AirSignatureDB: 3D Signature Resources

• AirSignatureDB is a dual-use resource defined by a captured T3AAS-v1 corpus and synthetic databases that support 3D on-air signature acquisition and verification.
• The captured dataset uses stereo-vision with a custom pen tool to record pen tip and tail trajectories, processed through the two-stream SliT-CNN for robust biometric performance.
• The synthetic databases employ the Sigma-Lognormal model with full, kinematic, and duplicated synthesis modes to generate neuromotor-plausible signatures and improve data augmentation.

AirSignatureDB denotes a line of 3D on-air signature resources introduced in two distinct 2024 studies. In one usage, the name refers to a captured stereo-vision corpus denoted T3AAS-v1, built around simultaneous observation of pen tip and pen tail trajectories and benchmarked with the SliT-CNN architecture (Atreya et al., 2024). In the other, it refers to synthetic 3D on-air signature databases generated from 3DIIT-Signatures and Deep3DSigAir through a Sigma-Lognormal synthesis framework, including full synthesis, kinematic synthesis, and duplicated synthesis (Ferrer et al., 2024). Taken together, these resources situate AirSignatureDB at the intersection of biometric acquisition, trajectory modeling, and automatic signature verification.

1. Terminological scope and research context

The term AirSignatureDB is not used uniformly across the cited literature. In "Enhancing 3D-Air Signature by Pen Tip Tail Trajectory Awareness: Dataset and Featuring by Novel Spatio-temporal CNN," it denotes a newly collected 3D air-signature corpus, explicitly denoted T3AAS-v1, acquired with a stereo camera and a custom pen tool that exposes both tip and tail trajectories (Atreya et al., 2024). In "Synthesis of 3D on-air signatures with the Sigma-Lognormal model," it denotes synthetic databases that reproduce the user counts and genuine/forgery structure of pre-existing 3D on-air signature collections, namely 3DIIT-Signatures and Deep3DSigAir (Ferrer et al., 2024).

This dual usage is significant because it separates two complementary research objectives. The captured corpus addresses acquisition, representation, and discriminative modeling under a concrete sensing setup. The synthetic corpus addresses data generation, augmentation, and the neuromotor plausibility of artificial 3D signatures. A common misconception is to treat AirSignatureDB as a single homogeneous benchmark; the literature instead uses the name for both a real stereo-vision dataset and a family of synthetic counterparts.

2. Captured stereo-vision corpus: T3AAS-v1

The captured AirSignatureDB, or T3AAS-v1, was created to capture both the pen tip and pen tail trajectories in three dimensions without requiring specialized wearable sensors (Atreya et al., 2024). The acquisition setup uses a Zed2 stereo-vision camera with VGA output at up to 100 fps, typically operating at $\geq 60$ fps after rendering feedback, and a custom pen tool consisting of a lightweight stick with two color-coded spheres, orange for the tip end and green for the tail end. During capture, the stereo SDK performs one-time lens-distortion correction and epipolar alignment, while auto white balance remains enabled.

Forty-five volunteer signers each contributed 25 genuine English signatures in a single session. For skilled forgery, 12 imitations per genuine user were collected after practice by forgers. Of the 25 genuine samples per user, 16 were reserved for training, 4 for validation, and 5 for testing.

Aspect	Specification	Notes
Acquisition hardware	Zed2 stereo camera	VGA, up to 100 fps, typically $\geq 60$ fps
Writing instrument	Custom pen tool	Orange tip sphere, green tail sphere
Genuine data	45 signers, 25 genuine signatures each	Single session
Skilled forgery	12 imitations per user	Practiced by forgers
Split	16 train / 4 validation / 5 test	Per user

The raw acquisition pipeline is frame-based. The stereo camera outputs synchronized left and right frames. For each frame, a simple HSV-based bandpass filter isolates each colored ball, followed by morphological cleanup and circle fitting using Davies–Er’s modified Hough method. Each signature is stored as a CSV with one row per stereo frame and 12 columns: $(x, y, r)$ for green/left, orange/left, green/right, and orange/right, all normalized by frame dimensions as $(x/\text{width}, y/\text{height}, r/\text{height})$. When the tail ball is occluded, the representation records $(-1,-1,-1)$ tuples.

