## 4 Results
### Cylinder
#### 4.1.2 Flow Transition Localization
In order to compare the results of the located flow transition line in the entire flow visualization, the two introduced localization methods were repeated for each row of the temporal mean value, temporal standard deviation and PC 2 flow visualization image in Figure 5. The localization results are shown in Figure 7 with a single thermographic raw image as background and the located flow transition lines plotted in red for the mean value, blue for the temporal standard deviation and green for the PCA flow visualization result. A comparison shows that the locations of the flow transition lines in the flow visualizations based on the two classical methods have a higher random and systematic error than those in the results based on the PCA. Consequently, the lowest systematic error \(\sigma_{\text{syst}}\) for either localization method in any of the classical image processing flow transitions amounts to \(8.33^{\circ}\) for the intensity gradient approximation of the mean value, while the localization based on the intensity approximation in the PCA is the lowest with \(3.58^{\circ}\). The random error \(\sigma_{\text{rand}}\) of the PCA result is also lower than in the classical methods with \(0.06^{\circ}\). The minimal random error in any of the classical methods' flow visualizations is \(1.24^{\circ}\) for the approximation of the intensity gradient of the mean value. An overview over all errors is given in table 1. To conclude, the PCA image processing is able to create a flow visualization with an increased CNR between the laminar and turbulent flow regime that maximizes the global distinguishability. As a result, the approximation of the intensity profile as well as the \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{\(\theta_{\text{tr}}\) in \({}^{\circ}\)} & \multicolumn{3}{c}{\(\sigma_{\text{rand}}\) in \({}^{\circ}\)} & \multicolumn{3}{c}{\(\sigma_{\text{syst}}\) in \({}^{\circ}\)} \\ \cline{2-10}  & **Mean** & **std** & **PCA** & **Mean** & **std** & **PCA** & **Mean** & **std** & **PCA** \\ \hline Intensity approximation & 140.7 & 119.4 & 113.1 & 10.78 & 39.84 & 0.22 & 31.26 & 9.93 & **3.58** \\ Intensity gradient approximation & 117.8 & 118.6 & 114.4 & 1.24 & 34.14 & **0.06** & 8.33 & 9.59 & 4.89 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Located flow transition position \(\theta_{\text{tr}}\) and corresponding random and systematic error \(\sigma_{\text{rand}}\) and \(\sigma_{\text{syst}}\) by means of both localizations methods for each image processing methods’ resulting flow visualization in the cylinder object experiment at a \(\text{Re}=5.1\times 10^{5}\). Temporal mean value (mean), temporal standard deviation (std) and PCA. All values are normalized to the angular position [0\({}^{\circ}\),180\({}^{\circ}\)] on the cylinder. Figure 7: Comparison of the located laminar turbulent flow transition line by means of the temporal mean value (red), temporal standard deviation (blue) and PCA (green) flow visualization of the image series. Flow transition localization based on the approximation of the intensity profile (top) and approximation of the intensity gradient profile (bottom). For both methods, the localization in the PCA result has qualitatively the lowest random and systematic error. intensity gradient profile are able to auto-position themselves around the flow transition and minimize the systematic error of the flow transition localization in the PCA result. Additionally, the steep intensity step between the flow regimes is increased in the PCA-based flow visualization, minimizing the random error of the flow transition localization with both localization methods. The PCA image processing therefore enables a more robust flow transition localization in the considered measurement configuration.