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

• URL: http://arxiv.org/abs/2507.10009v1
• Date: Mon, 14 Jul 2025 07:41:56 GMT
• Title: Binomial Self-Compensation: Mechanism and Suppression of Motion Error in Phase-Shifting Profilometry
• Authors: Geyou Zhang, Kai Liu, Ce Zhu,
• Abstract summary: We propose an image-sequential binomial self-compensation (I-BSC) to weight sum the homogeneous fringe images instead of successive phase frames.<n>I-BSC outperforms existing methods in reducing motion error while achieving a quasi-single-shot frame rate.
• Score: 29.19420538435485
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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