Robust Phase-Shifting Profilometry for Arbitrary Motion

TL;DR

The paper tackles motion-induced errors in phase-shifting profilometry by separating ghosting artifacts (image misalignment) from ripple-like distortions (phase deviation) and introducing a robust two-stage framework (RPSP-AM) that handles 6-DoF, non-rigid, and multi-target motion. Ghosting is mitigated with pixel-wise optical-flow-based alignment, while ripple distortions are suppressed using an image-sequential binomial self-compensation (I-BSC) method that computes a motion-error-free phase with a single arctangent. Extensive experiments show state-of-the-art performance across challenging dynamic scenarios, including significant reductions in RMSE compared to prior methods, and the approach extends PSP applicability to real-world dynamic contexts. The work also demonstrates favorable computational efficiency and provides open-source implementation of I-BSC.

Abstract

Phase-shifting profilometry (PSP) enables high-accuracy 3D reconstruction but remains highly susceptible to object motion. Although numerous studies have explored compensation for motion-induced errors, residual inaccuracies still persist, particularly in complex motion scenarios. In this paper, we propose a robust phase-shifting profilometry for arbitrary motion (RPSP-AM), including six-degrees-of-freedom (6-DoF) motion (translation and rotation in any direction), non-rigid deformations, and multi-target movements, achieving high-fidelity motion-error-free 3D reconstruction. We categorize motion errors into two components: 1) ghosting artifacts induced by image misalignment, and 2) ripple-like distortions induced by phase deviation. To eliminate the ghosting artifacts, we perform pixel-wise image alignment based on dense optical flow tracking. To correct ripple-like distortions, we propose a high-accuracy, low-complexity image-sequential binomial self-compensation (I-BSC) method, which performs a summation of the homogeneous fringe images weighted by binomial coefficients, exponentially reducing the ripple-like distortions with a competitive computational speed compared with the traditional four-step phase-shifting method. Extensive experimental results demonstrate that, under challenging conditions such as 6-DoF motion, non-rigid deformations, and multi-target movements, the proposed RPSP-AM outperforms state-of-the-art (SoTA) methods in compensating for both ghosting artifacts and ripple-like distortions. Our approach extends the applicability of PSP to arbitrary motion scenarios, endowing it with potential for widespread adoption in fields such as robotics, industrial inspection, and medical reconstruction.

Figures (16)

• Figure 1: Diagram of motion errors in PSP: a) ghosting artifacts: induced by the image misalignment and b) ripple-like distortions: induced by the phase deviation.
• Figure 2: Pipeline of RPSP-AM. Ghosting artifacts and ripple-like distortions are eliminated successively through optical-flow-based image alignment and I-BSC. We omit the speckle pattern used for phase unwrapping in this diagram.
• Figure 3: Left: mechanism and characteristic of ripple-like distortions. Right: P-BSC zhang2024binomial exponentially reduces the motion error by leveraging the inherent property of the phase sequence. Inspired by P-BSC, we propose an I-BSC to more effectively and efficiently suppress ripple-like distortions by directly processing the image sequence.
• Figure 4: Comparison between P-BSC zhang2024binomial and our I-BSC. P-BSC zhang2024binomial computes the arctangent function $K+1$ times to have a phase sequence, and then sums the phase sequence weighted by binomial coefficients. Our I-BSC sums the homogeneous fringe images, weighted by binomial coefficients, to generate four compensated fringe images, and then compute the motion-error-free phase. The arctangent function is computed only once.
• Figure 5: The sum of the error terms along the diagonal direction precisely yields the high-order difference form error terms (Eq. (\ref{['EQ:IBSCError']}) to Eq. (\ref{['EQ:IBSCError2']}))..