# Reconstruction of Isolated Moving Objects by Motion-Induced Phase Shift Based on PSP
## 4 Experiments  
The experimental setup is shown in Figure 1. It includes two color cameras (Manta 504C with 2452 \(\times\) 2056 resolution, Allied Vision Technologies Inc., Freistaat Thuringen State, Germany) and a projector (Wintech DLP PRO 4500 with 912 \(\times\) 1140 resolution, Wintech Digital System Technology Corp., Beijing, China). Please note, only one camera is used in the proposed method. The isolated models shown in Figure 1b are reconstructed by the proposed method based on three-step PSP. As the isolated objects are reconstructed, the dual-frequency phase unwrapping method is employed. Two-dimensional movement is applied on the object during the reconstruction. The same with the method in [16], a red fringe pattern is projected for convenient movement tracking. With the captured images, the red channel provides the sinusoidal fringe information, and the blue channel contains the pure object image without the fringe pattern. Then, the phase information and object movement information can be retrieved from the images in different channels. Three images are captured, respectively, during the projection of the high frequency (30 pixel/fringe) and low frequency (150 pixel/fringe), and Figure 1c,d show their first image. At the beginning, the high frequency fringe pattern is projected and three images with object motion are captured, as shown in Figure 2a-c. Then, the low frequency fringe pattern is projected and three images with motion are captured, as shown in Figure 2d-f.  
Figure 1: The isolated objects and fringe pattern. (**a**) The structure of the reconstruction system; (**b**) the image of the isolated objects; (**c**) the fringe pattern of high frequency; (**d**) the fringe pattern of low frequency. As the fringe pattern is projected in red color, therefore, in the object image shown in Figure 3a, the sinusoidal fringe pattern is contained in the red component (as shown in Figure 3b). In the blue component, the pure object image can be found as presented in Figure 3c. The SIFT (scale-invariant feature transform) [21] algorithm is implemented on the blue component images to track the object movement, as shown in Figure 4. Then, the rotation matrix and translation vector are calculated by the SVD (singular value decomposition) algorithm [18]. Figure 4: The result of the SIFT algorithm. Figure 3: The red component and blue component of the captured image. (**a**) The fringe pattern of the object; (**b**) the red component image of (**a**); (**c**) the blue component image of (**a**). Figure 2: The captured object images of different frequencies. (**a–c**) The object image of high frequency; (**d–f**) the object image of low frequency. Based on the movement information, the wrapped phase maps for the two frequencies are obtained. The results are shown in Figure 5. A significant position mismatch is introduced by the object motion. In order to unwrap the phase value of the high frequency, the phase value of the low frequency was unwrapped, as given in Figure 6a. The position mismatch between the wrapped phase maps of the two frequencies should be removed. The object position in the low frequency is moved to the object position in the high frequency. Then, the phase variation caused by the motion is compensated by Equation (18) (shown in Figure 6b). Then, the dual-frequency unwrapping method is applied, and the result is shown in Figure 6c. With the correct phase map, the object is reconstructed successfully, as presented in Figure 7a,b. It is apparent that the object is reconstructed well. The object is reconstructed by the traditional PSP for comparison (as given in Figure 7c,d). It can be seen that a high-accuracy result is achieved by the proposed method, and the motion-induced error is removed. Figure 5: The wrapped phase maps of the two frequencies. (**a**) The high frequency wrapped phase map; (**b**) the low frequency wrapped phase map. Figure 6: The unwrapped phase maps.