A Möbius transformation based model for fingerprint minutiae variations

Abstract

When an individual’s fingerprint is scanned, although the global fingerprint pattern is unchanged, at the local level, between different scans the minutiae pattern may vary. Minutiae translation and rotation are caused by changing finger orientation and position shift during fingerprint acquisition. Minutiae patterns may also suffer non-linear distortion due to finger skin elasticity. Despite a variety of approaches to detecting deformations in fingerprint images, there has been no method available for capturing minutiae variations between two impressions of the same finger in a unified model. In this paper we address this issue by proposing a unified model to represent minutiae variations between fingerprint scans and formulate the changes to minutiae feature patterns. We identify the Möbius transformation as a good candidate for modelling minutiae translation, rotation and non-linear distortion, that is, different types of minutiae variations are described in a single model. Not only do we mathematically prove that the Möbius transformation based model is a unified model for capturing minutiae variations, but we also experimentally verify the effectiveness of this model using a public database.