## 4 Results and Discussion
### Visualization of Classification Results  
The ultrasonic signals can be displayed in different ways for defect determination. Although A-scan is the common representation in nondestructive testing, it is usually beneficial to obtain a two-dimensional representation through a C-scan imaging process for defect determination. The C-scan shows the top view of the sample parallel to the scanning surface. By means of integrating amplitudes of A-scan signals within a time range over the surface, the C-scan image is able to confirm the presence of a defect in the sample according to the changes in amplitude. However, the traditional C-scan imaging process is too sensitive to the random noise during the scanning procedure.  
As an alternative for the traditional C-scan imaging process, our C-scan image is produced according to the following steps:  
* With the proposed classifier, the A-scan signal is indicated as a known type of defect classes which are provided as input for the C-scan imaging of the sample.
* For signal points in each defect class, a connected component labeling is performed on the C-scan image to further determine the defect area on the sample.
* We retain the points with neighbors belonging to the same class on the image and eliminate the others from the C-scan image as random noise.  
Figure 7 is naive C-scan image generated based on the amplitude of original signals. There are a lot of noise signals in the whole weld area. It can be explained that the way to generate images seems too sensitive to the amplitude variation of original signals. The above-mentioned procedures are then used to form Figure 8, which consists of processed C-scan images based on the classification results of the (a) fusion method, (b) automatic method, (c) time domain method, (d) frequency domain method and (e) time-frequency domain method, respectively, corresponding to Table 2.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Methods**} & \multicolumn{5}{c}{**Handcrafted Approach**} & \multirow{2}{*}{**Automatic Approach**} \\ \cline{2-2} \cline{4-6}  & **Time Domain** & **Frequency Domain** & **Time-Frequency Domain** & **Fusion** & **Approach** \\ \hline Accuracy & 0.961 & 0.903 & 0.948 & 0.988 & 0.982 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Performance comparison of the handcrafted features approach and the automatic approach.  
Figure 7: The C-scan image generated based on the amplitude of original A-scan signals obtained by detection.  
From Figure 8, some conclusions can be obtained as follows:  
1. The distribution of defects in each C-scan image conforms well to real defects made in the mockup.
2. The image quality of defects gradually decreases from top to bottom in Figure 8, which is consistent with classification results.
3. In terms of image quality, Figure 8a-e are superior to Figure 7. The proposed method is able to provide a higher credibility of C-scan visualization for defect determination.
4. The proposed method still cannot completely remove noise signals and the next step is to develop effective denoising algorithms for more accurate defect identification.  
Figure 8: Processed C-scan images based on different classification results: (**a**) fusion; (**b**) automatic method; (**c**) time domain; (**d**) time-frequency domain; (**e**) frequency domain.