## 4 Discussion  
Our experiments demonstrate that our density-based approach is well-suited to incorporate indications from heterogeneous sensors. The number of false alarms can be strongly reduced relative to single-sensor inspection while retaining most of the defects. Regarding our evaluation index,  
Figure 14: Influence of individual sensors on the fusion result, for the _median_ fusion rule and a fixed kernel size. Figure 13: Comparison between the weighted approach (as proposed; top row) and the unweighted variant, for the _product_ fusion rule. for 13/15 grooves, the fusion method performs as well as or better than single-sensor detection. The performance gain is most pronounced for the shallower defects, which usually generate less significant indications. We note that the principle to quantify agreement among sensors requires that all sensors yield redundant information about the object of interest, e.g., near-surface cracks in our case. That is, in NDT, all sensors must respond to the same flaw type in the same size range. If, in contrast, one of the sensors reports a defect that is not detectable by the other methods, it will be discarded as a \"false alarm\" by our technique, since it is not designed to fuse complementary information. This is the case for the shallowest investigated defect in the study. Similarly, groove nr. 8 is only found by single-sensor inspection but not by fusion, because TT lacks of a significant indication in that area. To apply a multi-sensor system despite such unexpected effects, mild fusion rules, such as _median_ or _sumlgnoreMax_, trade strong reduction of false alarms for the ability to compensate unknown sensor dropout. Another point concerns the relationship between fusion performance and spatial uncertainty. Specifically, the fusion performance is expected to improve with registration accuracy. This is because kernels can be made narrower for smaller registration errors, and therefore the likelihood of a non-defect-related indication due to spurious multi-sensor agreement is reduced. In any case, the actual registration error must be quantified to set the kernel size accordingly. Moreover, the fusion technique strongly benefits from realistic estimates of the local signal to noise ratios, which enter the fused density through weights. For the final detection after fusion, a threshold could be chosen to retain only the significant density peaks. Thus, only few parameters (localization uncertainty, fusion rule, density threshold) fully describe the methodology and are usually readily determined. Furthermore, if one is unsure about a fused indication, the original individual hits can always be reconsidered to collect additional evidence for or against the presence of a defect. After all, the density-based approach spatially associates neighboring hits and thus may serve as the basis for multi-sensor detection after feature extraction. For example, our density measure identifies narrow regions of increased defect likelihood. These regions can further be assessed by extracting features from each individual sensor in this region, which could be combined by some classification algorithm to reach a final conclusion. Concerning the number of sensors, we suggest using at least three different sources of information, as presented here. However, our experiments show that improved performance over single-sensor inspection is possible already for two sensors. Note that the more fusion inputs are provided, the higher the likelihood of the purely coincidental agreement between at least two sensors. Therefore, the rule _sumlgnoreMax_ (Equation (7)) will have to be extended if even more sensors are included, whereas the _median_ rule and _product_ rule is expected to perform well regardless of the number of sensors. We would also like to point out the limitations of the current study. Whereas the eroded grooves facilitate detection assessment for well-defined defect depths, their linear shapes do not resemble natural defects.