## 4 Results and Discussion  
The TFM images of branch pipe fillet welds are denoised, as shown in Figure 9, respectively. Compared with the artifacts in Figure 3, it is obvious that the regional wavelet denoising algorithm has a good effect on the elimination of artifacts. After the post-processing of the algorithm, the image edge (detection contact surface) still has a small range of residual artifacts. The contact surface artifacts are mainly caused by the interface characteristics of ultrasonic testing, involving acoustic propagation characteristics and acoustic impedance characteristics. In addition, although the wavelet region denoising method can achieve the purpose of image segmentation and region denoising, the edge artifacts of the TFM image are serious, and the coefficients of the edge image generated by wavelet transform are higher than the set threshold, so the characteristics of the image edges are partially preserved. Because the defects that affect the quality of the weld are usually located at the root and inside of the weld, the existence of artifacts on the edge of the contact surface will not affect the characteristic analysis of the weld.  
Figure 8: Branch pipe sample and inspection status.  
Figure 9: _Cont._In Figure 9, the blue area represents the non-defect area, the yellow represents the defect transition area, and the red represents the defect area. The defect features obtained from the TFM image processed by the minimum matrix method are shown in Figure 10.  
In Figure 10, the gray-white area represents the non-defect area, yellow represents the defect edge area, and red represents the defect core area. Finally, the minimum rectangle method is used to analyze the image defect characteristics combined with the welding process. The feature analysis results are shown in Table 2. In order to highlight the defect characteristics of the TFM image and avoid the interference of artifacts of adjacent contact surfaces, according to the \(c_{w}\) and the \(T_{w}\) in Table 1, the vertical coordinate of the defect location needs to be reduced by 11.7 mm.  
Figure 9: Weld defects. (**a**) Left side weld inspection (T-90-25-B). (**b**) Right side weld inspection (T-90-25-B). (**c**) Left side weld inspection (T-90-35-B). (**d**) Right side weld inspection (T-90-35-B). (**e**) Left side weld inspection (T-90-40-B). (**f**) Right side weld inspection (T-90-40-B). (**g**) Left side weld inspection (T-90-45-DC). (**h**) Right side weld inspection (T-90-45-DC). (**i**) Left side weld inspection (T-90-45-B). (**j**) Right side weld inspection (T-90-45-B). (**k**) Weld defects (Y-90-25-NB).  
Figure 10: Feature analysis. (**a**) Left side weld inspection (T-90-25-B). (**b**) Right side weld inspection (T-90-25-B). (**c**) Left side weld inspection (T-90-35-B). (**d**) Right side weld inspection (T-90-35-B). (**e**) Left side weld inspection (T-90-40-B). (**f**) Right side weld inspection (T-90-40-B). (**g**) Left side weld inspection (T-90-45-DC). (**h**) Right side weld inspection (T-90-45-DC). (**i**) Left side weld inspection (T-90-45-B). (**j**) Right side weld inspection (T-90-45-B). (**k**) Feature analysis (Y-90-25-NB).  
According to Table 2, the effective detection rate is 100%, the size detection sensitivity is 0.1 mm, the length range of various defects is 2.3 mm\(-\)6.3 mm, the width range is 0.6 mm\(-\)0.8 mm, and the angle range is 52\({}^{\circ}\)-75\({}^{\circ}\). Although the minimum rectangle method can simply and effectively implement the rectangular envelope of image features, it cannot accurately represent the range area and inevitably has errors, especially when the defect shape is extremely irregular. This method can lead to a large deviation between the rectangular envelope area and the actual defect area, which can result in a decrease in the accuracy of risk assessment.