**
**

It is important to establish and to measure the amount of independent variation
both within an iris and between different irises. There are correlations within
an iris because local structure is self-predicting; for example, furrows tend to
propagate themselves radially. Such self correlations limit the number of
degrees of freedom within irises. But even more important is the question of
whether systematic correlations exist between different irises.

This probability distribution suggests that they do not. It plots the probability
that bits in different positions within the IrisCode are set to 1, for a randomly
sampled population of different IrisCodes.

The fact that this distribution hovers near
0.5 indicates that all IrisCode bits are equally likely to be 0 or 1. This
property makes IrisCodes "maximum entropy" codes in a bit-wise sense. The fact
that this distribution is uniform indicates that different irises do not systematically
share any common structure. For example, if most irises had a furrow or crypt in the
12-o'clock position, then the plot shown here would not be flat.

The recognition of persons by their IrisCodes is based upon the failure
of a test of statistical independence. The plot shown here illustrates why
any given IrisCode is "statistically guaranteed" to pass
a test of independence against any IrisCode computed from a different eye.

## References

- Daugman J (1999) "Wavelet demodulation codes, statistical independence,
and pattern recognition." Institute of Mathematics and its Applications,
Proc. 2nd IMA-IP. London: Horwood, pp 244 - 260. (500K PostScript copy
here.)

- Daugman J (1993) "High confidence visual recognition of persons by a test
of statistical independence." IEEE Transactions on Pattern Analysis and
Machine Intelligence, vol. 15, no. 11, pp 1148 - 1160.
(.pdf)

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