## 5 Parameter Optimization Method Based on DE Algorithm
### L-Shade
### Effectiveness of the Proposed Gradient Computing Method

To verify the effectiveness of the proposed gradient computing method, the experiment is conducted to make comparison on reconstruction accuracy between two gradient computing methods: one includes the gradient of the guided image, the other does not. It is notable that the two methods use their own optimized values of parameters. A dumbbell gauge referred to the Germany guide line VDI VDE2634 Part2 [33] and is used for accuracy evaluation, as shown in Figure 5.

Figure 4: Device of speckle stereo image pairs acquisition. \begin{table}
\begin{tabular}{c c c} \hline \hline
**No.** & **Name** & **Optimized Value** \\ \hline
1 & R & 1 \\
2 & Eps & 0.8207 \\
3 & W\_AD & 0.3032 \\
4 & W\_Census & 0.2307 \\
5 & W\_grad\_x & 0.9224 \\
6 & W\_grad\_y & 0.6365 \\
7 & cen\_win\_h & 5 \\
8 & cen\_win\_w & 13 \\
9 & T\_ad & 0.4330 \\
10 & T\_census & 0.4155 \\
11 & T\_grad\_x & 0.0646 \\
12 & T\_grad\_y & 0.1515 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The specific value of each parameter in STMCF. The sphere diameter \(d_{\rm A}=50.7784\) mm, \(d_{B}=50.7856\) mm and sphere center distance \(D=100.0480\) mm. The distance between the dumbbell gauge and projector is \(\sim\)550 mm, the disparity range is \(-100\) to \(100\), which is the same as other measured objects. Table 4 shows a comparison of the results by projecting N speckle patterns (the bold figure indicates result with lower error, the same below). Note that points with large error near the boundary are deleted and the measured results are obtained by employing the commercial software Geomagic Studio. It can be seen from Table 4 that after including the gradient of the guided image, the errors are all decreased to varying degrees. Specifically, the error of sphere diameters \(d_{\rm A}\), \(d_{B}\) and sphere center distance D are reduced by \(39.4\%\), \(74.5\%\) and \(18.6\%\) on average, respectively. Above data prove that the proposed gradient computing method is effective. ### Experimental Comparison with the State-of-the-Art Method Based on Spatiotemporal Correlation

As one of the state-of-the-art methods based on spatiotemporal correlation, the spatiotemporal zero-mean normalized cross correlation (STZNCC) is widely used in random speckle 3D reconstruction [16; 25; 34; 35]. To validate the performance of STMCF, a series of comparative experiments between STZNCC and STMCF are carried out. #### 6.3.1 Comparison of Reconstruction Accuracy

Firstly, the dumbbell gauge mentioned in Section 6.2 is used for accuracy comparison. The errors of measured results by projecting N speckle patterns are listed in Table 5. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**N** & **Method** & **Abs.Err (\({}^{\rm 11}\))** (\(d_{\rm A}\))** & **Abs.Err (\(d_{\rm B}\))** & **Abs.Err (\(D\))** \\ \hline \multirow{3}{*}{3} & Not [2] & 0.0733 & 0.0794 & 0.0496 \\ \cline{2-5}  & Include [3] & **0.0282** & **0.0140** & **0.0315** \\ \hline \multirow{3}{*}{6} & Not & 0.0370 & 0.0871 & 0.0480 \\ \cline{2-5}  & Include & **0.0255** & **0.0101** & **0.0445** \\ \hline \multirow{3}{*}{9} & Not & 0.0256 & 0.0860 & 0.0629 \\ \cline{2-5}  & Include & **0.0113** & **0.0471** & **0.0487** \\ \hline \multirow{3}{*}{12} & Not & 0.0429 & 0.0681 & 0.0475 \\ \cline{2-5}  & Include & **0.0390** & **0.0123** & **0.0436** \\ \hline \hline \end{tabular} \({}^{(\rm 1)}\) Abs.Err = Absolute value of error. \({}^{\rm 2)} Not include the gradient of the guided image.\({}^{(\rm 9)}\) Include the gradient of the guided image.

\end{table} 
Table 4: Accuracy comparison between two gradient computing methods by measuring a dumbbell gauge. (Unit: mm). Figure 5: A dumbbell gauge. The results indicate that although when N = 3, the error of STMCF is a little greater than that of STZNCC in terms of \(d_{B}\), the rest of the errors of STMCF are lower than STZNCC.