[Paper Review] Fingerprint Analysis with Marked Point Processes

Peter Forbes, Steffen L. Lauritzen+1 more|arXiv (Cornell University)|Jul 22, 2014

Biometric Identification and Security24 references3 citations

TL;DR

This paper proposes a Bayesian fingerprint matching framework using marked Poisson point processes to model minutiae (ridge endings and bifurcations) with location, orientation, and type. It employs an efficient Monte Carlo algorithm to compute the likelihood ratio for the prosecution vs. defence hypothesis, achieving strong performance on an NIST-FBI database of 258 fingerprint pairs.

ABSTRACT

We present a framework for fingerprint matching based on marked point process models. An efficient Monte Carlo algorithm is developed to calculate the marginal likelihood ratio for the hypothesis that two observed prints originate from the same finger against the hypothesis that they originate from different fingers. Our model achieves good performance on an NIST-FBI fingerprint database of 258 matched fingerprint pairs.

Motivation & Objective

• To develop a statistically rigorous, probabilistic framework for fingerprint identification that quantifies the weight of evidence using likelihood ratios.
• To address the lack of scientific research on the discriminatory power and error rates of fingerprint identification despite its over a century-long use in forensics.
• To model fingerprint minutiae as marked point processes incorporating spatial location, orientation, and type (ending, bifurcation, or unobserved).
• To enable automated fingerprint identification and courtroom-ready evidence evaluation through a fully Bayesian alignment procedure.
• To improve upon existing models by integrating similarity transformations (translation, rotation, scaling) and handling low-quality prints with sparse minutiae.

Proposed method

• Model fingerprints as marked Poisson point processes on the complex plane, where each minutia is represented as a triple (location in ℂ, orientation on 𝕊¹, type in {−1,0,1}).
• Use complex normal and von Mises distributions to model the spatial and angular distribution of minutiae under the prosecution and defence hypotheses.
• Formulate the likelihood ratio as the ratio of marginal likelihoods under the same-finger (Hp) and different-finger (Hd) hypotheses.
• Implement a Gibbs sampler with auxiliary variables to jointly sample the matching configuration ξ, transformation parameters (ψ, τ), and noise precision σ.
• Use a Metropolis–Hastings step with an efficient proposal that updates only the match for a randomly selected minutia in B, leveraging conditional probabilities based on spatial and angular alignment.
• Normalize proposal densities by discarding common terms, enabling fast computation of transition probabilities in the MCMC algorithm.

Experimental results

Research questions

• RQ1 How can a probabilistic model be constructed to quantify the weight of evidence in fingerprint comparisons using marked point processes?
• RQ2 What is the performance of a Bayesian likelihood ratio framework for fingerprint matching on real-world data with varying print quality?
• RQ3 How can similarity transformations (translation, rotation, scaling) be consistently modeled and marginalized in a Bayesian framework for fingerprint alignment?
• RQ4 Can an efficient Monte Carlo algorithm be designed to compute the marginal likelihood ratio without requiring full enumeration of all possible matches?
• RQ5 How does the model handle low-quality fingermarks with few minutiae, and what is its robustness to missing or noisy data?

Key findings

• The proposed marked point process model achieves strong performance on the NIST-FBI fingerprint database, successfully distinguishing matched pairs from unmatched ones.
• The Monte Carlo algorithm efficiently computes the marginal likelihood ratio by integrating over transformations and matching configurations, enabling practical forensic application.
• The model effectively handles the challenges of arbitrary coordinate systems and low-quality prints by modeling spatial and angular features jointly with complex normal and von Mises distributions.
• The use of auxiliary variables and a tailored Metropolis–Hastings sampler allows for fast, high-proposal acceptance rates in the MCMC chain, ensuring convergence and mixing.
• The framework provides a principled Bayesian alternative to heuristic fingerprint matching, offering a quantifiable weight of evidence through the likelihood ratio.
• The method is robust to missing minutiae and performs well even when only a small number of features are present, as demonstrated on the NIST-FBI dataset with 258 matched pairs.