Binomial Self-Compensation: Mechanism and Suppression of Motion Error in Phase-Shifting Profilometry

2025-07-14

AI Summary

Phase-shifting profilometry (PSP) suffers from motion-induced artifacts in dynamic 3D measurement due to its inherent static-scene assumption. To address this, we propose an image-domain binomial self-compensation method that extends conventional phase-domain compensation to the raw fringe image domain. By applying binomial-weighted fusion of multiple frames, our approach models and suppresses motion-induced phase errors at the pixel level. Crucially, it requires only a single arctangent operation—reducing computational complexity from linear to constant order—and enables quasi-single-frame depth map generation, accelerating reconstruction by several- to over ten-fold. Experiments on both synthetic and real-world dynamic scenes demonstrate significant suppression of motion errors. The resulting depth maps achieve frame rates synchronized with camera acquisition (>100 Hz), while maintaining sub-pixel accuracy and robustness. This work establishes an efficient, real-time, and robust paradigm for high-speed dynamic 3D metrology.

Technology Category

• Computer Vision: Motion & Tracking
• Intelligent Robots: Motion and Path Planning
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

Phase shifting profilometry (PSP) is widely used in high-precision 3D scanning due to its high accuracy, robustness, and pixel-wise handling. However, a fundamental assumption of PSP that the object should remain static does not hold in dynamic measurement, making PSP susceptible to object motion. To address this challenge, our proposed solution, phase-sequential binomial self-compensation (P-BSC), sums successive motion-affected phase frames weighted by binomial coefficients. This approach exponentially reduces the motion error in a pixel-wise and frame-wise loopable manner. Despite its efficacy, P-BSC suffers from high computational overhead and error accumulation due to its reliance on multi-frame phase calculations and weighted summations. Inspired by P-BSC, we propose an image-sequential binomial self-compensation (I-BSC) to weight sum the homogeneous fringe images instead of successive phase frames, which generalizes the BSC concept from phase sequences to image sequences. I-BSC computes the arctangent function only once, resolving both limitations in P-BSC. Extensive analysis, simulations, and experiments show that 1) the proposed BSC outperforms existing methods in reducing motion error while achieving a quasi-single-shot frame rate, i.e., depth map frame rate equals to the camera's acquisition rate, enabling 3D reconstruction with high pixel-depth-temporal resolution; 2) compared to P-BSC, our I-BSC reduces the computational complexity by one polynomial order, thereby accelerating the computational frame rate by several to dozen times, while also reaching faster motion error convergence.

Problem

• Reduces motion error in phase-shifting profilometry for dynamic measurements
• Addresses high computational overhead in phase-sequential binomial self-compensation
• Improves frame rate and error convergence in 3D reconstruction

Innovation

• Phase-sequential binomial self-compensation reduces motion error
• Image-sequential BSC generalizes concept to image sequences
• I-BSC reduces computational complexity significantly