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Unformatted text preview: Due: Dec 9, 2008, 4pm CS 257 (Luke Olson): Homework #11 Problem 1 Problem 1 Consider a database of 10 faces in faces.zip . Each is 50 by 50 pixel grayscale in PNG format: person1.png person2.png person3.png person4.png person5.png person6.png person7.png person8.png person9.png person10.png We would like to query this database to see if a person with a disguise of sunglasses ( disguise s.png ) or a musctache ( disguise m.png ) is in there. We will use SVD to look at “eigenfaces” of the database to compare with the disguises. step 1 Read all person * .png files in as 50 by 50 grayscale images and line up in a 2500 by 10 matrix X . step 2 Find the “average” of these faces step 3 Normalize all of the faces in X about this average face step 4 Perform an efficient SVD (not storing zero singular values) on X to generate the eigenfaces (stored in U ). step 5 Use d of the eigenfaces to find a projection of each face onto each of the eigenfaces. w = U(:,1:d)’ * A step 6 Read in a disguise image. step 7 Average this image with the database. step 8 Also project this image onto the eigenfaces. step 9 Compare this project to each of the projections above. That is, compare U(:,1:5)’ * newA to w above. step 10 Determine which face is closest to the disguise. So far, faces.m performs this task. Problem: which disguise is more effective? Using d = 1 is a very cheap comparison. Increasing d quickly becomes much more expensive (if the database is large). So the problem is, which disguise requires more eigenfaces to resolve the match with confidence. What to hand in: a discussion of which disguise is harder using evidence from the output of faces.m . You should only need to change d in line 3. Solution When using a disguise that covers the mouth, the top three matches stabalize when d = 3. When using a disguise that covers the eyes, the best guess isn’t correct until we’ve used the whole database with d = 9. Therefore, we can surmise that disginguishing between faces is much more difficult using this algorithm when we can’t see the eyes. Grading Total 2 points. Page 1 of 7 Due: Dec 9, 2008, 4pm CS 257 (Luke Olson): Homework #11 Problem 2 Problem 2 In this problem we will investigate the effectiveness of SVD as an image compressor. Use svd error.m to test the quality of an SVD compressed image versus the cost. Test four images: iguana.jpg , test1.png , test2.png , and test3.png . What to turn in: a comment on the performance of SVD for the 4 images (What do you notice? How effective is SVD in each case? Are there artifacts in the image that you can attribute to good/bad performance?)attribute to good/bad performance?...
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- Spring '08
- Regression Analysis, Singular value decomposition, Linear least squares, Total least squares, Luke Olson