Homework #2: Feature-DetectionConsider the three images2. Compute Edgels (30 Points)3. Contour Follower (30 Points)Homework #2: Feature-Detection Due Wednesday, February 13th 2002.Professor Davi GeigerMake sure you did homework 1 and look/read at lecture materials. Problem 1d have an extra 10 points value if you do the extra work..CONSIDER THE THREE IMAGES Test Image Test+Noise Image Face Image1. JUNCTION DETECTION (40 Points +10 Extra Points)a. Compute ),,,(~syxIcfor the 16 valuesand 3 scales, s= 3, 5,7ake sure you compute only within a frame of 8 pixels away from the boundaries (largest scale).Show-Print the results as images for and s= 3, 7 (these are 6 prints to show per image, use one page per image, i.e., 3 pages.)Reminder),,,(~syxIc: pseudo code for y  1 …N-2 for x  1 …N-2 for s  3,5,7 if (y  s and x  s and x  N-s-1)for    ),(1),,,(~1),,,(~yxIssyxIsssyxIc end  (end loop for s)1end  (end loop for x)end  (end loop for y)b. Compute ),,,(~syxIDcfor the 8 valuesand 2 scales, s= 3, 7ake sure you compute only within a frame of 8 pixelsaway from the boundaries (largest scale).Show-Print the results as images for and s= 3, 7 (these are 6 prints to show per image, use one page per image, i.e., 3pages)c. Compute the homogeneity measure )7,,(~yxH using 437 s, i.e.,6110))7,,,(~(|)3,,,(~)7,,,(~|)7,,(~yxIyxIyxIyxHccc here =1 is a small value, to make sure the division is stable in case 0)7,,,(~yxIc. Show-Print the results in one page, one result per image. d. Detect junctions by choosing thresholds TTH, (If you choose these parameters via exam-ining the histogram, then print the histogram and you will get 10 points extra). The thresholdsfor the Face image are probably different/lower than for the first two images. At the Test Im-age and Test+Noise Image, the thresholds should leave only the detection of junctions wherethey really are (don’t forget to eliminate junctions where the difference in angle is larger than3Also, experiment with s=3 and s=7, and give both results (the best threshold valuemay be lower for s=7 than for s=3, on all the three images, as there are more averages).2. COMPUTE EDGELS (30 POINTS)e. Compute ),(maxyxs, from|),,,(ˆ| syxID, for s= 3, 7and DO NOT use a homogeneitymeasure. Select appropriate threshold T, and it is probably different for the Face Image. Ex-periment with s=3 and s=7, and give both results (the best threshold value may be lower fors=7 than for s=3, across the three images, as there are more averages). Show it as an image:the higher is ),(maxyxs, the brighter the image. Show for both, s=3 and s=7, i.e., a total ofsix images .f. Filter previous results with the homogeneity measure, )7,,(~yxH and HTwhich you alreadycomputed in the first part of the homework. Show the new results (total of six images again)3. CONTOUR FOLLOWER (30 POINTS)Extract contours as described in the lecture3.doc from the three images and show the results as im-ages, with contours as black in a white background (like a line drawing). Choose three different start-ing points for each image and run the contour follower. Apply the same three points for the Test im-age and for the Test+Noise image. (Altogether there will be one line drawing result per image, andeach result will contain three contours.) The pseudocode for the contour follower is in lecture 3 as2Contour-Follower(xc , yc) if (Edgel(xc , yc )  NIL) Link-neighbors+(xc , yc ,max) Link-neighbors-(xc , yc ,max) end