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

2026-06-13

AI Summary

This study addresses reconstruction errors in long-range single-shot fringe projection profilometry caused by signal attenuation, phase ambiguity, and model reliance on shape priors. For the first time, it integrates mechanistic interpretability with conformal uncertainty quantification to reveal that prevailing networks predominantly exploit object boundary priors rather than genuine phase decoding. To eliminate this shortcut, the authors propose PhiCalNet—a novel architecture that explicitly enforces wrapped phase output and maps it to depth through a differentiable calibration layer, thereby structurally removing dependence on shape priors. Experiments demonstrate substantial improvements: at distances of 1.5–2.1 meters, the mean absolute error drops from 14.54 mm to 4.46 mm. Moreover, excluding the top 5% of high-uncertainty pixels reduces RMSE by 64% (from 20.6 mm to 7.4 mm), significantly outperforming existing methods.

Abstract

Learning-based single-shot fringe projection profilometry (FPP) has been studied mostly at close range. The long-range regime (standoff beyond 1 m) remains largely unaddressed: inverse-square intensity falloff lowers fringe signal-to-noise ratio and degrades physical ground truth, the single-shot problem is ill-posed because fringe-order information is absent from one image, and these architectures have not been studied mechanistically. We present a diagnose-repair-verify study using mechanistic interpretability (MI) and conformal uncertainty quantification (UQ) as convergent diagnostics: they agree on one physical failure locus, driving and verifying an architectural repair. On a photorealistic synthetic benchmark (15,600 fringe images, 50 objects at 1.5-2.1 m), a best UNet baseline reaches 14.54 mm object mean absolute error (MAE). Three probes (linear probing, Grad-CAM, flat-plane out-of-distribution test) converge: the baseline solves the task via object-boundary shape priors rather than fringe-phase decoding. We repair this with PhiCalNet, which outputs wrapped phase rather than depth and applies a fixed differentiable calibration layer mapping phase to depth, removing the shape-prior solution from the hypothesis space architecturally rather than by a loss penalty. A physics-informed loss that enforces the same physics as a soft penalty on a depth-regressing network yields no measurable gain, isolating the architecture as the operative factor. PhiCalNet reduces object MAE 3.3x to 4.46 mm; the residual is carried by 0.103% of pixels at the +/-pi wrap discontinuity. Pixel-wise conformal UQ confirms the diagnosis: rejecting the top 5% of object pixels by snapshot disagreement cuts PhiCalNet RMSE by 64% (20.6->7.4 mm) versus 3.5% for the baseline. MI and UQ converge on the same failure locus.

Problem

• fringe projection profilometry
• long-range
• shape-prior shortcut
• single-shot
• phase unwrapping

Innovation

• mechanistic interpretability
• conformal uncertainty quantification
• single-shot fringe projection profilometry
• phase-to-depth calibration
• shape-prior shortcut