Non-iterative three dimensional reconstruction method of the structured light system based on polynomial distortion representation

•We proposed a new projector model and reorganized the expressions of the projector distortion with polynomial.•We simplified the reconstruction to a problem of solving a quartic polynomial.•The proposed method is non-iterative, and it includes the tangential distortion into the reconstruction.

In monocular structured light system, the iterative reconstruction method makes the measurement time-consuming, and the measurement accuracy is often hindered by the fact that the first-order radial distortion is included only. Compared with the conventional projector model, a new projector model, including both radial and tangential distortion, is proposed in this paper, which is described with the pinhole model according to the light direction. Furthermore, the iterative method is replaced by solving a quartic polynomial problem directly based on the proposed projector model. Experimental results show that the measurement accuracy and the efficiency are improved obviously. The standard deviation of the proposed method is 0.037mm, which is about a third of 0.113mm of the iterative method. The time consumed by the proposed method is 3.3% of that by the iterative method when one hundred thousand points are reconstructed.