Why False Match Probability does not Accumulate in Large Database Searches

Because the binomial tail of the distribution generated when different irises are compared attenuates so rapidly, very small adjustments in the Decision Threshold allow truly huge databases to be searched without suffering False Matches. The binomial tail (solid curve) is governed by factorial terms since the comparisons of bits in IrisCode phase sequences are Bernoulli trials; other biometrics that are not based on complex random phase sequences do not have this felicitous property. The rate of attenuation is such that each reduction in the decision threshold by 1 percentage point in Hamming Distance (-0.01) causes a nearly 10-fold further reduction in False Match probability. Some illustrative values are given in this table of cumulatives under the tail of the distribution:

Decision Threshold Odds of False Match
0.33 1 in 4 million
0.32 1 in 26 million
0.31 1 in 185 million
0.30 1 in 1.5 billion
0.29 1 in 13 billion

Since very small reductions in the decision threshold have such dramatic effects on the False Match probability, it is possible to accommodate extremely large search databases -- even the sizes of national populations -- by making just modest reductions in the Hamming Distance decision criterion. This is the reason why the United Arab Emirates deployment can perform 3 Billion iris comparisons every day without getting False Matches. The actual function embedded into my algorithms for determining the acceptance threshold criterion HD when the size of the search database is N, is:

For all biometrics, the fact that the odds of making False Matches would otherwise grow with the number of enrolled templates in a database (rather like playing a game of Russian Roulette an increasing number of times) means that if they can operate in Identification mode at all, they must reduce their decision thresholds relative to Verification mode. A powerful aspect of the iris biometric based on phase sequences, is that the binomial distributions generated by comparing bits in IrisCodes have such rapidly attenuating tails that with minute adjustments in decision threshold, national sized databases can be accommodated while keeping the net False Match probability still minuscule. For this reason, it is important to understand that the often cited figure of "1 in a million" as the False Match rate for iris recognition should be regarded as NET of the total database size. (A common error is to multiply that rate by the database size to infer a net rate, ignoring the intrinsic adjustment explained above.)

Further information about these issues can be found on the page: statistical demands of identification vs verification.

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