## 3 Experiment Result and Discussion
### Sizing Results on Experimental Thermograms  
The thermogram captured at 5.6 s from the heating beginning is shown in Figure 5a. In this thermogram, defect D9 has the best contrast indication compared to that in other thermograms. The gray level ROI image is shown in Figure 5b. From this image, it can be seen that the defects present indications with various observable levels. The defect depth is a crucial factor resulting in the difference in contrast indications of defects. A deeper defect presents a lower observable indication and a more blurry contour according to heat conduction theory. Non-uniform heating is another reason for the different defect indications. As stated previously, the centers of lamps were not aligned to the horizontal center line of the specimen, which resulted in a serious non-uniform heating condition. More heating energy was obtained by the upper part of the specimen. For defects in regions obtaining lower heating energy, they presented lower contrast indications. The amplified views of the defects in the right column are shown in Figure 5c. It can be seen that D3 presents as a distinct defect, while D6 and D9 have low contrast indications and blurry contours because D6 and D9 are deeper than D3 and they obtained less heating energy. D9 has extremely low observability and its contour is too blurry to be located, which makes the sizing of this defect a challenge. This can also be observed in Figure 6, which shows the intensity profile along the line across the right column defects. The contrast between defect and sound region varies greatly for D3, D6, and D9. Sizing results of FWHM for these defects are also demonstrated in Figure 6. We can see that D3 was sized with the highest accuracy by FWHM due to its distinct contrast indication. However, the estimated sizes of D6 and D9 by FWHM deviated from the real sizes, with large errors of 4.7 mm and 5.3 mm, respectively. This result demonstrates that the sizing accuracy of FWHM closely depends on the contrast level of the defect indication. Figure 4: Details of the specimen. The denoised thermogram after averaging processing and Gaussian low pass filtering is shown in Figure 7a. Figure 7b depicts the prominent oriented gradient map of this denoised thermogram. In Figure 7b, it can be observed that pixels on defect contours have larger gradient values in the prominent oriented map. After implementing NMS on the prominent gradient map, one-pixel width contours of the defects were obtained and are shown in Figure 7c. As can be seen, the circular shape of each defect has been retained well. Using the ratio between physical size and pixel number of the tested specimen, defect sizes were calculated, and the results are illustrated in Figure 7c. The calculated results show that the estimated size is approximately equal to the real diameter (15 mm) for all defects, including the hardly observable D9. Most defects are accurately sized with a tiny error of 0.2 mm (3.25%). As a comparison, the Canny operator was also employed on the denoised thermogram to size the defect, and its sizing results are shown in Figure 7d, which indicates that most defects were  
Figure 5: Raw thermogram and preprocessed thermogram: (**a**) raw thermogram captured at 5.6 s after the beginning of heating with testing direction of 0\({}^{\circ}\); (**b**) preprocessed thermogram through gray level transformation and the region of interest (ROI) extraction; (**c**) amplified display of the right column defects. Figure 6: Intensity profile along the investigated line shown in Figure 5b and estimated sizes by full width at half maximum (FWHM). sized by the Canny operator with an error of 3.2 mm (21%). The maximum sizing error of the Canny operator is 4.6 mm (31%). A detailed comparison of the proposed approach to the Canny operator and the FWHM is shown in Table 1. It can be observed that, when employing the Canny operator to detect defect contours, the sizing error is generally larger than that of the proposed approach.