Statistical Models for Assessing the Individuality of Fingerprints

Abstract

Abstract-Following the Daubert ruling in 1993, forensic evidence based on fingerprints was first challenged in the 1999 case of the U.S. versus Byron C. Mitchell and, subsequently, in 20 other cases involving fingerprint evidence. The main concern with the admissibility of fingerprint evidence is the problem of individualization, namely, that the fundamental premise for asserting the uniqueness of fingerprints has not been objectively tested and matching error rates are unknown. In order to assess the error rates, we require quantifying the variability of fingerprint features, namely, minutiae in the target population. A family of finite mixture models has been developed in this paper to represent the distribution of minutiae in fingerprint images, including minutiae clustering tendencies and dependencies in different regions of the fingerprint image domain. A mathematical model that computes the probability of a random correspondence (PRC) is derived based on the mixture models. A PRC of 2.25 10 6 corresponding to 12 minutiae matches was computed for the NIST4 Special Database, when the numbers of query and template minutiae both equal 46. This is also the estimate of the PRC for a target population with a similar composition as that of NIST4.

Entropy of the Retina Template

“…The entropy in a fingerprint has been analysed by Zhu, Dass and Jain [17], who proposed a family of mixture models to simulate the occurrence of minutiae locations and orientations in a fingerprint. They simulated imposter matches and determined an equation for the probability p that fingerprints from different people would match on certain numbers of minutiae [17].…”

Longitudinal study of fingerprint recognition

“…Although the uniqueness of fingerprints has been studied by (i) estimating the probability of a random correspondence (i.e., two different fingerprints selected at random will be sufficiently similar to be claimed as a mate) (6)(7)(8) or (ii) measuring the evidential value § of latent fingerprint comparisons (9) (terminologies indicated with § are defined in SI Appendix, section S2), the persistence of fingerprints has been generally accepted based on anecdotal evidence, including case studies conducted by Herschel (10) and Galton (11) (SI Appendix, section S4), and the anatomical structure of friction ridge skin-the ridge pattern formed in the inner (dermal) layer during gestation remains unchanged with the protection of the outer (epidermal) layer (12).…”

A generative model for fingerprint minutiae

“…During the past two decades, a number of models have been proposed for various fingerprint features, including singular points [6], ridge orientation field [23,20,19,22], minutiae [11,24,7], and pores [13]. In this paper, our focus is on the statistical models for minutiae, particularly, ridge endings and bifurcations.…”

“…Pankanti et al [11] devised a minutiae model which assumes that (i) the occurrence of a minutia is a random event, (ii) individual minutiae are independent of each other, and (iii) the minutiae in a fingerprint are uniformly distributed. Zhu et al [24] showed that minutiae, instead of being uniformly distributed, tend to cluster in the regions where ridge orientation changes abruptly (e.g., around delta and core points). Based on this observation, they proposed to first partition the minutiae into several clusters and then model the minutiae distributions in each cluster by using a mixture of Gaussians.…”

“…The drawback of this model is that it is finger-specific; in other words, a mixture of Gaussians is learned for each finger, which makes it tedious and computationally expensive. Chen et al [7] further improved the model of [24] by deriving a mixture of Gaussians for the fingerprints in each of the five major fingerprint classes (i.e., arch, tented arch, left loop, right loop and whorl).…”