Several standardized preprocessing forms are derived from the raw sequence. These are the raw 12-column CSV, a 2D interpolated pen-tip trace obtained by a B-spline through the 2D tip positions from the left camera, a 3D tip-tail trajectory CSV reconstructed by disparity $(x_{\text{right}}-x_{\text{left}})$ and stored as a 6-column CSV per timestamp, and a 3D interpolated tip-tail spline in which both tip and tail trajectories are resampled to a fixed length, commonly 512 points. This suggests that the corpus is designed not only as a benchmark dataset but also as a representation testbed spanning stereo measurements, reconstructed 3D trajectories, and interpolation-normalized inputs.

3. Trajectory representation and the SliT-CNN framework

In the SliT-CNN formulation, each sample is cast as a time sequence of six-dimensional vectors formed by the 3D positions of the tip and tail (Atreya et al., 2024):

$$p_{\text{tip}}(t) = [X_{\text{tip}}(t), Y_{\text{tip}}(t), Z_{\text{tip}}(t)]^\top,$$

$$p_{\text{tail}}(t) = [X_{\text{tail}}(t), Y_{\text{tail}}(t), Z_{\text{tail}}(t)]^\top.$$

Spatial derivatives define instantaneous velocity and acceleration,

$$v(t) = \frac{d\,p(t)}{dt}, \qquad a(t) = \frac{d^2\,p(t)}{dt^2},$$

although only the positional channels are directly used in the SliT-CNN framework. After resampling, each stream forms a fixed-size tensor of shape $(T \times 3)$ with $\geq 60$0.

SliT-CNN—short for Sliding Time CNN—is a 2D convolutional network that treats the time axis as one spatial dimension and the coordinate channels as the other. In the two-stream variant, tip and tail trajectories are processed separately before late fusion. Per stream, the architecture uses:

• Input: tensor of shape $\geq 60$1, with $\geq 60$2
• Conv Layer 1: 64 filters of size $\geq 60$3, stride $\geq 60$4, LeakyReLU, then layer normalization
• Conv Layer 2: 128 filters of size $\geq 60$5, stride $\geq 60$6, LeakyReLU, then max-pooling $\geq 60$7
• Flatten $\geq 60$8 LeakyReLU $\geq 60$9 Dropout $(x, y, r)$0 $(x, y, r)$1 Fully Connected (512-dim) $(x, y, r)$2 Softmax

The two 512-dimensional stream outputs are concatenated into a 1024-dimensional joint representation, followed by a final fully connected layer with Softmax to produce class probabilities over the 45 signers, or binary genuine/forgery decisions depending on the task.

Training uses cross-entropy loss and the Adam optimizer with $(x, y, r)$3, $(x, y, r)$4, and initial learning rate $(x, y, r)$5. The reported augmentation protocol rotates each trajectory about the origin by $(x, y, r)$6, $(x, y, r)$7, $(x, y, r)$8, $(x, y, r)$9, $(x/\text{width}, y/\text{height}, r/\text{height})$0 and scales along $(x/\text{width}, y/\text{height}, r/\text{height})$1 or $(x/\text{width}, y/\text{height}, r/\text{height})$2 by factors 0.95, 1.00, 1.05, yielding 30$(x/\text{width}, y/\text{height}, r/\text{height})$3 augmentation. Early stopping via validation set is used, and the best checkpoint is selected for testing. The absence of velocity and acceleration channels in the CNN input, despite their explicit formulation, indicates a design choice favoring direct spatio-temporal encoding of resampled coordinates.

4. Benchmarking on captured and external datasets

The benchmark protocol for the captured AirSignatureDB reports recognition accuracy and Equal Error Rate (EER) for random and skilled forgery verification, with Receiver Operating Characteristic (ROC) curves plotted per dataset (Atreya et al., 2024). On T3AAS-v1, the main reported results are as follows.

