## 4 Comparison of Different Techniques and Discussion  
The features and fused images of the X-ray and ultrasonic testing were analyzed using the response operating characteristics (ROC) curves and the area under curve (AUC) values. The photo of the sample with defects before bonding, as shown in Figure 2, was used as the reference image to evaluate the quality of the fusion results: the form and position of the defects was extracted from this photo to evaluate the accuracy of the features and fused images, in terms of inclusion-type defect recognition. First, registration (including interpolation and normalization) and coordinate matching have been applied to the image,  
Figure 13: Examples of different combinations of fused features and used fusion algorithms: (a) U5X4 average; (b) U4X1 difference; (c) U2X1 Hadamard; (d) U6X1 Dempster Shafer Positive; (e) U6X4 saliency. considering the fusion data size. Then, the defect positions have been determined via postprocessing of the edge detection algorithm. The fusion results of each defect have been evaluated separately, considering this image. The results are evaluated using the area under curve estimations of response operating characteristic curves. An arbitrary reference matrix was constructed based on the known location of the defects, with defected regions given the value 1 and perfectly bonded regions--0. By knowing the position of the defects, it was possible to create a mathematical formulation of a defect and a non-defect matrix that was used for comparing techniques. Every reference matrix was converted to binary so that the ROC curve could be used for the evaluation. Histogram-based segmentation was carried out. The segmented pixels in the matrix were then categorized into one of four categories: true positive (TP) indicates the presence of a defect in the defect position, false positive (FP) indicates the defect in a perfect bond region, true negative (TN) represents the defect-free good bond region, and false negative (FN) represents the defect-free position. The true positive and false positive rates for each segmented matrix were calculated in accordance with specific and sensitivity information and could be mathematically expressed as follows:  
\[R_{TP}=\frac{N_{TP}}{N_{TP}+N_{FN}}\;(\mathrm{X})\]  
\[R_{FP}=\frac{N_{FP}}{N_{FP}+N_{TN}}\;(\mathrm{X})\]  
where \(R_{TP}\) is the true positive rate, \(R_{FP}\) is the false positive rate, \(N_{TP}\) is the number of true positives, \(N_{FN}\) is the number of false negatives, \(N_{FP}\) is the number of false positives, and \(N_{TN}\) is the number of true negatives. Figure 14 shows the average performance of the distinctive features, according to the ROC curves and AUC values. It could be observed that in the case of the inclusion type of the defect, all features extracted from radiography data perform better according to the ROC curves and the AUC values. The fused results were evaluated with distinctive features that were extracted from the results obtained by different techniques and are presented in Figure 15. The analysis of the results shows that from the fusion algorithms used, simple average and saliency gave the best results in the case of a brass inclusion type of defect. It is surprising that the performance of the Hadamard and Dempster-Shafer algorithms was much worse than expected. For ultrasonic features in terms of suitability for fusion, the best performance was  
Figure 14: Overall defect detection performance of different features, according to ROC curves and AUC values. achieved when using following features: ultrasonic signal attenuation (U2), peak-to-peak (U4), and absolute energy (U6). Although all radiographic features performed similarly, the final result was more influenced by the fusion algorithm.