 ## 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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