## 3 Experiment Setup
a is the linear coefficient and b is the nonlinear coefficient that minimize the correlation between \(D_{raw}\) and \(\frac{I_{raw}}{a*(D_{raw})^{-b}}\)  
\[I_{comp}=\frac{I_{raw}}{a*(D_{raw})^{-b}};\;\text{where}\;a,b=\underset{a,b}{ \text{argmin}}\;Correlation(\frac{I_{raw}}{a*(D_{raw})^{-b}},D_{raw}) \tag{1}\]  
Ideally, the intensity variation caused by the distance variation between the participants' faces and the light source should be inversely proportional to the square of the distance (i.e., inverse square law of light propagation). However, in reality, skin conditions as well as the illumination angle change from person to person [35; 36] and we found that different values of the nonlinear coefficients are needed to minimize the correlation between the \(D_{raw}\) and \(I_{comp}\) across different participants. In this study, the range of the nonlinear coefficient is set between 0.1 and 5. Based on the above logic, we compensate for the motion artifact and extract HR using the following steps (Figure 6): (a) ROI-1 is defined and tracked in all frames using a Kanade-Lucas-Tomasi feature tracker [37]; (b) the intensity across pixels within ROI-1 is averaged; (c) within a time window, using the relationship described in Equation (1), we calculate the compensated intensity \(I_{comp}\) that has the minimum correlation between the depth signal \(D_{raw}\) and \(I_{comp}\); (d) a bandpass filter between 40 BPM and 150 BPM (which is the common resting HR range) is applied to the compensated signal \(I_{comp}\); (e) a Fourier transform of the data is taken on the motion-compensated intensity signal \(I_{comp}\) to find the HR, where HR is determined as the frequency component with the highest amplitude. In this study, we compare the performance of the motion-compensated HR results against the results that \"do not use the motion compensation\". The results that \"do not use motion compensation\" refer to HR reading derived using the same steps above except for the step of using the depth information to compensate for the motion artifacts. RR extraction is more straightforward as we directly measure the chest wall movement from respiration using the depth signal from the chest region. Specifically, RR is extracted using the following steps (Figure 7): (a) ROI-2 is defined and tracked in all frames; (b) calculate the average depth across all pixels within ROI-2; (c) apply Fourier transform to the depth signal and apply bandpass filter between 5 BPM to 30 BPM to find the highest peak as the RR value. Figure 6: HR extraction process from the 3D video streams of a ToF camera. To test the effectiveness of the HR/RR monitoring system, 29 participants from varying demographics were recruited in the study so that performance among different skin colors, genders, and ages could be compared. The study is approved by the Institutional Review Board at the University of Michigan and informed consent was obtained from every participant. All 29 participants were classified as either lighter skin color group or darker skin color group based on their Fitzpatrick skin type, a numerical classification for skin type based on a self-reported questionnaire [38]. Participants with skin type I-III were classified into the lighter skin color group, while participants with skin type IV-VI were classified into the darker skin color group. A total of 17 participants in this study were within the lighter skin color group, while the remaining 12 participants were considered as being within the darker skin color group. In terms of gender, 18 participants were male and 11 participants female. As for age, we recruited participants from 18 years old to 72 years old. All participants were divided into groups older than 35 years old and younger than 35 years old. In this study, 8 participants were older than 35 years old and the remaining 21 participants were younger than 35 years old. The demographics of the participants are shown in Table 3. A total of 10 60 s videos at 10 frames per second are obtained from each participant.