发表机构
Department of Mechanical Engineering, Iowa State University; College of Engineering, University of Georgia（爱荷华州立大学机械工程系; 佐治亚大学工程学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究远距离单次条纹投影轮廓术存在的形状先验捷径问题，提出PhiCalNet方法，通过输出包裹相位表示并映射到深度，消除形状先验解决方案，降低物体平均绝对误差，提升了轮廓术性能。
AI 中文摘要
直接回归深度的单次条纹投影轮廓术（FPP）网络可以利用形状先验捷径，从物体边界而非条纹相位恢复深度。在一个逼真的合成基准测试中（15600幅条纹图像，50个物体，距离1.5 - 2.1米），最佳的UNet基线在物体平均绝对误差（MAE）为14.54毫米时趋于平稳，增加数据或容量都无法消除捷径。我们引入了PhiCalNet，它输出包裹相位表示$(\sin\phi, \cos\phi)$并通过固定的可微校准层将其映射到深度，从架构上消除形状先验解决方案。由于无条纹顺序时单次映射非单射，PhiCalNet将条纹顺序作为辅助输入，敏感性分析表明该假设能容忍实际解码误差。PhiCalNet将物体MAE降低3.3倍至4.46毫米，其残差在$\pm\pi$包裹不连续处限于0.103%的像素，三帧扩展可达1.16毫米。两项检查结果一致：可解释性使相位成为最易解码的内部特征，逐像素共形不确定性量化（据我们所知是FPP中的首次）将误差定位在同一不连续处，通过快照差异拒绝前5%的像素可将均方根误差降低64%，而基线仅降低3.5%。
英文摘要
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.
Comments23 pages, 8 figures. Part 2 of a two-part study. Part 1 (diagnosis): arXiv:2606.17093
