# Motion-Induced Phase Error Compensation Using Three-Stream Neural Networks
## 4 Conclusions and Discussion  
In this paper, we present a motion-induced error compensation method based on deep learning and computer graphics. By building the virtual system referring to an actual FPP system and performing image rendering, we can simulate the measurement process of a dynamic scene realistically and provide sufficient data for network training. Then, the proposed three-stream neural networks are trained using synthetic data and process three different orders of three-step fringe patterns in time series. The experimental results demonstrate that the motion-induced error introduced by various motion types can be reduced effectively compared with the traditional three-step PSP. Compared with existing methods, the proposed method has several improvements in accuracy, ability of dealing with non-uniform motion and efficiency. Compared with FTP assisted methods, the well-trained neural networks can avoid artificial filter design, which enable our method to provide more detailed and lossless results in dealing with complex objects. Compared with motion prediction methods, the proposed dataset generation method can realize the accurate simulation of non-uniform motion and has the advantage  
Figure 8: Measurement results of a rotating scene in an actual FPP system. (**a**) Rotating sculpture. (**b**) One of the deformed fringe patterns. (**c-e**) Reconstructed results of 12-step PSP, 3-step PSP, and proposed method, respectively. (**f-h**) Local enlarged results corresponding to (**c-e**). (**i**) Section line in 400 th row of the height (Z) distributions of three methods. of dealing this type of motion. Moreover, there are no additional images except basic three-step PSP fringe patterns needed during the experiment, and each high frequency deformed fringe patterns can reconstruct a new 3D result, which improves the efficiency of 3D reconstruction. However, there are several aspects that need to be further improved in the future investigation. Firstly, the simulated environment is confined in a laboratory condition, that is, the background behind the measured object is black, and rendered images should not be overexposed, which may cause a limited performance of the model in practical application. Moreover, there are three main noise sources that remain to be researched, including capturing noise of the camera and light of the source, motion noise that related to the camera and projector, and rendering noise in a virtual FPP system. Therefore, a more general dataset establishment method should be considered to adapt different situation. Secondly, due to the difficulty of modeling the complex 3D rigid motion (for example, irregular shake, random walk) and non-rigid motion, and the limited generalization capabilities of designed three-streams neural networks, our method might not perform an effective error compensation in these cases. Thirdly, with the decrease of projection-acquisition rate relative to motion, the phase error of the proposed method will inevitably increase, as shown in Figure 9. According to our simulation, to achieve a high accuracy measurement (phase error < 0.01\(\pi\)), the projection-acquisition rate should be at least about 30 fps when the movement speed of object is 50 mm/s. Lastly, the binary defocus techniques [40] are usually used to improve the measurement speed, and it will lead to a hybrid phase error caused by defocusing and motion, which are not considered in our work. So, how to design a model to balance both of mentioned factors is the key point of high-speed measurement. **Author Contributions:** Conceptualization, Y.L., W.G., J.S., Z.W. and Q.Z. ; methodology, Y.L. ; software, Y.L. ; validation, Y.L. ; formal analysis, Y.L. and W.G. ; investigation, Y.L. and W.G. ; resources, Y.L. ; data curation, Y.L. ; writing--original draft preparation, Y.L. ; writing--review and editing, Y.L., W.G., J.S., Z.W. and Q.Z. ; visualization, Y.L. ; supervision, J.S. and Q.Z. ; project administration, Q.Z. ; funding acquisition, J.S. and Q.Z.