Global models for the orientation field of fingerprints: An approach based on quadratic differentials

Abstract

Quadratic differentials naturally define analytic orientation fields on planar surfaces. We propose to model orientation fields of fingerprints by specifying quadratic differentials. Models for all fingerprint classes such as arches, loops, and whorls are laid out. These models are parameterized by a few geometrically interpretable parameters that are invariant under euclidean motions. We demonstrate their ability in adapting to given observed orientation fields, and we compare them to existing models using the fingerprint images of the NIST Special Database 4. We also illustrate that these models allow for extrapolation into unobserved regions. This goes beyond the scope of earlier models for the orientation field as those are restricted to the observed planar fingerprint region. Within the framework of quadratic differentials, we are able to analytically verify Penrose's formula for the singularities on a palm [19]. Potential applications of these models are the use of their parameters as indexes of large fingerprint databases, as well as the definition of intrinsic coordinates for single fingerprint images.