## 5 Parameter Optimization Method Based on DE Algorithm
### L-Shade
Especially for N = 6, 9 and 12, the advantage is more obvious; the error of \(d_{A}\), \(d_{B}\) and \(D\), are at least 24.9% (N = 12), 36.6% (N = 9) and 16.0% (N = 9) lower than STZNCC, respectively. To further evaluate reconstruction accuracy of the object with complex surface, a plastic human face mask (see Figure 6a) is also tested. Its ground truth (see Figure 6b) is obtained by the industrial scanner ATOS Core 300 (the measurement accuracy is \(\pm\)0.02 mm, certified by the Germany guide line VDI VDE2634 Part2 [33]). The Geomagic Studio is employed to compare the differences between the reconstruction result and ground truth quantitatively. The error statistics of results, respectively using STZNCC and STMCF by projecting N speckle patterns, are presented in Figure 7.

It can be easily discovered from Figure 7 that with the increase of N, the errors of both STMCF and STZNCC tend to decrease. In Figure 7a, except for N = 12, the maximum errors of STMCF are all less than STZNCC. In Figure 7b,c, the performance of STMCF is better than STZNCC in all cases. Therefore, in general, the accuracy of reconstructing the human face mask using STMCF is higher than that of STZNCC. Figures 8-11 shows reconstruction results and corresponding error distribution maps of the plastic human face mask, respectively, using STMCF and STZNCC by projecting N (N = 3, 6, 9, 12) speckle patterns. It can be observed from Figures 8-11 that the quality of both results obtained by STMCF and STZNCC becomes better with the increase of N. Besides, by carefully comparing the error distribution maps between STZNCC and STMCF in Figures 8-11, we can find that the result of STMCF is more accurate in most areas. Above conclusions are consistent with the results shown in Figure 7.

Figure 7: Error statistics comparison between STZNCC and STMCF of measuring a plastic human face mask. (**a**) maximum error; (**b**) average error; (**c**) standard deviation. Figure 8: (a) 3D reconstruction result of the plastic human face (N = 3); (b) Corresponding error distribution map. Figure 9: (a) 3D reconstruction result of the plastic human face (N = 6); (b) Corresponding error distribution map. Figure 11: (**a**) 3D reconstruction result of the plastic human face (N = 12); (**b**) Corresponding error distribution map. Figure 10: (**a**) 3D reconstruction result of the plastic human face (N = 9); (**b**) Corresponding error distribution map. #### 6.3.2 Comparison of Computation Time

The computation time comparison between STZNCC and STMCF by projecting N speckle patterns are illustrated in Figure 12. It is worth mentioning that both methods use the coarse-to-fine matching strategy proposed in [25]. The results show that the computation time of both STZNCC and STMCF will rise when N increases. Moreover, although when N = 12, the computation time for a dumbbell gauge of STMCF is slightly higher than that of STZNCC, the computation time of STMCF is less than STZNCC in most cases. #### 6.3.3 Comparison of Real Human Face Reconstruction

In order to further verify the performance of STMCF in actual application situations, the author's face under various expressions is reconstructed by STMCF and compared with the results of STZNCC, as shown in Figure 5:0

Figure 5:1 Computation time comparison between STZNCC and STMCF by projecting N speckle patterns: (**a**) a dumbbell gauge; (**b**) a plastic human face mask. Figure 5:2 Comparison of real human face reconstruction respectively using (**a**) STMCF (N = 12); (**b**) STZNCC (N = 12). By careful observation, it can be found that the results of STMCF display contour details of the human face as clearly as that of STZNCC. More importantly, the smoothness of major areas on the human face (such as forehead, cheek and chin) is significantly better than STZNCC. Therefore, the effect of 3D face reconstruction using STMCF is more realistic. ### Discussion

This paper reports a novel random speckle 3D reconstruction scheme, in which STMCF is proposed and a parameter optimization method based on DE algorithm is designed.