Space oriented filters. Application

Filters are applied to rectangular transforms of the eye.

Images:

 
The source image is similar to: 

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The transformation is done with the wavelet transformation tools, and using oriented filters. 
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We obtain nbr_orientations * nbr_levels images. It is noticed that the greatest quantity of information is on the first orientation (at the top, on the right: horizontal orientation). Indeed, we have already noticed that the information on the iris is more abundant in a circular course than in radial course.

The computation of the results:

The concept of " proximity " between 2 irises is defined here with the operator correlation.
Thus, for each level of the decomposition, we extract the corresponding image (according to the 1st orientation: at the top, on the right) in order to intercorrelate it with the image extracted on the target.
 
 
Example of extracted cell: 

This cell is the orientation 1 (horizontal) and order (or scale) 2 of the image above. 
 

Despite of the noise, we notice: 

  • The low number of colors. A compression by reduction in the precision of the colors is possible.
  • Many vertical " bars ". An original compression could exploit this characteristic. 

To compare 2 irises, we compare their 2 decompositions, image by image. I.e. orientation by orientation and level by level.
 

Results:

With a base of 15 images, out of 5 irises (3 different photographs per iris), no impostor succeeded in exceeding the score of one authenticated true (i.e. there is no confusion between impostor and authenticated).
 
Results of the comparisons. 

In X-coordinate: images. For each eye, we have use 3 different images, which corresponds to 3 photographs of the same eye, taken at different moments. 

In ordinate: values. The initial image is identical to itself and thus has an equal correlation has 1. One authenticated has a value from approximately 0.3 to 0.8. An impostor receives a usual value at approximately 0.07. 

In green: the worst of the cases (worst authenticated with worst impostor) 
In blue: the average case. 
In red: the best case (the best authenticated with best impostor)

The attentive observation of these curves shows a significant detail:
An impostor carries out a better result on the " Best case " than the worst authenticated of the " Worst case ".
If this impostor had carried out an imposture of this " quality " on the worst of the authenticated, would he have succeeded in being authenticated?
Fortunately, it seems that it is not the case: The information obtained by this method is not equiprobable and an impostor carrying out a better score than the worst of the authenticated is as probable as an impostor carrying out better score than the best of the authenticated.
 
Thus, it was seen that worst case is very different from best.
We look at the " distance " between the worst of the authenticated and the best of the impostors:		                                                Worst  Mean  Best
Score of worst of authenticated 
--------------------------------= 2.40   5.15   8.49 
Score of best impostor
NB: With a simple filter(medfilter2), the worst of the scores passes from 2.4 to 3.16.
 

Improvements:
 

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