1. A method for eye detection based on SVD transform Somayeh Danafar Lila Taghavi Alireza Tavakoli

2. Outline The advantages of algorithm SVD in a nutshell The methodology Results from a number of images The result of interest points algorithm The algorithem’s errors

3. :‏The algorithm is robust relative to Changes in lighting Eye color and complexion Blurring Introduction of glasses Different resolutions Complex background Variability in scale and orientation

4. Singular Value Decomposition in a Nutshell U and V are orthogonal matrices  i = i ( A T A) i=1,…,N

5. Different coefficients of Da f1(D a )=  N-3 +  N-2 +  N-1 f2(D a )=  1 +  2 +  3

6. Eye Detection The algorithm proceeds in four steps : 1. Variance reduction 2. Application of SVD transform with a nonlinear function f 3. Application of edge detection algorithm 4. Separation of boundary edges f=  1/(1+s(t)) for t=1,..,8

7. Edge Detection f2(D a )=  1 +  2 +  3 g(D a )=f2(D a )f

8. Original Image SVD transform uses the exponential of a linear function of diagonal part of the SVD decomposition. SVD Transform in diffident coefficients of the sigma in the SVD Using Edge Detection Using noise removal -= minusequal The Methodology

9. - = SVD Transform Edge detection Edge detection with noise removal

12. Rotate :65 ْ

13. Rotate: 45 ْ

14. Variation in lighting

15. Introduction of glasses

16. Effect of change in orientation and closure of eyes

17. Application to images with a complex background

19. The SVD transform

20. The SVD transformsFinal result

21. The result of svd transform Final result Original image

22. SVD versus Interest Points algorithm 25 points 60 points 43 points 3 points 14 points 10 points

23. The errors in SVD: 1) Missing one eye 2) Detecting additional points