## 5 Discussion
For example, if we assume the user is sitting at 50 cm away from the camera, for the ToF camera with 149-degree diagonal FOV and half-inch imaging sensor size (diagonal), we could roughly calculate how many pixels the ROI landmarks will shift across two different frames using Equation (4), where \(D_{user}\) is the distance between the camera and the driver, \(\theta\) is the half angle of the horizontal field of view, \(L\) is the horizontal size of the imaging sensor, \(\mu\) is the pitch of the pixel, \(v\) is the velocity of the motion and \(FPS\) is the frame rate of the camera. \[N_{pixel}=ceiling(\frac{L}{D_{user}*2\mu*\tan(\theta)}*\frac{v}{FPS}) \tag{4}\]  
The above equation makes the rough estimation that the image fills the entire sensor, and the active area of the pixel is small. In this case, we consider the head of the user is moving at 50 cm/s (typical for a fast head turning), and Table 3 shows the number of pixels the ROI landmark would transit at different frame rates. The lower the frame rate, the larger the motion (more pixels transitioned) seen by the face tracking algorithm between two frames and, therefore, a higher possibility for the face tracker to output erroneous estimations of facial landmark positions [11]. The erroneous landmarks can cause the detected ROI-1 to change over time, leading to time-varying intensity changes in the measured signal. When the frame rate reaches 105 fps, the motion across two consecutive frames will not move more than 1 pixel across different frames. Of course, a higher frame rate does not solve all the challenges of HR measurements in NIR, but it should alleviate the burden of the motion compensation as well as the face tracking algorithm. In the future, with ToF cameras of higher resolution and the frame rate being developed [39], the robustness of tracking fast motion could be increased and reduce the effects of the driver's active motion on the HR measurements. Another potential improvement for the CVSM system proposed in this study is to combine the depth-based motion compensation with other post-processing methods to improve the reliability of the HR measurements. For example, in the 2020 study from [PERSON] et al. [11], a sparse matrix estimation method is used to further reject noise from \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Frame Rate (FPS)** & **15** & **30** & **60** & **105** \\ \hline Npixel & 7 & 4 & 2 & 1 \\ \hline Success Rate & 58.7\% & 68\% & 76\% & N/A \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Success rate and number of pixels transitioned across two consecutive frames at different frame rates. Figure 22: HR measurement error rate when participants drive on the highway recorded at 60 FPS (**left**), 30 FPS (**middle**) and 15 FPS (**right**). the remote PPG signal. The sparse matrix estimation method makes the assumption that the HR signal is common across different ROIs on the face while the noises/artifacts will differ within different ROIs. Therefore, by extracting the common signal across multiple ROIs, one can differentiate the HR signal from the external interferences. However, such method may not be directly applicable to the CVSM demonstrated in this study because the localized VCSEL source causes intensity from all regions on the face to change in a similar pattern against the motion from the user. If different ROIs on the face share the same artifacts/noise, the sparse frequency matrix method from [11] could still pick the artifacts/noises as the HR signal. For example, Figure 23 shows an example of an erroneous HR measurement using the sparse matrix estimation method. We extract intensity signals from three ROIs from cheek, nose and forehead, respectively, and apply the Autosparse PPG method from [9] to the extracted signals to find the common frequency components across these three ROIs. Figure 23a shows that the signals from the cheek, nose and forehead show similar patterns of artifacts.