NPC-SPU: Nonlinear Phase Coding-Based Stereo Phase Unwrapping for Efficient 3D Measurement

3D imaging based on phase-shifting structured light is widely used in industrial measurement due to its non-contact nature. However, it typically requires a large number of additional images (multi-frequency heterodyne (M-FH) method) or introduces intensity features that compromise accuracy (space domain modulation phase-shifting (SDM-PS) method) for phase unwrapping, and it remains sensitive to motion. To overcome these issues, this article proposes a nonlinear phase coding-based stereo phase unwrapping (NPC-SPU) method that requires no additional patterns while maintaining measurement accuracy. In the encoding stage, a novel nonlinear distortion feature is introduced, while the signal-to-noise ratio of the phase codeword is preserved. In the decoding stage, a local phase unwrapping method that does not require additional auxiliary information is first proposed, closely associating the distortion information in the local wrapped phase. Then, a pre-calibrated stereo constraint system is used to filter potential matching phases, significantly reducing phase ambiguity and computational costs. Finally, to avoid the time-consuming and complex intensity kernel matching used in traditional methods, we propose a local phase correlation matching (LPCM) technique that enables lightweight and robust phase unwrapping. Experimental results demonstrate that this algorithm significantly enhances 3D reconstruction performance in scenarios with large depth, large disparity, complex colored structures, and dynamic scenes. Specifically, in dynamic environments (20mm/s), the proposed method achieves a lower measurement error rate (0.7829% vs. 6.4962%) with only 3 patterns, compared to the traditional three-frequency heterodyne (T-FH) method (using 9 patterns). Additionally, its measurement accuracy outperforms the advanced SDM-PS method, which also uses 3 patterns (0.1102 mm vs. 0.3232 mm).