Method	Accuracy	EER
Interpolated TipTail Simple GRU	90.94%	random 6.25%, skilled 10.36%
Single-stream SliT-CNN	93.72%	random 4.68%, skilled 5.21%
Two-stream SliT-CNN	97.21%	random 1.74%, skilled 2.30%
VGG16 on 2D splines	98.60%	random 0.86%, skilled 0.71%

These results place the two-stream SliT-CNN substantially above the Simple GRU baseline on the captured corpus, while VGG16 on 2D splines attains the highest reported accuracy and the lowest reported EER at the cost of 134 M parameters. The paper also reports external benchmarking. On LeapMotionAirSignature, the two-stream SliT-CNN achieves 90.95% accuracy with $(x/\text{width}, y/\text{height}, r/\text{height})$4, compared with 4.27% for Simple GRU, while VGG16 again reaches higher accuracy at approximately 97.49% but at more than 134 M parameters. On SVC 2004, where online pen trajectories are projected into 3D, single-stream SliT-CNN reaches 95.94% accuracy, $(x/\text{width}, y/\text{height}, r/\text{height})$5, and $(x/\text{width}, y/\text{height}, r/\text{height})$6, whereas PenTip Simple GRU attains 96.87% accuracy, $(x/\text{width}, y/\text{height}, r/\text{height})$7, and $(x/\text{width}, y/\text{height}, r/\text{height})$8.

A reported ablation study concludes that jointly modeling tip and tail in two streams yields approximately 3–4% absolute gain in accuracy and up to 4% reduction in EER relative to single-stream and non-augmented variants, with only a modest increase in parameters of about 4 M and modest increase in inference time. This suggests that the tail trajectory contributes discriminative structure that is not fully recoverable from pen-tip dynamics alone.

5. Synthetic AirSignatureDB and the Sigma-Lognormal model

The synthetic usage of AirSignatureDB is grounded in the Sigma-Lognormal model, which treats each stroke as a neuromotor command with a bell-shaped velocity profile and extends the formulation to 3D on-air signing (Ferrer et al., 2024). The synthetic databases replicate the user and sample cardinalities of two publicly available corpora.

Source collection	Real-data structure	Synthetic AirSignatureDB counterpart
3DIIT-Signatures	80 genuine writers, 20 genuine repetitions each	80 virtual signers, each with 20 genuine synthetic 3D signatures
Deep3DSigAir	40 genuine users, split into 10 for training and 10 for testing, 25 skilled forgeries per user	40 virtual signers, each with 10 synthetic train-genuine, 10 test-genuine, and 25 synthetic skilled-forgeries

For 3DIIT-Signatures, acquisition uses a Leap Motion controller at $(x/\text{width}, y/\text{height}, r/\text{height})$9 Hz, with a right-handed Cartesian $(-1,-1,-1)$0 coordinate system in millimetres, stored as CSV rows $(-1,-1,-1)$1. For Deep3DSigAir, acquisition uses an Intel Creative senz3D depth camera, also at $(-1,-1,-1)$2 Hz, with the same $(-1,-1,-1)$3 format. For augmentation experiments, up to 10 duplicates per genuine signature are generated through the DS method.

The model gives the instantaneous speed of stroke $(-1,-1,-1)$4 as

$(-1,-1,-1)$5

where $(-1,-1,-1)$6 is the arc length between target points, $(-1,-1,-1)$7 is the temporal onset of the lognormal pulse, and $(-1,-1,-1)$8 and $(-1,-1,-1)$9 encode the log-scale and log-variance of the neuromuscular response. Adjacent strokes overlap in time, so the total velocity is $(x_{\text{right}}-x_{\text{left}})$0. Once the stroke velocities are known, the sampled 3D arcs reconstruct the complete signature trajectory as

