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

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The Methodology

The Methodology

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SVD Transform

Edge detection

Edge detection with noise removal

Rotate :65 ْ

Rotate: 45 ْ

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