###### Abstract
To best replicate the experiment's procedure, the computer configuration used in the research is listed in Table 1. One of the novelties of our experiment involves converting the time sequence in-air signature signals into a visible three-dimensional signature representation based on the in-air signature trajectory restoration. Finger movement trajectory restoration is widely used in medical studies for patients with amyotrophic lateral sclerosis (ALS) disease [19]. In research by [PERSON] et al. [20], electrocorticography (ECoG) signals were obtained to investigate neural reactions while patients conducted finger movements. Finger trajectory was learned using CNN [21] and LSTM [22] models. Similarly, in the study by [PERSON] et al. [23], the neural reactions of patients during the movements could be observed based on EEG, which could be used as the database for training models. In our experiment, which is different from medical research fields using EEG, the in-air signature signals can be recorded by the accelerometer and gyroscope sensors embedded inside the smartwatch and the in-air signature trajectories can be restored based on the derivation of the acceleration signals (as covered later in the data processing section). In the study by [PERSON] et al. [5], the researchers proposed a new method called 3 DAirSig, which mainly uses multidimensional dynamic time warping (MD-DTW); they collected 600 signature samples taken from the participants. Similar to the study by [PERSON] et al. [24], in this experiment, the 3D spatial signals of the signatures were \begin{table}
\begin{tabular}{c c} \hline \hline  & **Computer Configurations** \\ \hline
**Item** & **Property** \\ \hline Processor & 12 th Gen Intel(R) Core(TM) i7-12700 KF 3.61 GHz \\ \hline Installed RAM & 32.0 GB (31.8 GB usable) \\ \hline System type & 64-bit operating system, x64-based processor \\ \hline GPU & NVIDIA GeForce RTX 3080 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Computer configurations. taken into consideration. The signal analysis was in real-time, and a convolutional neural network was used to track the finger trajectories. The experiment shows an equal error rate (EER) of 0.46%. [PERSON] et al. designed the software called MagiSign [2] for the experiment. The software is based on the magnetic sensor embedded in the mobile phones and the participants can accomplish the signing registration process by using the magnet to draw their signatures around the mobile phone. [PERSON] et al. [25] collected in-air signatures from 50 participants to form an in-air signature dataset, and 6 participants mimicked the signing processing of the 50 participants to form a forgery dataset. The researchers used the DTW algorithm and LCS algorithm for the recognition, and the DTW algorithm outperformed the LCS, which gave 2.80% EER. In the study by [PERSON] et al. [26], the researchers collected signatures from 100 participants via a Microsoft Kinect sensor, and a self-designed algorithm was applied to the experiment to find the area of the palm location; the experiment used motion history image (MHI) to classify the in-air signatures from those participants and it achieved 90.4% accuracy. [PERSON] et al. [27] investigated the effect of orientation on sensors and proposed an adaptive orientation method to learn and detect the pattern of data from different dimensions and process the sensor data separately based on each orientation. The ability and sensitivity of modern sensors to work as biometric confirmation have also been verified by [PERSON] et al. 's research [28], in which multi-layer perceptrons (MLPs) were implemented to recognize the user's identity through embedded sensors in portable devices. In the study by [PERSON] et al. [29], the effects of the spatial positions of portable devices were investigated through supervised learning, which helped improve the adaptability of in-air signatures in real applications. In the study by [PERSON] et al.