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

arXiv: https://arxiv.org/abs/2606.17093 · HTML: https://mlsanity.com/paper/2606.17093/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 35 references that are in the map.
- First posted on arXiv 13 Jun 2026.

## Builds on (most cited first, 8 of 8)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [Shortcut Learning in Deep Neural Networks](https://mlsanity.com/paper/2004.07780/) (2020)
- [TransUNet: Transformers Make Strong Encoders for Medical Image Segmentation](https://mlsanity.com/paper/2102.04306/) (2021)
- [Domain Randomization for Transferring Deep Neural Networks from Simulation to the Real World](https://mlsanity.com/paper/1703.06907/) (2017)
- [Understanding intermediate layers using linear classifier probes](https://mlsanity.com/paper/1610.01644/) (2016)
- [High-Resolution Image Synthesis and Semantic Manipulation with Conditional GANs](https://mlsanity.com/paper/1711.11585/) (2017)
- [Hformer: Hybrid CNN-Transformer for Fringe Order Prediction in Phase Unwrapping of Fringe Projection](https://mlsanity.com/paper/2112.06759/) (2021)

## Abstract (arXiv)

Learning-based single-shot fringe projection profilometry (FPP) has been studied almost entirely at close range, and the networks used are evaluated only on aggregate error, leaving open whether they recover depth from fringe phase or from object-level shape cues that correlate with depth. This paper diagnoses that question mechanistically in the long-range regime (standoff beyond 1 m). Using FPP-ML-Bench, an open photorealistic synthetic benchmark (15,600 fringe images, 50 objects at 1.5--2.1 m), we first formalize why the single-shot fringe-to-depth mapping is more severely ill-posed at long range: it is non-injective without fringe-order information, and the depth error from an incorrect fringe order grows as Z2 in the working distance. Systematic ablations, extended with a multi-frame study, establish a best UNet baseline at 14.54 mm object mean absolute error (MAE), 18% of the 80 mm object depth range, with only a 1.9× spread across four architectures, indicating a representational rather than a capacity-bound limit. A mechanistic interpretability study, the first applied to an FPP network, localizes the cause: linear probing shows edges are 2.82× more decodable than depth, Grad-CAM shows attention favoring boundaries over fringes by 1.28×, and an in-range flat-plane test collapses a featureless plane to background depth despite valid fringes. The baseline solves the task via object-boundary shape priors rather than fringe-phase decoding. Because the shortcut is a hypothesis-space property, additional data or larger models will not remove it, motivating an architectural repair that removes the shape-prior solution by construction.