## 3 Different Aspects of Colour-Based Method
### Both Illumination Variations and Motion Artefacts
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Ref.**} & **Used Sensors with Parameter** & **Vital Signs** & **ROIs** & **Used Technique** & **Distance (m)** & \
\begin{tabular}{c} **No. of** \\ **Participants** \\ **at a Time** \\ \end{tabular} & **Results** \\ \hline \multirow{2}{*}{[PERSON] et al. [95]} & \multirow{2}{*}{Digital camera 30 fps} & \multirow{2}{*}{HR} & \multirow{2}{*}{Brow area} & EEMD & 0.07–0.09 m & 1 & PCC = 0.91 \\ \cline{1-1} \cline{5-7}  & & & & & & \\ \cline{1-1} \cline{5-7}  & & Digital camera & & & & & \\ \cline{1-1} \cline{5-7}  & Resolution 1280 \(\times\) 720 & & & & & & \\ \hline \multirow{2}{*}{[PERSON] et al. [92]} & Digital camera & & & & & & \\  & Resolution 5 & HR, RR, &
\begin{tabular}{c} Forehead \\ and cheek \\ \end{tabular} & & & & & & \\  & & and cheek & & & & \\  & & & & & & \\ \hline \multirow{2}{*}{[PERSON] et al. [93]} & Webcam resolution & & & & & & \\  & 640 \(\times\) 480, 30 fps & & & & & \\ \cline{1-1} \cline{5-7}  & & & & & & & \\ \hline \multirow{2}{*}{[PERSON] et al. [94]} & Webcam resolution & & & & & & \\  & 640 \(\times\) 480, 30 fps & & & & & & \\ \cline{1-1} \cline{5-7}  & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: iPPG based methods concern about illumination variations. To explain how CCA works as BSS [100], let us consider \(j\) and \(k\) to be two multidimensional random signals with \(N\) mixtures. The linear combinations of these signals are known as the canonical variates and can be written as follows:  
\[j = W_{j_{1}}j_{1}\ +\ W_{j_{2}}j_{2}\ +\ \ldots\ W_{j_{N}}j_{N}\ =\ W_{j}^{T}j \tag{7}\] \[k = W_{k_{1}}k_{1}\ +\ W_{k_{2}}k_{2}\ +\ \ldots\ W_{k}k_{N}\ =\ W_{k}^{T}k \tag{8}\]  
where the weighting vectors of \(j\) and \(k\) are \(W_{j}\ =\ \left[W_{j_{1}},W_{j_{2}},W_{j_{N}}\right]^{T}\) and \(W_{k}\ =\ \left[W_{k_{1}},W_{k_{2}},W_{k_{N}}\right]^{T}\), respectively, which maximise the correlation between \(j\) and \(k\) by resolving the following maximisation problem:  
\[\rho\ =\ cor\ (j,k)\ =\ max_{W_{j},W_{k}}cor\ (j,k)\ =\ \frac{E[k]}{ \sqrt{\left[E^{j}\right]E[k^{2}]}}\] \[=\ \frac{W_{j}^{T}C_{k}W_{k}}{\sqrt{\left(W_{j}^{T}C_{j}W_{j} \right)\left(W_{j}^{T}C_{k}W_{k}\right)}} \tag{9}\]  
where the non-singular within-set covariance matrices of \(j\) and \(k\) are \(C_{jj}\) and \(C_{kk}\), respectively; \(C_{jk}\) is the between-sets covariance matrix; and \(E\) represents the expected value operator of the corresponding variables. The maximisation problem with respect to \(W_{j}\) and \(W_{k}\) can be resolved as follows:  
\[\left[ \begin{array}{cc}C_{jj}&0\\ 0&C_{kk}\end{array} \right]^{-1}\!\!\left[ \begin{array}{cc}0&C_{jk}\\ C_{kj}&0\end{array} \right]\left[ \begin{array}{c}\widehat{W}_{j}\\ \widehat{W}_{k}\end{array} \right]\ =\ \rho\left( \begin{array}{c}\widehat{W}_{j}\\ \widehat{W}_{k}\end{array} \right) \tag{10}\]  
After solving Equation (10), a complete explanation of the canonical correlations can be written as follows:  
\[\left\{ \begin{array}{cc}C_{jj}{}^{-1}C_{jk}\widehat{W}_{k}\ =\ \rho\widehat{W}_{j}\\ C_{kk}{}^{-1}C_{kj}\widehat{W}_{j}\ =\ \rho\widehat{W}_{k}\end{array} \right. \tag{11}\]  
The \(K\) approximations of the source signals, \(z_{i}(t)\), \(i\) = 1,2,..., \(K\), can be obtained by:  
\[z_{i}(t)\ =\ \widehat{W}_{j}^{T}j(t)\approx_{i}(t) \tag{12}\]  
It is noted from Equation (12) that the CCA technique yields the same outcome when employed with a given dataset; which is not possible in case of the ICA technique. Furthermore, spectral analysis and filtering were done using FFT and two Butterworth bandpass filters, respectively. Finally, HR and RR were extracted using a peak detection algorithm. To obtain experimental results, the authors considered 15 subjects with different skin tones in four different  
Figure 7: System overview of the noise removal technique using a UAV [97]. scenarios such as without movement, different facial expressions, talking and different illumination levels.