## 3 Experiment Result and Discussion
### Sizing Results on Experimental Thermograms
FWHM provides a slightly lower accuracy than the proposed approach for distinct defects (D1, D2, and D3). However, the sizing accuracy of FWHM decreases greatly for blurry defects. In contrast, the proposed approach provides satisfactory sizing result for these blurry defects with an accuracy similar to those for the distinct defects. In order to investigate the performance of the proposed approach further, we tested the specimen repeatedly by rotating the specimen 90\({}^{\circ}\) each time. Because lamps and specimen are not located at the same height as described previously, top row defects always obtain more heating energy. As a result, thermograms captured in each test vary greatly due to this non-uniform heating. The raw thermogram with maximum contrast for D9 and the contour detection result of the proposed approach for the testing directions of 90\({}^{\circ}\), 180\({}^{\circ}\), and 270\({}^{\circ}\) are shown in Figure 8. It can be observed that shapes of all defects are described well by the proposed approach. The detailed sizing results for each test are illustrated in Table 2. The maximum sizing error is 1.8 mm considering all tests. From the mean error averaged on four tests, it can be found that sizing errors of all defects except D5 are within 1 mm. By observing the surface of the tested specimen, we found that the surface corresponding to D5 is \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Methods**} & \multicolumn{8}{c}{**Sizing Error (mm)**} \\ \cline{2-10}  & **D1** & **D2** & **D3** & **D4** & **D5** & **D6** & **D7** & **D8** & **D9** \\ \hline
**Canny operator** & 4.6 & 1.7 & 3.2 & 3.2 & 2.8 & 3.2 & 3.2 & 3.2 & 3.2 \\
**FWHM** & 0.3 & 0.3 & 0.3 & 3.3 & 1.2 & 4.7 & 2.6 & 1.7 & 5.6 \\
**Proposed approach** & 0.2 & 0.2 & 0.2 & 1.7 & 1.3 & 0.2 & 0.2 & 0.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Performance comparisons of sizing methods. Figure 7: Intermediate result and contour detection result: (**a**) denoised image; (**b**) prominent gradient map; (**c**) sizing result of the proposed approach (inverse displayed for clarity); (**d**) sizing result of the Canny operator (inverse displayed for clarity). extruding due to the machining process. We think such a special surface condition corresponding to D5 is the possible reason for its special sizing error, which is slightly larger than those of other defects. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline  & & \multicolumn{4}{c}{**Estimated Size by the Proposed Approach (mm)**} \\ \cline{3-6}
**Defect** & **Defect Diameter (mm)** & \multicolumn{4}{c}{**Testing Direction**} & \multirow{2}{*}{**Mean Error**} \\ \cline{3-6}  & & & \(0^{\circ}\) & \(90^{\circ}\) & \(180^{\circ}\) & \(270^{\circ}\) \\ \hline D1 & & & 14.8 & 15.2 & 15.2 & 15.2 & 0.1 \\ D2 & & & 14.8 & 15.2 & 15.2 & 16.7 & 0.5 \\ D3 & & & 14.8 & 15.2 & 15.2 & 16.7 & 0.5 \\ D4 & & & 13.3 & 15.2 & 15.2 & 15.2 & 0.3 \\ D5 & 15 & & 16.3 & 16.7 & 16.8 & 16.7 & 1.6 \\ D6 & & & 14.8 & 13.7 & 13.7 & 15.2 & 0.7 \\ D7 & & & 14.8 & 16.7 & 15.2 & 13.6 & 0.1 \\ D8 & & & 14.8 & 15.2 & 15.2 & 15.2 & 0.1 \\ D9 & & & 14.8 & 16.7 & 15.2 & 16.7 & 0.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Estimated defect sizes. Figure 8: Raw thermogram and contour detection result: (**a**) Raw thermogram with maximum contrast for the lowest observable defect with testing directions of \(90^{\circ}\), \(180^{\circ}\), and \(270^{\circ}\) (from top to bottom). (**b**) Contour detection result of the proposed approach (inverse displayed for clarity).