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Image Compression using Singular Value Decomposition

Image Compression using Singular Value Decomposition. Math 320 Kristen Cunanan Michael Tzen. Reading a matrix into Matlab. Command: data=imread(“title”,”format”). Singular Value Decomposition. SVD in Matlab.

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Image Compression using Singular Value Decomposition

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  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

  6. Using 1 Singular Value

  7. Using 11 Singular Values

  8. Using 31 Singular Values

  9. Using 51 Singular Values

  10. Using 91 Singular Values

  11. 269 Singular Values

  12. Eigenfaces/Facial Recognition

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

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

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

  16. Covariance Matrix • Get the Covariance Matrix of S

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

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

  19. .87 + .2 = + .10 + .1

  20. Euclidean distance

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

  22. Otherwise McMillen = Will Smith?

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