$(x_{\text{right}}-x_{\text{left}})$1

AirSignatureDB is assembled through three synthesis modes. Full Synthesis (FS) draws 2D virtual target points using real-signature statistics, projects them onto a 3D sinusoidal surface, connects successive points by planar circular arcs, assigns timestamps with $(x_{\text{right}}-x_{\text{left}})$2 s, computes $(x_{\text{right}}-x_{\text{left}})$3, $(x_{\text{right}}-x_{\text{left}})$4, $(x_{\text{right}}-x_{\text{left}})$5, and samples each stroke at $(x_{\text{right}}-x_{\text{left}})$6 Hz. Kinematic Synthesis (KS) takes a known 3D trajectory, detects salient points by multi-scale curvature peaks in the $(x_{\text{right}}-x_{\text{left}})$7, $(x_{\text{right}}-x_{\text{left}})$8, and $(x_{\text{right}}-x_{\text{left}})$9 projections, fits lognormal strokes, and resamples the trajectory. Duplicated Synthesis (DS) perturbs an existing iDeLog3D parameterization by controlled randomness $$p_{\text{tip}}(t) = [X_{\text{tip}}(t), Y_{\text{tip}}(t), Z_{\text{tip}}(t)]^\top,$$0, deletes or inserts up to 5% of target points, and applies a sinusoidal warp plus small random 3D rotation and translation. The paper further states that the proposal is also valid for synthesizing 3D air writing and gestures.

6. Evaluation, availability, limitations, and use cases

The synthetic AirSignatureDB is evaluated with a DTW-based ASV system using $$p_{\text{tip}}(t) = [X_{\text{tip}}(t), Y_{\text{tip}}(t), Z_{\text{tip}}(t)]^\top,$$1 and first and second derivatives as features, trained on 5 random genuine per user and tested on the remaining genuine signatures plus all forgeries, with 10 repetitions and average DET curves and EER reported (Ferrer et al., 2024). A Manhattan-distance verifier is also tested for generalization.

On the 3DIIT-Signatures subset, the reported EER is approximately 15.37% for the real data, 15.89% for the KS DB, and 14.20% for the FS+DS DB. On the Deep3DSigAir subset, the real random-forgery EER is 0.32%, compared with 0.31% for KS DB and 0.27% for FS+DS DB; the real skilled-forgery EER is 5.06%, compared with 5.45% for KS DB and 3.80% for FS+DS DB. When each genuine is augmented with 10 DS duplicates, the DTW-ASV EER drops from 15.37% to 5.10% on 3DIIT, from 0.32% to 0.27% for Deep3DSigAir random, and from 5.06% to 1.91% for Deep3DSigAir skilled.

A human perception test further evaluates realism. In Part I, using 12 one-shot videos, the False-Machine Rate (FMR) is 47.65% and the False-Human Rate (FHR) is 45.67%. In Part II, using 5 paired videos and asking which sample is machine-generated, the average accuracy is 56.32%, described as near chance. A plausible implication is that the synthetic signatures can function not only as algorithmic augmentation but also as perceptually credible surrogates in controlled experimental settings.

Availability differs by resource. The captured T3AAS-v1 dataset and benchmarking code are publicly available at https://github.com/atrey-a/T3AAS-v1-benchmarking (Atreya et al., 2024). The synthetic databases AirSignatureDB-3DIIT and AirSignatureDB-Deep3DSigAir, together with the FS, KS, and DS synthesizer code, are released for non-commercial research at https://github.com/ulpgc-ideTIC/AirSignatureDB (Ferrer et al., 2024). Reported use cases for the captured corpus include touchless authentication in augmented and virtual reality, pen-based gesture security, and low-cost in-air signature systems for devices lacking tactile surfaces. Reported limitations include sensitivity to occlusions, especially when the tail ball disappears, and the requirement of a stereo camera setup. The authors of the captured-dataset study nonetheless characterize the resource as one of the first large-scale 3D pen tip-tail signature corpora, and describe SliT-CNN as an efficient spatio-temporal feature extractor suitable for edge-embedded biometric authentication.