Phase-connected-region-based local graph cut for phase unwrapping in speckle-assisted fringe projection profilometry

Speckle-assisted fringe projection profilometry enables fast and accurate 3D measurements, but speckle mismatches on complex geometry often cause phase-unwrapping errors. To overcome this problem, we propose a phase-connected-region-based local graph cut (PCR-LGC) method for robust phase unwrapping. This method uses five patterns, where a four-step phase shifting scheme recovers the wrapped phase and one speckle image assists phase unwrapping. Phase-connected regions (PCRs) are introduced as basic units, reformulating phase unwrapping from the pixel level to the region level, thereby reducing the problem scale and improving robustness. A coarse-to-fine segmentation strategy enhances the reliability of PCR partitioning by combining phase continuity with edge cues. At the region level, an energy function is constructed that jointly accounts for speckle texture and the distribution characteristics of phase orders implied by phase shifting, and it is solved by a confidence-guided local graph cut algorithm. Experiments demonstrate that PCR-LGC achieves robust phase unwrapping and produces more continuous and detailed 3D point clouds. Quantitative evaluations show a mean absolute diameter bias of 0.08 mm and a phase unwrapping error rate below 0.15%, indicating that PCR-LGC is a reliable approach for structured light 3D reconstruction.