Authentics' Hamming Distances

 
Figure 10: Hamming distances between pairs of different iris codes for each given iris, allowing for n=7 different degrees of eye or head tilt.

Figure 10 shows the distribution of Hamming distances computed between 1,208 pairs of different images of given irises (``authentics"). Different images of the same iris never yield a Hamming distance of zero, because of variations in the Subject's angle of gaze, degree of eyelid occlusion, specular reflections from the cornea or corrective lenses, random silhouettes of the eyelashes upon the iris, and light-driven as well as uncontrolled oscillations in pupillary dilation (``hippus") which cause some folding and unfolding of iris tissue that would not be captured by the homogeneous rubber sheet model. Nonetheless, these Hamming distances (again with 7 possible relative orientations of the eye) are clearly substantially smaller than those seen in Figure 9 for imposters. This distribution has a mean of µ = 0.084 and standard deviation = 0.0435. The solid curve plots a binomial as defined previously in (22) but with p=0.084, and N=41 chosen in order to match the observed since the standard deviation of a binomial distribution is = (pq/N)^½ where q=1-p. Continuous interpolation of these binomial distributions, as well as estimation of their factorial terms, was done by Stirling's approximation which errs by less than 1% for :