## 4 Experiments and Analysis
### Accuracy Analysis  
Due to the filtering operation used in the proposed method, in order to verify the measuring accuracy of the proposed method objectively, several compared experiments were conducted among FTP [13] based on a well-known FFT technique in which the filtering operation is used, [PERSON]'s method [25] (Zhu), and the proposed method (Prop). One of them is to measuring a \"heart\" model as shown in Figure 11a. Figure 11b shows one of the three captured deformed patterns with the proposed method and the corresponding extracted nearly unbroken sinusoidal deformed pattern is shown in Figure 11c. Figure 11d shows one of the three captured sinusoidal deformed patterns with [PERSON]'s method. Figure 11e shows the reconstructed 3D shape result with FTP from Figure 11c. Figure 11f shows the reconstructed 3D shape result with [PERSON]'s method from the three captured sinusoidal deformed patterns. Figure 11g shows the reconstructed 3D shape result with the proposed  
Figure 10: Experiment for measuring crab model: (**a**) Measured crab model, (**b**) captured three deformed patterns, (**c**) corresponding Fourier spectrum, (**d**) extracted three deformed patterns, and (**e,f**) wrapped phase and reconstructed result. method from the extracted three deformed patterns as shown in Figure 11c. It can be seen that there some ripples on the surface of the reconstructed 3D shape with FTP, but the surface of the reconstructed 3D shape with Prop is smooth and close to that with Zhu. In order to further analyze the results in detail, the cutaway views at 140 columns from 1 to 255 rows of Figure 11e-g are shown in Figure 11h, the corresponding zoom in of \"ear\" part (the dotted circle region, A) and the smooth slope part (the dotted rectangle region, B) are shown in Figure 11i-j, respectively; it can be seen that the \"ear\" part with FTP is lost but well reconstructed with the proposed method and close to that of Zhu. It can be seen that if we directly used one of the three extracted nearly unbroken sinusoidal deformed patterns to reconstruct the 3D shape of the measured object with well-known FTP, it may lead to some measuring errors caused by filtering operation. However, in our proposed method, all the three extracted nearly unbroken sinusoidal deformed patterns are used to reconstruct the 3D shape of the measured object. The measuring errors can be improved by the constraint of multiple frames deformed patterns and the complementarity of the three extracted phase-shifting deformed patterns. It also can be seen that even though in the smooth region, the reconstructed surface of the proposed method is more close to that of Zhu than that of FTP. So the measuring accuracy of the proposed method is higher than that of FTP and close to that of Zhu. In order to further analyze the measuring accuracy of the proposed method, lots of planes with known heights are measured. Table 1 shows the measuring results of six planes with known heights of 3.00 mm, 5.00 mm, 9.00 mm, 14.00 mm, 25.00 mm, and 35.00 mm. \(h_{0}\) denotes the measured plane with known height and \(h_{avg}\) denotes the mean measuring height. The MAE denotes the mean absolute error and the RMS denotes the root of mean square error. It can be seen that the MAE is less than 0.082 mm and the RMS is less than 0.045 mm, so the proposed method has higher measuring accuracy. Figure 11: Compared experiments: (**a**) Measured “heart” model, (**b**) captured deformed pattern with Prop, (**c**) corresponding extracted deformed pattern, (**d**) captured deformed pattern with Zhu, (**e**) Reconstructed result with FTP, (**f**) reconstructed result with Zhu, (**g**) reconstructed result with Prop, and (**h–j**) correspond to cutaway views in 140 columns in (**e–g**). At the same time, in order to show the details of the above measured planes used for calibration, the reconstructed result for measuring the plane with height of 5.00 mm is shown in Figure 12a, it can be seen that the reconstructed 5.00 mm plane's surface is relatively much smooth with the proposed method.