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 ( A T A) i=1,…,N

Different coefficients of Da f1(D a )=  N-3 +  N-2 +  N-1 f2(D a )=  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(D a )=  1 +  2 +  3 g(D a )=f2(D a )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 -= minusequal The Methodology

- = SVD Transform Edge detection Edge detection with noise removal

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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 transformsFinal 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