General methods
In connection with the iris

The iris is a little contrasted area of the eye:

In comparison with its immediate environment (the black of the pupil and the white of the remainder of the eye), the iris is a zone with weak contrast. Thus, for a device of capture, its full range of contrast will go from the very dark black to the very clear white.
This is at the same time an advantage and a disadvantage.

In practice, over 128 values, the variations are spread out over 35 to 45 values. That is to say a report/ratio S/B from approximately 35 with 40dB.


 

Spectrum of the iris:

The transform of Fourrier 2D of an iris is noticed below:


Figure 3 is obtained by carrying out a polar transformation = > rectangular, with teta constant (method 2, to see further). Then, the rectangular transform " fft2 " produces the coefficients of Fourrier.
The columns are increasing according to teta. The lines are increasing according to R.

It is noticed that information is primarily at the highest frequencies.

With the reading of this figure, one could believe that the values are distributed in a horizontal way:

The values are distributed primarily on the high and low edges. Thus, the quantity of information present on each line varies much according to N°of the line. On the other hand, the quantity of information present on each column varies little according to N°of the column.
One deduces from it that the columns contain more information than the lines!
The information contained on the iris seems more to be distributed more in a circular way. But it as should be noticed as the average perimeter of an iris is much more significant than its ray. It can thus be carrying much more information.

One should not forget the role of the polar = > rectangular transform. It is possible that it is here, responsible for a such distribution.

Denoising / Filtering:

Because of the importance of the components high frequencies, one can seek with knowing if useful information here is in these frequencies or if it is not absolutely necessary of noise from the sensor. Let us cancel the values at certain frequencies:
Effect of the suppression of 80% of the components low frequencies. Figures 2 and 3 show the left higher part of an iris. The useful image is here in gray. The white of the eye is in top, on the left. The pupil is in bottom, on the right. Figure 2 is the image source and figure 3, the modified image.
 

For more speed, one can use a simpler filtering and more running, with filters RII or RIF and a convolution 2D. The filter will be thus a high pass one, with a high frequency cut-off and a significant attenuation. However, no precise value imposes the choice of a particular filter.
 

Here an example based on a filtering band suppressor centered in average frequencies. The lowest frequencies are so little significant here that filtering in average region has the effect of a low-pass filtering.

Figure 1: FFT 2D of the image of a complete eye. Figure 2: FFT 2D of the filtered image. One notices the standardization of low and intermediate frequency.

The implementation of this filter is carried out, under Matlab, with the command < medfilt2(source) >, which carries out a local approximation with an interpolation of the type " nearest ". One obtains a standardization of the values in low and average tape as well as a general attenuation of the noise.



 

Filtering based on wavelets:

The operation of filtering can be carried out with the tool for processing of the signal which is the theory of the wavelets. Firstly, the use of the wavelets to compute filtering can be seen as penalizing in time calculation and not very practical. On the other hand, if the wavelets are used in the next stages of the processing, some stages could be done as one.

The use of the wavelets is described after. One is interested here only in the results and not in the methods.

Within the framework of the multiresolution analysis, filters are deduced from the wavelets. These filters are (generally) per pair High-Pass (here G(z)) / Low-Pass (here H(z)). The residue (A1(x)) is obtained by applying the filter Low-Pass (H(z)). This residue corresponds to the remainder after a decomposition by a wavelet.
The process can be iterated, on the condition of carrying out a decimation (resolution divided by 2) between the filters. Below : a decomposition of order 3:

Thesource  image is replaced here by x[n ]; Dx 1,2 and 3 are the coefficients of the decomposition to order 1,2 and 3; Ax 1,2 and 3 are the residues of order 1,2 and 3. A decimation is carried out with each stage.

Denoising can be done on orders 1 or 2 only.
Below : Pictures denoised with such method.


Approximation at order 2 (low-pass residue)

The principal problem is the side effect, that leads to small waves on the extremities.
But the main parameters of the iris are well kept.
 
 
 

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