## 3 Results  
To demonstrate the feasibility of signature-based (and, more generally, handwriting-based) person recognition, we applied Dynamic Time Warping (DTW) to compute the distance between the vectors for each person's trial. DTW is a method used to compare two sequences of data even if they vary in length. For example, if two people sign their names at different speeds, DTW can align the signatures for comparison regardless of time differences. Following this, we calculated the average intra-person and inter-person distances for comparison. DTW is effective for comparing time-varying sequences, allowing us to capture subtle differences in handwriting dynamics both within the same person (intra-person) and between different individuals (inter-person). For sensors that capture multi-axis data, such as magnetometers, accelerometers, and gyroscopes, we computed the magnitude to simplify the complex multidimensional data. Magnitude represents a scalar quantity derived from measurements along the X, Y, and sometimes Z axes, depending on the sensor type, which were calculated as  
\[\text{Magnitude}=\sqrt{X^{2}+Y^{2}+Z^{2}}\]  
where \(X,Y\), and \(Z\) are the measurements along the X, Y, and Z axes, respectively. This unified metric consolidates all directional components into a single value, making it easier to compare overall motion characteristics. By using magnitude, we can more effectively assess and compare variability in movement between different individuals. In the following paragraphs, we present the results of the DTW analysis, including graphs that visually confirm our findings. Although based on a small sample size, the results demonstrate clear similarities in handwriting dynamics within the same individual and noticeable differences between various users. These observations are supported not only by the numerical values but also by the graphical representations, which further validate the consistency of intra-person similarities and inter-person differences. The analysis was conducted on sensor measurements collected during the task of writing the phrase \"We trust you\" using both a stylus and a finger across 5 different attempts by each of 5 users. In accordance with what has been mentioned, the apparatus makes use of a smartwatch to gather data by using the accelerometer and gyroscope. Figure 7 displays the acceleration in three directions for three distinct users during various attempts to write the phrase \"We trust you\". Upon examining the acceleration values in the X, Y, and Z directions, it is evident that the observed data exhibit a high degree of similarity across the three writing trials peformed by the same individual. While consistency is observable among identical  
Figure 6: A study volunteer practices writing at the beginning of the experiment using a stylus. A participant writing a phrase utilizing the proposed apparatus in a controlled environment (**left**). The perspective of the smartphone camera when detecting the AruCo market (**right**). users, there are certain variations in attempts made by different subjects. Since the writing pace is likely to change from one user to the next, the sensor readings reflect this variability. Table 3 compares the intra-person and inter-person variability for accelerometer measurements across the X, Y, and Z axes, as well as the magnitude, using a stylus and a finger. It is evident that intra-person variability is consistently lower than inter-person variability across all measurements. For example, with the stylus, the intra-person variability for the magnitude is 8.50, while the inter-person variability is substantially higher at 117.23. Similarly, for the finger, the intra-person variability for the magnitude is 4.70 compared to 124.68 for inter-person variability. These results highlight that while individuals show consistent measurements in their trials, differences between individuals introduce considerable variability.