Computation of Likelihood Ratios in Fingerprint Identification for Configurations of Any Number of Minutiæ

Abstract

Recent court challenges have highlighted the need for statistical research on fingerprint identification. This paper proposes a model for computing likelihood ratios (LRs) to assess the evidential value of comparisons with any number of minutiae. The model considers minutiae type, direction and relative spatial relationships. It expands on previous work on three minutiae by adopting a spatial modeling using radial triangulation and a probabilistic distortion model for assessing the numerator of the LR. The model has been tested on a sample of 686 ulnar loops and 204 arches. Features vectors used for statistical analysis have been obtained following a preprocessing step based on Gabor filtering and image processing to extract minutiae data. The metric used to assess similarity between two feature vectors is based on an Euclidean distance measure. Tippett plots and rates of misleading evidence have been used as performance indicators of the model. The model has shown encouraging behavior with low rates of misleading evidence and a LR power of the model increasing significantly with the number of minutiae. The LRs that it provides are highly indicative of identity of source on a significant proportion of cases, even when considering configurations with few minutiae. In contrast with previous research, the model, in addition to minutia type and direction, incorporates spatial relationships of minutiae without introducing probabilistic independence assumptions. The model also accounts for finger distortion.

Separating the real from the synthetic: minutiae histograms as fingerprints of fingerprints

“…Further research, exploiting the abundance of optional statistical methods, may choose likelihood ratios [61], say, for improved quantification.…”

Combining evidence using likelihood ratios in writer verification

“…While LR D , which has a constant number of parameters, is simple to compute, there is a severe loss of information in going from probabilities of points in 2n-dimensional space to probabilities of a scalar value. However, due to its simplicity, the distance method is been widely used in fingerprint identification, 4 speaker verification, pharmaceutical tablet comparison, 8 etc.…”

“…4,7 The distance-based approach assumes that k = [k 1 , .., k n ], and q = [q 1 , .., q n ] are points in a fixed-dimensional vector-space and that there exists a scalar distance D(k, q) between them. A likelihood ratio is defined as follows The number of parameters needed to characterize the probability distributions in Eq.…”

“…The probabilistic approach is to determine the likelihood ratio positive (LR+) [1][2][3][4][5][6] whose numerator is the joint probability of the evidence and source under the null, or identification, hypothesis that the evidence arises from the source and the denominator is the joint probability under the alternate, or exclusion, hypothesis that the evidence does not arise from the object. The evidence is deemed to have arisen from the source if LR+ > 1 and not from the source otherwise.…”

Are there population differences in minutiae frequencies? A comparative study of two Argentinian population samples and one Spanish sample

“…These models have been based on very heterogeneous, and generally very small, samples and very disparate approaches (studying different types of minutiae, different fingerprint patterns, different fingers and different finger areas) see [17,18]. Recently, Neumann et al [22][23][24] and Egli et al [25] reported on the use of likelihood ratios as a means of objectively assessing the evidential weight of corresponding minutiae between a fingermark and a fingerprint.…”