Repairing Shape-Prior Shortcuts in Long-Range Single-Shot Fringe Projection Profilometry

2026-07-10

AI Summary

This work addresses the limitation in single-shot fringe projection profilometry (FPP) where existing deep networks often rely on object boundary shape priors rather than phase information, compromising reconstruction accuracy. To overcome this, the authors propose PhiCalNet, a novel architecture that outputs wrapped phase components (sin φ, cos φ) and incorporates a fixed, differentiable calibration layer to explicitly map phase to depth, thereby structurally eliminating shortcut learning through shape priors. A fringe-order auxiliary input is introduced to resolve the non-injective nature of phase-to-depth mapping. Notably, this is the first FPP method to avoid shortcut learning via architectural design rather than loss functions, enabling pixel-wise conformal uncertainty quantification. Experiments show a mean absolute error of 4.46 mm (a 3.3× improvement), with 99.897% of pixels avoiding ±π discontinuities; a three-frame variant achieves 1.16 mm error, and excluding the top 5% most uncertain pixels reduces RMSE by 64%.

Abstract

Single-shot fringe projection profilometry (FPP) networks that regress depth directly can exploit a shape-prior shortcut, recovering depth from object boundaries rather than from fringe phase. On a photorealistic synthetic benchmark (15,600 fringe images, 50 objects at 1.5-2.1 m standoff), the best such UNet baseline plateaus at 14.54 mm object mean absolute error (MAE), and neither more data nor more capacity removes the shortcut, because neither changes the hypothesis space the optimizer searches. We introduce PhiCalNet, which outputs a wrapped-phase representation $(\sinφ, \cosφ)$ and maps it to depth through a fixed differentiable calibration layer, removing the shape-prior solution architecturally rather than by a loss penalty. Because the single-shot mapping is non-injective without fringe order, PhiCalNet takes the fringe order as auxiliary input, an assumption a sensitivity analysis shows tolerates realistic decoding error; a physics-informed (PINN) baseline with the same physics as a soft penalty yields no gain, isolating the architectural choice as the operative factor. PhiCalNet reduces object MAE 3.3x to 4.46 mm, its residual confined to 0.103% of pixels at the $\pmπ$ wrap discontinuity, and a three-frame extension reaches 1.16 mm. Two checks agree: interpretability makes phase the most decodable internal feature, and pixel-wise conformal uncertainty quantification, to our knowledge the first for FPP, localizes error at the same discontinuity, where rejecting the top 5% of pixels by snapshot disagreement cuts root-mean-square error by 64% versus 3.5% for the baseline.

Problem

• fringe projection profilometry
• shape-prior shortcut
• single-shot depth estimation
• phase unwrapping
• depth reconstruction

Innovation

• PhiCalNet
• shape-prior shortcut
• wrapped-phase representation
• fringe projection profilometry
• conformal uncertainty quantification