## 3 Implementation and Validation of the Proposed Framework through a One-Inch Block Experiment
### Image Quality Assessment  
The effectiveness of each algorithm in modifying image quality was measured based on the classical entropy \((E)\), \(PSNR\), and \(SSIM\), and the output image quality was estimated using the no-reference image quality index metrics, i.e., \(BR\), \(NQ\), and \(PQ\). They focused only on the quality and index changes due to image enhancement procedures applied to the underexposed images captured by the vision-based HS system. Quality assessment was conducted on all enhanced photogrammetry images with the statistics shown in Table 3. The coefficient of variations \((CV)\) were computed from 50 output images for each enhancement method and index, and the index change \((\Delta_{input})\) was measured from the mean difference between each algorithm and input index. Although uniform boundary conditions of enhancement algorithms were applied to the 50 input images, some variations based on \(CV\) percentage were observed in the output images, especially when the enhancement was conducted using the HRDC method. No reference index metrics also measure input image \(CV\) within 1.6-9.4% with more variants computed by \(NQ\) index, as listed in Table 3. The input images were visually dark and underexposed; however, they were taken from different positions and orientations towards the specimen. Because the monitoring depends entirely on the ambient lights and the lighting cannot be controlled to evenly illuminate the templates, changing the camera positions while taking pictures affected the images captured by the camera sensor. Overall, the observation based on the output image statistics in Table 3 shows that the implementation of the image enhancement algorithm modifies the input image characteristics, and some metrics detect major changes compared to other indices. These variations cannot be identified merely from the output image perception or gray level histogram. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline  & & \multicolumn{4}{c}{\(R_{1}\) (pix.)} & \multicolumn{4}{c}{\(R_{2}\) (pix.)} \\ \hline
**Point** & **1** & **2** & **3** & **4** & **5** & **6** & **CV** & **1** & **2** & **3** & **4** & **5** & **6** & **CV** \\  & & & & & & & & **(\%)** & & & & & & & **(\%)** \\ \hline CS (\({}^{\text{a}}\)) & 19.09 & 19.18 & 18.75 & 19.3 & 19.32 & 19.38 & 2.41 & 15.95 & 15.91 & 15.19 & 16.24 & 16.41 & 16.31 & 5.56 \\ CLAHE (\({}^{\text{b}}\)) & 19.81 & 19.73 & 19.69 & 20.33 & 20.46 & 20.28 & 3.42 & 16.59 & 16.2 & 17.17 & 17.4 & 17.4 & 17.19 & 5.75 \\ HE (\({}^{\text{c}}\)) & 20.89 & 21 & 20.7 & 20.97 & 20.94 & 20.99 & 1.08 & 17.65 & 17.57 & 17.01 & 17.71 & 17.78 & 17.63 & 3.17 \\ HRIO (\({}^{\text{d}}\)) & 19.1 & 18.55 & 18.58 & 20.39 & 20.68 & 20.96 & 11.08 & 16.1 & 15.41 & 15.2 & 17.26 & 17.62 & 17.88 & 14.00 \\ HRDC (\({}^{\text{e}}\)) & 20.73 & 20.98 & 20.66 & 20.85 & 21.07 & 20.93 & 1.48 & 17.44 & 17.51 & 17.02 & 17.59 & 17.8 & 17.61 & 3.00 \\ \hline \(CV\) (\(\%\)) & 4.33 & 5.48 & 5.13 & 3.24 & 3.40 & 3.40 & 4.60 & 5.89 & 6.29 & 3.39 & 3.32 & 3.57 & \\ \hline \hline \end{tabular}  
* (\({}^{\text{a}}\)) contrast stretching, (\({}^{\text{b}}\)) contrast limited adaptive histogram equalization, (\({}^{\text{d}}\)) histogram equalization, (\({}^{\text{d}}\)) haze removal with an inverted operation, and (\({}^{\text{e}}\)) haze-removal with single dark channel prior.  
\end{table} 
Table 2: Two-directional radii, \(R_{1}\) and \(R_{2}\), for identification of object points.