Novel reaction-diffusion PDE model for fingerprint-like pattern emergence via the Schnakenberg mechanism

TL;DR

This paper introduces a novel reaction-diffusion PDE model based on the Schnakenberg mechanism, incorporating anisotropic diffusion aligned with ridge orientations, to simulate fingerprint patterns and minutiae emergence, aligning well with real fingerprint data.

Contribution

The work presents a new anisotropic reaction-diffusion model that can generate realistic fingerprint patterns and minutiae, providing insights into fingerprint formation and identification.

Findings

Model successfully reproduces four basic fingerprint classes.

Generated minutiae distribution matches real fingerprint data.

Patterns exhibit diverse fingerprint features on a fingertip-like domain.

Abstract

Fingerprint analysis and fingerprint identification have been the most widely used tools for human identification. To this day, various models have been proposed to explain how fingerprints are formed, ranging from the fibroblast model, which focuses on cell-collagen interactions, to the buckling of thin layers model, both yielding significant results. In this work, we present a reaction-diffusion model of Schnakenberg type, featuring an anisotropic diffusion matrix that follows the ridge orientations supplied by other traditional fingerprint-generation models, and notably yet allows minutiae -- i.e. characteristic microstructures embedded in fingerprints -- to emerge. The statistical analysis of the minutiae distribution in a randomly generated fingerprint collection is consistent with observations in real fingerprints. The model can numerically generate fingerprint-like patterns corresponding to the four basic classifications -- arches, ulnar loops, radial loops, and whorls -- as well as a variety of derived forms. The generated patterns emerge on a convex domain that mimics the geometry of a fingertip, exhibiting the diverse types of minutiae typically analyzed in fingerprint identification and showing strong agreement with those observed in human fingerprints. This model also provides insight into how levels of certainty in human identification can be achieved when based on minutiae positions. All the algorithms are implemented in an open source software named GenCHSin.