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

TL;DR

The paper tackles the challenge of reproducing realistic fingerprint patterns and minutiae with a mechanistic model. It proposes a two-species Schnakenberg reaction-diffusion system with an anisotropic diffusion tensor $D$ guided by ridge-direction maps derived from centers and deltas on a fingertip-shaped domain, solved via finite elements and implemented in GenCHSin. The authors show that the model naturally generates arch, loop, and whorl patterns and key minutiae, including short-range structures, and validate the outputs with real-fingerprint statistics, AFIS-like tests, and a Poisson description of minutiae coincidence. The work provides a flexible, open-source platform for large-scale synthetic fingerprint generation, enabling study of identification certainty and privacy-preserving data for AI training.

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.

Figures (12)

• Figure 1: The fundamental classification of fingerprint patterns, introduced by Juan Vucetich, which is based on the presence or absence of a delta structure, illustrated as a red triangle in the figures. Depending on the number of deltas (or their absence), fingerprint patterns can be categorized as follows: a) Simple arch b) Simple external loop c) Simple internal loop d) Mononuclear whorl.
• Figure 2: Classification of different minutiae based on the basic structures observed in fingerprint patterns.
• Figure 3: A set of fingerprints used to obtain the values in Table \ref{['Tabla']}. Red stars indicate the positions of centers and deltas, while blue segments are used to measure ridge angles.
• Figure 4: Examples of two distinct synthetic fingerprints generated using the proposed model. Red rectangles highlight the presence of short-range structures such as hooks, islands, and dots in each image.
• Figure 5: a) Plot of the activator $u$ at the end of the simulation process. b) Result of applying the cutting and black-and-white filter to the corresponding image.