# Novel Boundary Edge Detection for Accurate 3D Surface Profilometry Using Digital Image Correlation
## 3 Experimental Results and Accuracy Analyses  
The proposed approach was developed using C++ on a personal computer with 3.2 Hz i5-4570 CPU and 4 GB RAM. The 3D optical probe was incorporated with a three-axis scanning stage via Ethernet to detect speckle images. Three experiments with different setups were conducted using the probe and the developed approach to evaluate their effectiveness. First, to verify the accuracy of the developed approach, the reconstruction of a pre-calibrated gauge block with a step height of 9.000 mm and a coordinate measuring machine (CMM) calibrated circle target with a thickness of 5.000 mm was performed. Figure 14 shows the reconstruction results of the pre-calibrated gauge block. Repeated tests yielded improvements in the width-measuring error, standard deviation, and measurements of 1.06%, 315 \(\upmu\)m and 22-fold, respectively; compared with the results obtained by the traditional DIC. Figure 14 also shows the improvement in accuracy obtained via 3D profiles and the corresponding measured speckle images with 2D edge detection of each step. The experimental results obtained verified the superiority of the developed approach to the traditional DIC for measuring surface contours, especially for edge measurement and reconstruction.  
Figure 15 shows the reconstruction results of the pre-calibrated circle target. As can be seen, the measurement error was kept within 0.4% of the original diameter while the standard deviation was maintained at 267 \(\upmu\)m. In comparison with traditional DIC, the developed approach achieved an 18-fold improvement in diameter measurement, indicating the superiority of the proposed method for critical dimension measurement. The comparison of different measurement results is shown in Table 1.  
Figure 14: Measurement results obtained using the proposed approach for reconstruction of the pre-calibrated gauge block: (**a**) speckle image; (**b**) 3D result measured using traditional DIC; (**c**) initial edge reconstruction using the proposed approach, in which some edge positions are still missing from its original object shape; and (**d**) 3D map reconstructed using the proposed edge detection method.  
Edge detection was also performed on industrial workpieces to validate the feasibility of the developed method. Figure 16 shows the surface profile reconstruction of a 3D-printed hammer using the proposed approach, while Figure 17 compares the 3D map of a molding part obtained using both traditional DIC and the developed method. Experimental results and analyses revealed that traditional DIC has difficulty providing reliable edge information. The critical dimension could not be reconstructed accurately and conventional 2D image edge-detection technique had to be employed in conjunction to accomplish the measurement. The developed method achieved a 15-fold improvement in measurement, with error controlled within 1%.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Case**} & **CMM** & **Traditional DIC** & \multicolumn{4}{c}{**Developed Approach**} \\ \cline{2-7}  & **Mean Diameter** & **Mean Diameter/Width** & **Mean Diameter/Width** & **Standard or Width (mm)** & **Standard Deviation (jmm)** & **Measurement Error (\%)** & **Measurement Improvement (\%)** \\ \cline{2-7}  & **or Width (mm)** & **(mm)** & **(C)** & **Deviation (jmm)** & **(D)** & **(E)** \\ \hline Circular plate (diameter) & 45.473 & 41.513 & 45.253 & 267 & 0.4\% & **1800\%** \\ \hline Gauge block (width) & 29.98 & 22.97 & 29.662 & 315 & 1.06\% & **2204\%** \\ \hline \hline \end{tabular} Note: \(\text{D}=\frac{\left|C-A\right|}{A}\), \(\text{E}=\frac{C-B}{A-B}\).  
\end{table}
Table 1: Comparison of measurement accuracy and improvement achieved by coordinate measuring machine (CMM), traditional digital image correlation (DIC) and, the developed approach.  
Figure 15: Pre-calibrated circle target reconstructed with edge detection.  
Figure 16: Reconstruction of a 3D-printed hammer using the proposed approach.  
Figure 17: _Cont._