## 3 Different Aspects of Colour-Based Method  
### Motion Artefacts  
There are some studies that treat motion artefacts as a serious issue that have proposed various methods to suppress the motion artefacts based on blind source separation (BSS) or model-based methods, listed in Table 2.  
[PERSON] et al. [69] proposed an automatic and robust method to measure HR using a webcam considering three subjects at a time. They first introduced a novel method to remove motion artefacts using BSS based on independent component analysis (ICA). In their proposed method, first, the region of interest (ROI) is automatically detected using a face tracker. They used the OpenCV face detection algorithm which is based on the Viola and Jones (V-J) [52] method. The facial ROI is defined as a rectangular bounding box. Then, the ROI is decomposed into the RGB channels and spatially averaged to obtain the raw RGB traces. After that, ICA is applied on the normalised RGB traces to recover three independent source signals. To show how ICA [73] works as BSS, let us consider that source signals, \(s_{i}(t)\) = \([s_{1}(t),s_{2}(t),\ldots,s_{k}(t)]\), are independently transmitted by \(K\) sources. The observed signals, \(x_{i}(t)\) = \([x_{1}(t),x_{2}(t),\ldots,x_{k}(t)]\), by various sensors, \(i\) = 1, 2, \(\ldots\), \(K\) can be written as follows:  
\[x_{i}(t)\ =\ As_{i}(t) \tag{5}\] \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Ref.**} & **Used Sensors with** & **Vital Signs** & **ROIs** & **Used Technique** & **Distance (m)** & \begin{tabular}{c} **No. of** \\ **Participants** \\ **at a Time** \\ \end{tabular} \\ \hline \begin{tabular}{c} [PERSON] \\ et al. [68] \\ \end{tabular} & CCD 15 or 30 fps & HR and RR & \begin{tabular}{c} Face and \\ forehead \\ \end{tabular} & \begin{tabular}{c} Single/multichannel \\ analysis \\ \end{tabular} & 1-2 m & 1 \\ \hline \begin{tabular}{c} [PERSON] et al. \\ [70] \\ \end{tabular} & Webcam resolution & HR, RR and & Face & ICA & 0.5 m & 1 \\ \hline \begin{tabular}{c} [PERSON] et al. \\ [71] \\ \end{tabular} & Webcam resolution & HR & \begin{tabular}{c} Forehead, \\ nose and \\ mouth \\ \end{tabular} & ICA & 0.5 m & 1 \\ \hline \
\begin{tabular}{c} [PERSON] \\ et al. [72] \\ \end{tabular} & Webcam resolution & HR &
\begin{tabular}{c} Face and \\ forehead \\ \end{tabular} & PCA & 1 m & 1 \\ \hline \hline \end{tabular} Note: fps = frame rate; HR = heart rate; RR = respiratory rate.  
\end{table} 
Table 1: imaging photoplethysmography (iPPG) based methods under well controlled conditions. where mixing matrix \(A\) with column vectors \(a_{i}\) is unknown and \(n_{i}(t)\) is the additive noise. The observations, \(x(t)\), are mixtures or linear combinations of the source signals, \(s_{i}(t)\). To estimate \(A\) and \(s_{i}(t)\), it is assumed the all source signals are statistically independent and nongaussian. To reconstruct the source signals, \(u_{i}(t)\), the following expression can be used:  
\[u_{i}(t)\ =\ Wx_{i}(t)\ =\ W[As_{i}(t)]\approx_{i}(t) \tag{6}\]  
where \(W\) is the demixing matrix and it is the inverse of matrix \(A\). The joint approximate diagonalization of eigenmatrices (JADE) algorithm is then used to perform ICA. From three recovered independent source signals, the second component is always chosen as the desired source signal. Finally, FFT is used on the selected source signal to obtain the power spectrum. The pulse frequency is designated as the frequency that corresponds to the highest power in the spectrum within an operational frequency band. To conduct their experiment, [PERSON] et al. considered 12 participants remaining still and engaging in natural movement. Using Bland-Altman and correlation analysis, they compared the HR extracted from videos recorded by a basic webcam to an FDA-approved finger blood volume pulse (BVP) sensor and achieved high accuracy and correlation even in the presence of movement artefacts. They also measured the HR of multiple persons. The study considered small movements and did not consider illumination variations.