Image Compression using Singular Value Decomposition

1. Image Compression using Singular Value Decomposition Math 320 Kristen Cunanan Michael Tzen

2. Reading a matrix into Matlab Command: data=imread(“title”,”format”)

3. Singular Value Decomposition

4. SVD in Matlab we must do svd p times on each “page” of the array. Command: = svd(data(:,:,:i) i=1…p

5. Selecting for the number of Singular Values

7. Using 1 Singular Value

8. Using 11 Singular Values

9. Using 31 Singular Values

10. Using 51 Singular Values

11. Using 91 Singular Values

12. 269 Singular Values

13. Eigenfaces/Facial Recognition

14. Process • Is person X in the “training” group of M=50? • SVD on manipulated pictures • Is Euclidean distance in the threshold?

15. Prep Work Image I Data matrix  “Training Set” of images 

16. Subtracting the Mean • Compute the Mean of S = Training set • Subtract Mean from ea. face/vector in S

17. Covariance Matrix • Get the Covariance Matrix of S

18. SVD on C = • SVD method on C to get the eigenvalues/eigenvectors • Gives us the “important” values/vectors corresponding to each difference vector

19. Eigenvector = Eigenface • The eigenvectors obtained, are called Eigenfaces • Any can be written as a linear combination of the eigenfaces

20. .87 + .2 = + .10 + .1

21. Euclidean distance

22. Conclusion • If Value (Specified) • Human Face ~ 1500 range • McMillen = Bradd Pitt

23. Otherwise McMillen = Will Smith?