## 3 Experimental Setup
### Implementation
#### 3.2.2 Method B: Image Rotation and 1D Gradient Evaluation  
For the gradient evaluation method B, the thermographic image is rotated around the three rotation angles \(\alpha=0^{\circ}\), \(\alpha=\alpha_{1}\), and \(\alpha=\alpha_{2}\), see Figure 3, each time aligning another group of transition segments parallel to the \(x^{\prime}\)-axis of the rotated image and hence perpendicular to the vertical \(y^{\prime}\)-axis. By conducting a subsequent column-wise gradient evaluation of the \(\sigma=1\) px Gauss-filtered temperature profiles \((\text{T})_{j}\) for the \(j=1,...,J\) columns of the rotated image, the position of all local gradient maxima above the threshold \(\delta t_{\text{pre}}\) are saved. Because of the perpendicular alignment between the evaluation line and the respective transition segments, the local temperature gradients at the positions of the flow transition are maximized. The evaluation of all columns yields the collection of all local gradient maxima of the rotated image below the threshold. The gradient threshold \(\delta t_{\text{nat}}\) used for the rotation angle \(\alpha=0^{\circ}\) is higher than for the other rotation angles \(\alpha_{1}\) and \(\alpha_{2}\). This achieves a more robust detection of the natural flow transitions in the columns without a premature transition as the natural flow transition tends to develop a higher temperature gradient. The lower threshold \(\delta t_{\text{pre}}\) for the two rotation angles \(\alpha_{1}\) and \(\alpha_{2}\), on the other hand, preserves a higher sensitivity towards low gradients that can develop due to the premature flow transitions of low-contrast turbulence wedges. Combining all gradients of the \(\alpha_{1}\) and \(\alpha_{2}\) rotation yields all local gradient maxima positions \(\Delta_{\text{pre}}\) representing the premature flow transitions. The local gradient maxima positions representing the natural flow transition which are obtained by the rotation angle \(\alpha=0^{\circ}\) are further noted as \(\Delta_{\text{nat}}\). 3. Selection of Local Gradient Maxima  
After retrieving the local gradient maxima positions \(\Delta_{\text{nat}}\) and \(\Delta_{\text{pre}}\), the first step is an approximation of the natural flow transition by evaluating \(\Delta_{\text{nat}}\). The robust linear RANSAC regression algorithm of the _sklearn_ library is used as it excluded individual outliers. The result is the approximated linear course of the natural flow transition \((Y)_{\text{tr, nat}}\), which would be the flow transition if no premature transitions would exist. This approximation can be used in the following filtering steps. First, all columns with an entry in \(\Delta_{\text{nat}}\), which are near the approximated natural flow transition line, are set to the line's column value, respectively, deleting the outliers. Additionally, the amount of pixels of each image column represented in \(\Delta_{\text{nat}}\) is limited to one. Afterwards, holes of individual columns without a representative in \(\Delta_{\text{nat}}\) are filled if surrounded by columns that are included in \(\Delta_{\text{nat}}\). The next step is to further select positions from \(\Delta_{\text{pre}}\) by defining the region of plausible occurrences for the premature flow transition between the leading edge and the position of the approximated natural flow transition line. A second sub-routine deletes any pixel in \(\Delta_{\text{pre}}\) with less than two pixels in the neighboring area also included in \(\Delta_{\text{pre}}\), because it is considered to be an outlier. In a last step, each image column is analyzed separately. If a gradient representing the natural flow transition was detected, all entries in \(\Delta_{\text{pre}}\) for the given column are deleted. 4. Acquiring Flow Transition Line  
Combining the final \(\Delta_{\text{nat}}\) and \(\Delta_{\text{pre}}\) results in the collection \(\Delta_{\text{tr}}\) of all pixels in the image representing the flow transition line. The final part of the evaluation is divided in two steps.