## 3 Application to Experimental Data
### Evaluation  
In the following sub-sections, our fusion method is quantitatively evaluated with regard to the presented specimen. This evaluation focuses on detectability, meaning the ability to distinguish between grooves and background in the fusion result. Consequently, the ability to accurately localize a defect after fusion is not a part of this evaluation. For each detection result in the next sections, indications are assigned fuzzy membership values to the two sets \"defect\" and \"non-defect\", based on their distances to the known groove locations. Using this ground truth information, evaluation is carried out automatically by means of precision-recall-curves. Similarly to conventional Receiver Operating Characteristic (ROC) analysis [22], which is based on recall = true positive rate = #_true hits_/_#max possible true hits_ and false alarm rate = #_false hits_/_#max possible false hits_ for each possible detection threshold, we replace false alarm rate with precision = #_true hits_/_#all hits_. This choice is necessitated by the scattered nature of the hits, which allow an infinite number of possible false alarms, that is off-groove locations. Precision circumvents this restriction by relating hits to hits, rather than hits to non-hits. The two evaluation measures precision and recall are fuzzyfied in our evaluation to include the fuzzy membership per hit in the analysis ([23], p. 46). That is, each hit is allowed to be counted partially as a true positive and as a false alarm: Indications near known groove locations are evaluated nearly 100% as true positives, whereas hits that lie further away have an increasing share as a false alarm. The correspondence between distance to the nearest groove location and fuzzy membership is realized by a Gaussian membership function, whose spread parameter \(\sigma=0.2\) mm is set equal to the estimated mean registration error for our data set to account for the localization uncertainty. Once an evaluation curve in fuzzy ROC space per detection method and per groove is established, the area under each precision-recall-curve quantifies detection performance over the full range of detection thresholds. However, we do not compute the area under the whole curve, but only for the curve region where recall >0.5. We denote this measure by AUC-PR-0.5. This focuses our evaluation on thresholds that are low enough to ensure that at least half of a groove is detected. Furthermore, a single false alarm hit with higher intensity than the groove suffices to force the curve down to zero precision for small true positive rates, _i.e._, high thresholds, and therefore dominates the whole AUC measure. This is another reason for ignoring the lower half of the diagram in the computation of AUC-PR-0.5. Several regions on the specimen surface are marked to be excluded from the evaluation. These are areas near the border of the specimen, indications that result from experimental modification of the specimen surface and off-groove areas where real unplanned defects exist (which would otherwise be counted as false alarms). Not only are all of these disregarded regions removed from evaluation  
Figure 9: Result of decision level fusion. Darker markers correspond to increased detection confidence. The colors are scaled so that white represents zero fused intensity, and black corresponds to intensities at least as large as at the shallow defect nr. 14. Axes \(x\) and \(y\) are not to scale. after fusion, but already the hits in these regions are excluded from the density estimation, so that they don't affect the density in the surrounding regions. Furthermore, to evaluate detection performance per flaw depth, after fusion each groove is assessed individually while ignoring all others. All fusion results are evaluated at the same locations on the specimen surface defined by a dense grid with sampling distances \(\Delta_{x}=0.0289\) mm, \(\Delta_{y}=0.1258\) mm. This choice of grid resolution is given by the finest spatial sampling among all individual sensors in each spatial dimension.