## 3 Application to Experimental Data
### Individual Measurements and Processing
However, such performance is not guaranteed for other materials or in case of suboptimal surface conditions, so that a multi-method approach is still in demand. To take advantage of as many independent sources of information as possible during fusion, we intentionally lowered the quality of the MFL image before preprocessing and detection. This was done by separating the true defect indications from the background signal variations using the shift-invariant wavelet transform [20], and by reconstructing the signal with a factor of 0.02 for the noise-free component. Although this does not simulate a lower-quality MFL measurement in a physically realistic way, the approach allows making use of the acquired GMR signals as a third source of information. We justify this alteration in favor of demonstrating the capabilities of our fusion technique in other settings where individual inspection is in fact not reliable enough. Therefore, for the rest of the article, only this modified version of the MFL data is considered. To convey an impression of the signals, we show an exemplary portion of each preprocessed inspection image in Figure 5. The displayed part of the specimen surface is a 10 mm by 6.5 mm region around groove nr. 13 which is quite shallow, and thus generates relatively weak indications. The figure demonstrates the different signal patterns among sensors, concerning both the groove and the background variations. Also, the different pixel sizes are evident. A related plot is shown in Figure 6, where one-dimensional line scans crossing the groove reveal more clearly the individual sensor responses. The different spatial sampling positions are demonstrated by the line markers. Table 2 (respectively, Table S2) offers a quantitative comparison of the individual data sets. Figure 5: _Cont._  
Figure 5: Preprocessed sensor intensity images, zoomed to a region around the groove nr. 13. Higher intensities correspond to indications. **(a)** ET; **(b)** MFI; **(c)** TT. The vertical black line marks the location of the groove. Each image is shown in the respective sensor’s coordinate system, thus explaining the different spatial axis labels. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **ET** & **MFL** & **TT** \\ \hline \(\Delta_{x}\) in mm & 0.029 & 0.029 & 0.469 \\ \(\Delta_{y}\) in mm & 0.200 & 0.200 & 0.126 \\ Width of a typical indication, in mm & \(2\approx 69\Delta_{x}\) & \(0.6\approx 20\Delta_{x}\) & \(0.5\approx\Delta_{x}\) \\ Avg. nr. of hits per pixel & 0.0023 & 0.0031 & 0.0068 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Quantitative properties of the individual data sets. Figure 6: Preprocessed line scan per inspection method around groove nr. 13. **(a)** ET; **(b)** MFI; **(c)** TT. The signals are shifted so that each peak value is located at \(x=~{}0\). Note the different intensity scales. After individual preprocessing, the same detection routine was used for all three images to extract hit locations and confidences, which will later be fused at the decision level. To this end, we convert the signal intensities to confidence values and apply a threshold to extract only significant indications, as follows. Confidence values are computed by estimating the distribution function of background signal intensities from a defect-free area. This estimate serves as the null distribution \(p_{null}\left(x\right)\) in the significance test. For each image pixel's intensity \(y\), the probability \(p_{null}\left(y\geq x\right)\) is computed as the confidence. Pixels are considered significant here, if their confidence exceeds 99%. Additionally, only those hits that are local maxima with regard to their neighboring pixels along the horizontal axis (thus crossing the grooves) are retained. This constraint further filters many false alarms while making the detection results invariant to different peak widths. After detection, each hit is associated with its local signal to noise ratio, which will be used as the weight \(w_{d}\) during density estimation according to Equation (2).