  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 .
