# Robust Phase-Shifting Profilometry for Arbitrary Motion

arXiv: https://arxiv.org/abs/2507.10009 · HTML: https://mlsanity.com/paper/2507.10009/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 51 references that are in the map.
- First posted on arXiv 14 Jul 2025.

## Builds on (most cited first, 5 of 5)

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [RAFT: Recurrent All-Pairs Field Transforms for Optical Flow](https://mlsanity.com/paper/2003.12039/) (2020)
- [High-speed and high-efficiency three-dimensional shape measurement based on Gray-coded light](https://mlsanity.com/paper/2001.06790/) (2020)
- [Causes and Corrections for Bimodal Multipath Scanning with Structured Light](https://mlsanity.com/paper/1706.02715/) (2017)
- [Binomial Self-compensation for Motion Error in Dynamic 3D Scanning](https://mlsanity.com/paper/2404.06693/) (2024)

## Abstract (arXiv)

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.