Directional periodicity-aware factorized attention network for single-shot fringe projection profilometry

Single-shot fringe projection profilometry based on deep learning has emerged as a promising approach for real-time three-dimensional (3D) measurement. However, existing methods face challenges when dealing with practical fringe patterns that contain various degradations. Specifically, the captured fringe images inevitably include high-frequency sensor noise and shadow regions where fringe modulation is weak or absent. Most existing networks learn features indiscriminately from both reliable and corrupted regions, leading to biased depth estimation. Moreover, conventional attention mechanisms treat all spatial directions equally, ignoring the inherent directional periodicity of fringe patterns. In this paper, a novel deep learning framework, to our knowledge, named FPDNet is proposed, incorporating two specifically designed modules to address these issues. First, a pixel-wise reliability attention module (PRAM) is introduced, which incorporates local mean and variance statistics as physics-guided noise-discriminative features. Periodic fringe patterns, governed by their sinusoidal nature, exhibit predictable and structured local statistics, while noise introduces irregular statistical fluctuations that deviate from these expected patterns. PRAM leverages this distinction to generate pixel-wise reliability maps, enabling adaptive fusion of original features in reliable regions and context-compensated features in degraded regions through cascaded dilated convolutions. This physics-guided design effectively suppresses the adverse impact of noise on depth mapping learning. Second, a factorized efficient spatial attention (FESA) module is designed, which decomposes spatial attention into horizontal and vertical components using elongated convolutional kernels (7×1 and 1×7), explicitly exploiting the directional characteristics of fringe patterns for enhanced periodic structure extraction while suppressing directionally inconsistent noise. Comprehensive experiments on a public dataset with three noise levels demonstrate that the proposed FPDNet achieves a mean absolute error (MAE) of 1.339 mm under low-noise conditions, representing a 54.7% reduction compared to the baseline. Furthermore, the proposed method exhibits superior noise robustness, with only a 12.3% increase in MAE from low to high noise levels, significantly outperforming existing methods while maintaining real-time processing at 52 FPS.