A method for eye detection based on SVD transform
Somayeh Danafar
Lila Taghavi
Alireza Tavakoli
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
: 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
Singular Value Decomposition in a Nutshell
U and V are orthogonal matrices
i = i ( ATA) i=1,…,N
Different coefficients of Da
f1(Da)= N-3+ N-2+ N-1 f2(Da)= 1+ 2+ 3
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
Edge Detection
f2(Da)= 1+ 2+ 3 g(Da)=f2(Da)f
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
- =minus equal
The Methodology
The Methodology
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SVD Transform
Edge detection
Edge detection with noise removal
Variation in lighting
Introduction of glasses
Effect of change in orientation and closure of eyes
Application to images with a complex background
The SVD transform
The SVD transforms Final result
The result of svd transform
Final result
Original image
SVD versus Interest Points algorithm
25 points
60 points
43 points
3 points
14 points
10 points
The errors in SVD:
1) Missing one eye
2) Detecting additional points