## 2 Methodology  
We will now schematically describe the core idea of our approach before giving a more formal definition. To this end, assume that information about potential defect locations \(d=\left(d_{x},d_{y}\right)\), called _hits_ in the following, was obtained from different NDT data sets. For example, consider Figure 1 for an outcome of individual surface inspection using two NDT methods. In cases (a)-(d), each dot marks a hit generated by some detection rule per sensor. Among the hits, there are also false alarms, for instance indicating changes in material properties unrelated to a defect (structural noise). Such false alarms are illustrated by cases (b) and (c) in Figure 1. Using single-sensor inspection, these false alarms cannot be distinguished from indications produced by actual defects such as those shown in case (a). A multi-sensor data set, on the other hand, is able to reveal case (a) as a real defect by assessing the agreement among different detection methods. Here, agreement is expressed in terms of joint spatial density of hits, taking into account all sensors. Our rationale is that the joint hit density is higher over real defects than in other areas, provided sufficient signal to noise ratio (SNR) for at least two sensors. On the contrary, a clear conflict occurs where only one sensor generates hits, and thus the joint density is not significantly increased relative to the individual sensor density. This concept is depicted at the bottom of Figure 1, where for each sensor the spatial density of hits across the specimen surface is symbolized. Only in case (a) both sensors agree in increased spatial density, whereas in cases (b) and (c) the sensors do not agree. Although there is also agreement in case (d) as well, the joint density is not significant enough, indicating the low likelihood of defect presence. This example demonstrates the potential of the joint spatial density as the basic mechanism for multi-sensor detection. We propose evaluating the local hit density as a measure for multi-sensor data fusion at decision level. Figure 2 provides a flow chart of the individual steps. The first step consists of generating hypothesized defect positions from individual NDT images. Additionally, each hit is associated with its local signal to noise ratio, which will be used later as a weighting factor (not shown in the flow chart). Suitable detection techniques depend on the respective NDT modality, but often a simple threshold operation on the sensor intensities is appropriate. It is important to make the detection strategies focus on sensitivity rather than specificity, thus ensuring that all (unknown) real defect indications are retained for the final detection by fusion. At the same time, we would still want to discard as many false alarms as possible. The difficulty of facing this trade-off, which is typical for single-sensor detection, is however less critical for multi-sensor detection because the main work is done by the subsequent fusion procedure. Practical examples of single-sensor detection will be given in Section 3.2. The extracted hit locations from different NDT techniques are usually not expressed with respect to the same coordinate system. This is because rather than measuring at the very same locations on the specimen, it is often more practical to mathematically register the individual local coordinate systems after the measurements were carried out. Therefore, for each sensor pair, we find corresponding locations in the sensor data and fit a coordinate transformation model that minimizes the distance between each pair of corresponding locations. Note that, in contrast to fusion at the signal level, this transformation is not used here to interpolate the sensor data values. Rather, for decision-level fusion, the transformations allow to express the locations of the individual hits in a common coordinate system. We note that although each NDT method usually uses gridded measurement positions, the mapped  
Figure 1: Schematic representation of the principle of the approach.