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 .

The Kinematic Theory of rapid movements, and its associated Sigma-Lognormal, model 2D spatiotemporal trajectories. It is constructed mainly as a temporal overlap of curves between virtual target points. Specifically, it uses an arc and a lognormal as primitives for the representation of the trajectory and velocity, respectively. This paper proposes developing this model, in what we call the Kinematic Theory Transform, which establishes a mathematical framework that allows further primitives to be used. Mainly, we evaluate Euler curves to link virtual target points and Gaussian, Beta, Gamma, Double-bounded lognormal, and Generalized Extreme Value functions to model the bell-shaped velocity profile. Using these primitives, we report reconstruction results with spatiotemporal trajectories executed by human beings, animals, and anthropomorphic robots.

This paper proposes a method to generate the synthetic kinematic of signatures in 3D. The analysis of 3D signatures is becoming a hot topic due to the irruption of commercial off-the-shelf devices for easy acquisition of 3D movements. However, the novelty of this technology reveals the scarce publicly available signatures in 3D, which hinder their de-velopment. A solution is the synthesis of Signatures in 3D. As a first step, this paper synthesizes the kinematics of 3D signatures based on the Kinematic Theory of Rapid Movements and its associated Sigma-Lognormal model in 3D. To evaluate the method, we regenerate signature databases with synthetic speed profiles in all genuine and forgeries found in two 3D signature databases. Then, we analyze the similarities in the performance of a signature verifier when real and synthetic signatures are used in random and skilled forgeries experiments.

The Kinematic Theory of rapid movements and its associated Sigma-Lognormal model have been extensively used in a large variety of applications. While the physical and biological meaning of the model have been widely tested and validated for rapid movements, some shortcomings have been detected when it is used with continuous long and complex movements. To alleviate such drawbacks, and inspired by the motor equivalence theory and a conceivable visual feedback, this paper proposes a novel framework to extract the Sigma-Lognormal parameters, namely iDeLog. Specifically, iDeLog consists of two steps. The first one, influenced by the motor equivalence model, separately derives an initial action plan defined by a set of virtual points and angles from the trajectory and a sequence of lognormals from the velocity. In the second step, based on a hypothetical visual feedback compatible with an open-loop motor control, the virtual target points of the action plan are iteratively moved to improve the matching between the observed and reconstructed trajectory and velocity. During experiments conducted with handwritten signatures, iDeLog obtained promising results as compared to the previous development of the Sigma-Lognormal.

Developing an automatic signature verification system is challenging and demands a large number of training samples. This is why synthetic handwriting generation is an emerging topic in document image analysis. Some handwriting synthesizers use the motor equivalence model, the well-established hypothesis from neuroscience, which analyses how a human being accomplishes movement. Specifically, a motor equivalence model divides human actions into two steps: 1) the effector independent step at cognitive level and 2) the effector dependent step at motor level. In fact, recent work reports the successful application to Western scripts of a handwriting synthesizer, based on this theory. This paper aims to adapt this scheme for the generation of synthetic signatures in two Indic scripts, Bengali (Bangla), and Devanagari (Hindi). For this purpose, we use two different online and offline databases for both Bengali and Devanagari signatures. This paper reports an effective synthesizer for static and dynamic signatures written in Devanagari or Bengali scripts. We obtain promising results with artificially generated signatures in terms of appearance and performance when we compare the results with those for real signatures.

The synthetic generation of static handwritten signatures based on motor equivalence theory has been recently proposed for biometric applications. Motor equivalence divides the human handwriting action into an effector dependent cognitive level and an effector independent motor level. The first level has been suggested by others as an engram, generated through a spatial grid, and the second has been emulated with kinematic filters. Our paper proposes a development of this methodology in which we generate dynamic information and provide a unified comprehensive synthesizer for both static and dynamic signature synthesis. The dynamics are calculated by lognormal sampling of the 8-connected continuous signature trajectory, which includes, as a novelty, the pen-ups. The forgery generation imitates a signature by extracting the most perceptually relevant points of the given genuine signature and interpolating them. The capacity to synthesize both static and dynamic signatures using a unique model is evaluated according to its ability to adapt to the static and dynamic signature inter- and intra-personal variability. Our highly promising results suggest the possibility of using the synthesizer in different areas beyond the generation of unlimited databases for biometric training.

Handwritten signature datasets are really necessary for the purpose of developing and training automatic signature verification systems. It is desired that all samples in a signature dataset should exhibit both inter-personal and intra-personal variability. A possibility to model this reality seems to be obtained through the synthesis of signatures. In this paper we propose a method based on motor equivalence model theory to generate static Bengali signatures. This theory divides the human action to write mainly into cognitive and motor levels. Due to difference between scripts, we have redesigned our previous synthesizer [1,2], which generates static Western signatures. The experiments assess whether this method can approach the intra and inter-personal variability of the Bengali-100 Static Signature DB from a performance-based validation. The similarities reported in the experimental results proof the ability of the synthesizer to generate signature images in this script.