Synthesis of 3D on-air signatures with the Sigma-Lognormal model

TL;DR

The paper tackles generating realistic 3D on-air handwriting data for signature verification by leveraging the Sigma-Lognormal model. It introduces three methods—Full Synthesis (FS) to create master 3D signatures from virtual targets, Kinematic Synthesis (KS) to derive kinematics from a given trajectory, and Duplicated Synthesis (DS) to produce duplicates of real or synthetic samples—with extensions to 3D air writing and gestures and open datasets. Experimental results show that synthetic databases can mimic real data in verification tasks, that training with duplicates can reduce error rates for skilled forgeries, and that a human perceptual test cannot easily distinguish synthetic from real movements. The work provides practical tools for generating scalable 3D biometric databases while acknowledging potential security risks and offering datasets for research use.

Abstract

Signature synthesis is a computation technique that generates artificial specimens which can support decision making in automatic signature verification. A lot of work has been dedicated to this subject, which centres on synthesizing dynamic and static two-dimensional handwriting on canvas. This paper proposes a framework to generate synthetic 3D on-air signatures exploiting the lognormality principle, which mimics the complex neuromotor control processes at play as the fingertip moves. Addressing the usual cases involving the development of artificial individuals and duplicated samples, this paper contributes to the synthesis of: (1) the trajectory and velocity of entirely 3D new signatures; (2) kinematic information when only the 3D trajectory of the signature is known, and (3) duplicate samples of 3D real signatures. Validation was conducted by generating synthetic 3D signature databases mimicking real ones and showing that automatic signature verifications of genuine and skilled forgeries report performances similar to those of real and synthetic databases. We also observed that training 3D automatic signature verifiers with duplicates can reduce errors. We further demonstrated that our proposal is also valid for synthesizing 3D air writing and gestures. Finally, a perception test confirmed the human likeness of the generated specimens. The databases generated are publicly available, only for research purposes, at .

Figures (9)

• Figure 1: Graphical diagram of the contributions of this article: three methods for designing 3D signatures, their evaluation, and additional experiments.
• Figure 2: Generation of the action plan of letter "v" in 3D from the generated virtual target points and links in 2D through their projected points on a sinusoidal surface. The following abbreviations are used in the figure: $vp_j$ (blue) - the generated virtual target point in 2D; $mp_j$ (blue) - the middle target point in 2D; the planar links (blue) connecting two consecutive virtual target points in 2D; $vp_j$ (black) - the projection of the 2D virtual target points onto a 3D sinusoidal surface; $mp_j$ (black) - the 2D middle points projected onto the sinusoidal surface, and 3D planar links (magenta) between virtual target points.
• Figure 3: Example of a master 3D synthetic signature obtained with the FS method.
• Figure 4: Example of a 3D signature with a sampled trajectory and a synthetic velocity through the KS method.
• Figure 5: Examples of 3D real and duplicated signatures with the DS method.