Spatially Coupled Phase-to-Depth Calibration for Fringe Projection Profilometry
For researchers and practitioners in 3D optical metrology, this method improves spatial coherence in FPP calibration without sacrificing accuracy, offering a more efficient alternative to pixel-wise calibration.
The paper addresses spatial inconsistency in fringe projection profilometry by proposing a spatially coupled phase-to-depth calibration model that uses a single low-dimensional mapping shared across all pixels, achieving point-to-surface RMSE of about 12μm while improving spatial coherence and reducing runtime and storage requirements.
In fringe projection profilometry (FPP), depth is commonly recovered by fitting a phase-to-depth relation independently at each camera pixel. Although such pixel-wise calibration achieves high local accuracy, neighboring pixels can acquire markedly different calibration functions even when they observe the same smooth surface, producing spatially inconsistent geometry and structured surface artifacts. We propose a spatially coupled phase-depth transformation in which all pixels share a single low-dimensional mapping-global phase scalars combined with affine spatial terms on the undistorted reference-camera grid-rather than independent per-pixel fits, optionally augmented by a bounded, spatially smooth correction field. We further introduce a native-grid pairing scheme that constructs phase-depth calibration pairs directly on the reference-camera grid: when depth supervision comes from a rectified active-stereo pipeline, planes are fitted in stereo 3D and sampled back onto the camera grid along native rays, so the phase maps are never rectified. On a dental target with high-resolution scanner ground truth, the proposed model attains point-to-surface RMSE comparable to an active-stereo reference (about 12μm aggregate) while substantially improving spatial coherence over pixel-wise polynomial and rational calibration, and reduces the runtime mapping to a few element-wise operations per pixel with negligible parameter storage.