---
title: 'AirSignatureDB: 3D Signature Resources'
url: https://www.emergentmind.com/topics/airsignaturedb
type: topic
---

# AirSignatureDB: 3D Signature Resources

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 [2401.02649]. 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 [2401.16329]. 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 [2401.02649]. 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** [2401.16329].

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 [2401.02649]. 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 [2401.02649]:

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

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

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 **$T=512$**.

**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 **$(T \times 3)$**, with **$T=512$**
- **Conv Layer 1**: **64 filters** of size **$3 \times 30$**, stride **$(1,1)$**, **LeakyReLU**, then **layer normalization**
- **Conv Layer 2**: **128 filters** of size **$1 \times 8$**, stride **$(1,1)$**, **LeakyReLU**, then **max-pooling $(2 \times 1)$**
- **Flatten $\rightarrow$ LeakyReLU $\rightarrow$ Dropout $(p=0.25)$ $\rightarrow$ Fully Connected (512-dim) $\rightarrow$ 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 **$\beta_1 = 0.9$**, **$\beta_2 = 0.999$**, and initial learning rate **$10^{-5}$**. The reported augmentation protocol rotates each trajectory about the origin by **$-10^\circ$, $-5^\circ$, $0^\circ$, $5^\circ$, $10^\circ$** and scales along **$(x,z)$** or **$(y,z)$** by factors **0.95, 1.00, 1.05**, yielding **30$\times$ 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 [2401.02649]. 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 **$\text{EER}_{\text{random}} = 5.44\%$**, 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**, **$\text{EER}_{\text{random}} = 2.71\%$**, and **$\text{EER}_{\text{skilled}} = 3.30\%$**, whereas **PenTip Simple GRU** attains **96.87% accuracy**, **$\text{EER}_{\text{random}} = 2.87\%$**, and **$\text{EER}_{\text{skilled}} = 3.01\%$**.

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 [2401.16329]. 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 **$f_m = 60$ Hz**, with a right-handed Cartesian **$(x,y,z)$** coordinate system in **millimetres**, stored as CSV rows **$[t,x,y,z]$**. For **Deep3DSigAir**, acquisition uses an **Intel Creative senz3D depth camera**, also at **$f_m = 60$ Hz**, with the same **$(x,y,z)$** 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 $j$ as

$$
v_j(t) =
\frac{D_j}{\sigma_j \sqrt{2\pi}\cdot (t-t_{0,j})}
\cdot
\exp\left\{
-\frac{1}{2}
\left[
\frac{\ln(t-t_{0,j})-\mu_j}{\sigma_j}
\right]^2
\right\},
$$

where **$D_j$** is the arc length between target points, **$t_{0,j}$** is the temporal onset of the lognormal pulse, and **$\mu_j$** and **$\sigma_j$** encode the log-scale and log-variance of the neuromuscular response. Adjacent strokes overlap in time, so the total velocity is **$\sum_j v_j(t)$**. Once the stroke velocities are known, the sampled 3D arcs reconstruct the complete signature trajectory as

$$
(x_r(t), y_r(t), z_r(t)) = \sum_{j=1}^{N} (x_j(t), y_j(t), z_j(t)).
$$

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 **$N(0.1, 0.005)$ s**, computes **$D_j$, $\mu_j$, $\sigma_j$**, and samples each stroke at **$f_m$ Hz**. **Kinematic Synthesis (KS)** takes a known 3D trajectory, detects salient points by multi-scale curvature peaks in the **$xy$**, **$xz$**, and **$yz$** projections, fits lognormal strokes, and resamples the trajectory. **Duplicated Synthesis (DS)** perturbs an existing **iDeLog3D** parameterization by controlled randomness **$m \in (0,1)$**, 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 **$x,y,z$** 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 [2401.16329]. 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** [2401.02649]. 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** [2401.16329]. 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**.

Source: https://www.emergentmind.com/topics/airsignaturedb