## 3 Application to Experimental Data
### Evaluation
#### 3.4.1 Evaluation of Fusion Rules  
As described in Section 2.2.3, the three normalized per-sensor densities are fused at each location of interest on the specimen surface using some fusion rule. In this study, we compare the following eight functions: _minimum, geometric mean, harmonic mean, product, median, sum, sumlgnoreMax_ according to Equation (7), and the _maximum_. These are contrasted with single-sensor performance, both before and after individual kernel density estimation. All single-sensor hits are assessed here, in contrast to the fusion methods where hits below the per-sensor thresholds were discarded. For each groove, a separate ROC analysis was carried out to assess the influence of defect size. At this point, we emphasize that the results presented in this article are not representative for the general performance of each individual inspection method. It is possible that better individual results than shown here may be obtained by optimizing e.g., the specimen preparation, the sensors or the processing routines. This is especially true for the MFL data, which were artificially degraded as described in Section 3.2. Rather, in the following our focus is to demonstrate that our technique is able to perform well in the face of imperfect sources of information. The results are presented in Figure 10. In agreement with the visual impression from Figure 7, single-sensor performance (ET, MFL and TT) is unsatisfactory. Although the individual KDEs better pronounce the grooves against more randomly scattered background hits, false alarms still prevent reliable detection even for deep grooves (see TT-KDE and MFL-KDE). After purposely degrading the MFL data (see Section 3.2), the eddy current technique provides the best single-sensor detection results by reliably indicating groove depths no less than 55 \(\upmu\)m (groove nr. 8). In contrast, through multi-sensor fusion, most of the defects can be detected reliably. Two exceptions are the _sum_ and the _maximum_ rule, which perform poorly over most if not all grooves. These results are explained by the fact that _sum_ and _max_ do not quantify agreement among sensors, but instead retain all indications from any individual sensor in the fusion result. This is prone to false alarms, which is reflected by low evaluation scores. In contrast, the _minimum_, _geometric_ and _harmonic mean_ and the _product_ rule yield high scores for most defects. Apparently, grooves nr. 8 and 9 are hard to identify across many fusion methods despite the grooves' midsize depths. This suggests poor single-sensor SNR at these locations, thus leading to inter-sensor conflict, so that this groove is wrongly classified as a false alarm by the strict fusion methods _product_, _geometric_ and _harmonic mean_ and _minimum_. On the other hand, the milder fusion rules _median_ and _sumlgnoreMax_ tolerate unknown single-sensor dropout at the expense of comparably poor detection performance at the shallowest grooves. Specifically, whereas the _median_ rule might deteriorate in the face of overall low SNR by permitting too many false alarms,_sumlgnoreMax_ offers a good compromise between strictness and tolerance in our evaluation. However, for the detection of very shallow defects like groove nr. 14 in our specimen, stricter rules appear to offer better performance. The best fusion rule in this evaluation is the _geometric mean_, closely followed by the _harmonic mean_ and the _product_. As _product_ is conceptually extremely simple yet effective, it is considered the winner. Overall, the shallowest detectable groove depth in our study is given by 29 \(\upmu\)m at groove nr. 13. The 20 \(\upmu\)m groove nr. 14 could not be found reliably, although fusion offers improved detectability compared to single-sensor detection. The shallowest groove nr. 15 (11 \(\upmu\)m) is not distinguishable from background noise due to lack of single-sensor sensitivity. Additionally, the results are more clearly presented in Figure 11, where only the _product_ fusion is compared against the single-sensor KDEs.