique 4: Sobel edge detection The Sobel 3 x 3 templates are normally given as X-directionY-direction -1 0 1 1 2 1 -2 0 2 0 0 0 -1 0 1-1 -2 -1

8. 240-373: Chapter 8: Edge Detection 8 Example Image abs A + abs B Threshold at 12

9. 240-373: Chapter 8: Edge Detection 9

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12. 240-373: Chapter 8: Edge Detection 12 Second-order edge detection An image such as The basic Sobel vertical edge operator yields

13. 240-373: Chapter 8: Edge Detection 13 Second-order edge detection Applying the edge operator again yields This is similar to the differentiation operator applied to a straight line, e.g. if y = 3x - 2, then

14. 240-373: Chapter 8: Edge Detection 14 Second-order edge detection Laplacian template –can reduce gradient of lighting –enhances noise

15. 240-373: Chapter 8: Edge Detection 15 Pyramid Edge Detection Technique 5: Pyramid edge detection USE: To enhance substantial (strong and long) edges but to ignore the weak or short edges THEORY: –The image is cut down to quarter –Each pixel in the quarter-size image is an average of the four corresponding pixels in the full-size image

16. 240-373: Chapter 8: Edge Detection 16 Pyramid Edge Detection THEORY: (cont’d) –This repeats until unwanted edges are invisible –An edge detector is applied to the smallest image and where edge pixels have been found, an edge detector is applied to the corresponding four pixels in the next largest image

17. 240-373: Chapter 8: Edge Detection 17 Pyramid Edge Detection OPERATION: –Create a second image of size m/2 x n/2 by evaluating for each 0 < i < m and 0< j < n –This is repeated and each generated image is kept –With the smallest image, perform some edge detection--such as Sobel

18. 240-373: Chapter 8: Edge Detection 18 Pyramid Edge Detection OPERATION: (cont’d) –In pixels where edges are discovered, perform as edge detection operation on the group of four corresponding pixels in the next largest image –Continue to find the best edges down through the pyramid of images until the main edges in the original image have been discovered

19. 240-373: Chapter 8: Edge Detection 19 Edge Following Technique 7: Simple edge following USE: Knowing that a pixel is on an edge, the edge will be followed so that an objected is outlined OPERATION: –Suppose that a position on the edge has been identified, call it (x,y) and flag this position as used –Evaluate all the 3x3 Sobel gradient values centered on each of the eight pixels surrounding (x,y)

20. 240-373: Chapter 8: Edge Detection 20 Edge Following OPERATION: (cont’d) –Choose the three pixels with the greatest absolute gradient magnitude –Put these three pixel in a three-column array –Order them in row according to the gradient magnitude –Choose the one with greatest gradient magnitude

21. 240-373: Chapter 8: Edge Detection 21 Edge Following OPERATION: (cont’d) –Now this pixel will be one of the direction 0-7 with respect to the pixel (x,y) given by the following map, where * is the position of pixel (x,y) 0 1 2 7 * 3 6 5 4 –Call the direction of travel d –Repeat the algorithm but look at only pixels in d, (d+1) mod 8, and (d-1) mod 8 directions

22. 240-373: Chapter 8: Edge Detection 22 Edge Following OPERATION: (cont’d) –If no suitable high value of gradient magnitude is found, remove the pixel from the list and choose the next one of the three stored. Move up one row if all three are removed –Stop when the original pixel is reached, or execution has gone too long, or the number of rows in the list is very large