A Phase Recovery Method for Fringe Projection Profilometry Based on Multi-task Networks

3D reconstruction techniques have been extensively applied across a wide range of fields in recent years， including medical imaging， robotic navigation， virtual and augmented reality， 3D animation modeling， and online product inspection. Among these techniques， Fringe Projection Profilometry （FPP） has attracted significant attention owing to its non-contact measurement capability， full-field acquisition， and high spatial resolution. These advantages have led to its widespread adoption in industrial inspection， cultural heritage preservation， biomedical applications， and reverse engineering. Within an FPP system， phase recovery constitutes a fundamental and indispensable step， as both the accuracy and computational efficiency of phase estimation directly determine the quality of the reconstructed 3D surface and the overall system performance. Consequently， the development of fast， accurate， and robust phase recovery methods remains a central research topic in fringe projection profilometry.Traditional phase retrieval techniques mainly include Fourier Transform Profilometry （FTP） and multi-step Phase-Shifting Profilometry （PSP）. Multi-step phase-shifting methods achieve high phase accuracy by projecting and capturing multiple phase-shifted fringe patterns； however， their reliance on multiple frames significantly restricts their applicability in dynamic scenes or high-speed measurement scenarios. In contrast， Fourier transform-based methods can extract phase information from a single fringe image， offering improved measurement efficiency. Nevertheless， their performance tends to degrade considerably when dealing with complex surface geometries， depth discontinuities， severe noise， or strong surface reflectivity， resulting in reduced accuracy and robustness. In recent years， researchers have increasingly integrated deep learning with phase extraction and phase unwrapping processes， achieving high reconstruction accuracy while significantly reducing the number of required projection patterns. Compared with conventional analytical approaches， deep learning-based methods exhibit superior capability in handling noise， nonlinear distortions， and surface discontinuities. Despite these advantages， existing deep learning-based absolute phase recovery methods still suffer from several limitations. Existing deep learning-based absolute phase recovery methods mainly fall into two categories. The first predicts the numerator and denominator terms of wrapped phase at three different frequencies separately， then computes the absolute phase using multi-frequency or number-theoretic methods. The second employs either a dual-network or dual-decoding architecture to separately predict the numerator and denominator terms of the high-frequency wrapped phase along with the fringe order， thereby obtaining the absolute phase. The former suffers from error accumulation during multi-frequency unwrapping， leading to significant inaccuracies and poor stability. The latter incurs high computational complexity and low inference efficiency due to the multi-network or dual-decoder design.Aiming to address the issues of error accumulation and high model complexity inherent in existing methods， this paper proposes a novel multi-task phase recovery framework based on GD-UNet （UNet with an Information Gather-and-Distribute Mechanism）. The proposed method enables simultaneous prediction of the wrapped phase and fringe order within a single network， thereby allowing direct recovery of the absolute phase. Built upon the classical UNet architecture， the proposed model incorporates residual modules to enhance feature extraction capability and improve training stability. In addition， by integrating an information gather-and-distribute mechanism， the network supports multi-task learning and directly outputs the numerator and denominator of the wrapped phase as well as the corresponding fringe order. This unified design eliminates the need for multiple networks， effectively reducing computational complexity and inference time. Furthermore， to enhance the robustness of fringe order prediction-particularly in challenging regions such as object boundaries， sharp depth discontinuities， and highly reflective surfaces-a fringe order correction strategy based on Connected Domain Segmentation （CDS） of the wrapped phase is introduced. The proposed CDS-based correction method exploits the spatial continuity of the wrapped phase， under the assumption that all pixels within the same connected domain theoretically share an identical fringe order. Since prediction errors tend to occur more frequently near domain boundaries， the final fringe order for each connected region is determined through majority voting， thereby effectively suppressing local misclassifications. This strategy significantly improves the stability and accuracy of fringe order estimation without introducing additional computational burden. Extensive experiments are conducted to evaluate the performance of the proposed method under various conditions， including different surface materials， complex geometries， and discontinuous scenes. Both quantitative and qualitative comparisons with state-of-the-art methods demonstrate that the proposed GD-UNet-based framework achieves superior phase recovery accuracy while maintaining lower model complexity and faster inference speed.The experimental results indicate that the proposed approach effectively mitigates error accumulation， enhances robustness against noise and surface reflectivity， and exhibits strong generalization capability across diverse measurement scenarios. In conclusion， this paper aims to achieve stable and high-precision phase recovery from a single fringe image in complex scenes containing large surface discontinuities or isolated objects through a unified network model. A single-frame phase extraction method is presented， in which only one fringe image is required， and a single network simultaneously predicts the numerator and denominator of the wrapped phase as well as the fringe order map. The proposed approach demonstrates clear advantages in both accuracy and efficiency. Comprehensive experimental evaluations confirm that the method achieves excellent measurement accuracy and strong robustness in challenging scenarios， including complex surface reconstruction， high noise interference， and multi-material object measurement.