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.

翻译：在条纹投影轮廓术（FPP）中，通常通过在每个相机像素处独立拟合相位-深度关系来恢复深度信息。尽管这种逐像素标定实现了较高的局部精度，但相邻像素即使观测相同的平滑表面，也可能获得截然不同的标定函数，从而产生空间不一致的几何结构和结构化的表面伪影。我们提出一种空间耦合的相位-深度变换：所有像素共享一个单一的低维映射——全局相位标量结合无畸变参考相机网格上的仿射空间项，而非独立的逐像素拟合，并可选地叠加一个有界且空间平滑的校正场。我们进一步引入一种原生网格配对方案，直接在参考相机网格上构建相位-深度标定对：当深度监督来自经校正的主动立体系统时，在立体三维空间中拟合平面，并沿原生光线将平面采样回相机网格，从而相位图始终未经校正。在带有高分辨率扫描仪真值的牙科目标上，所提模型达到了与主动立体参考相当的点到表面均方根误差（约12微米整体误差），同时显著改善了相较于逐像素多项式和有理标定的空间一致性，并将运行时映射简化为每个像素的少量元素操作，参数存储可忽略不计。