Decision Confidence Levels

The Bernoulli representation noted above for this pattern recognition task clarifies the calculation of confidence levels associated with any decision, including extrapolation of confidence levels into the region between the two distributions where no Hamming distances were observed empirically. As specified in (23) - (26), the conditional probabilities of personal identity or non-identity given a particular observation can be calculated as the cumulative integrals under the two density distributions, taken from opposite directions up to whatever Hamming distance was observed. More generally, for any given operating choice of Hamming distance criterion, the latent probabilities of the two types of errors can be calculated by evaluating these cumulative integrals up to the chosen operating criterion.

 
Table 1: Performance tabulated as error probabilities for several decision criteria. Compare this to the greatly improved False Accept Odds in the 1996 BT Evaluation.

Empirically, comparisons of iris codes computed from the available database of eye images produced no Hamming distances in the range of 0.25 to 0.35, so the use of any criterion in this range would produce 100% correct performance. However, the natures of the two distributions seen in Figure 11 and described by (22) and (34), allow us to calculate theoretical probabilities for False Accept and False Reject over this range. These probabilities are tabulated in Table 1. As the operating criterion is increased, the theoretical probability of a False Accept of course increases, while that of a False Reject decreases. The cross-over error rate occurs at a Hamming distance criterion of about 0.321, at which point both the False Accept error rate and the False Reject error rate are, theoretically, one in 131,000. This cross-over error rate suggests adopting a Hamming distance close to 0.32 as a balanced operating criterion, although of course more conservative or more liberal decision criteria may be more suitable for different applications. Any such criterion is easily implemented, with performance consequences as listed in Table 1.

Finally, it is interesting to examine the posterior confidence levels associated with ``typical" decisions for accepting an authentic, and for rejecting an imposter. The means of the two distributions in Figure 11 indicate typicality. In the typical imposter comparison, which generates a Hamming distance of 0.45 after the ``best of n" provision for eye rotation or head tilt, the confidence with which the Subject is rejected (given this observation) corresponds to a conditional False Reject probability one in 10^9,6, or one in 4 billion. In the typical authentic comparison, which generates a Hamming distance of only 0.084, the confidence with which the Subject is accepted (given this observation) corresponds to a conditional False Accept probability of one in 10³¹.