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## Decision Environment for Iris Recognition

The performance of any biometric identification scheme is characterized
by its "Decision Environment." This is a graph of the two histograms
that the test generates: one when comparing SAME persons or samples, and
the other when comparing DIFFERENT ones. Ideally these two distributions
should be well separated, since any overlap between them causes errors in
decision making: SAME would be confused as DIFFERENT, and vice versa.
One metric for "decidability," or decision-making power, is d'. This is
defined as the separation between the means of the two distributions,
divided by the square-root of their average variance. According to tests
conducted by British Telecom (data shown in the graph above), the decidability
for iris recognition is d' = 11.36, which is far higher than for any
other known biometric. Decidability metrics such as d' can be applied
regardless of what measure of similarity a biometric uses. In the particular
case of iris recognition, the similarity measure is a Hamming Distance: the
fraction of bits in two IrisCodes that disagree. The distribution
on the left in the graph shows the results when different images of the
same eye are compared; typically about 10% of the bits may differ. But
when IrisCodes from different eyes are compared, the distribution on the right
is the result: the fraction of disagreeing bits is very tightly packed
around 45%. Because of the narrowness of this right-hand distribution,
which belongs theoretically to the family of binomial derivatives
(see scientific papers for mathematical details),
it is possible to make identification decisions with astronomic levels of
confidence. For example, the odds of two different irises agreeing just
by chance in more than 75% of their IrisCode bits (i.e. having a Hamming
Distance of 0.25 or lower) is only one in 10-to-the-16th power.

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