# Binomial Self-compensation for Motion Error in Dynamic 3D Scanning

arXiv: https://arxiv.org/abs/2404.06693 · HTML: https://mlsanity.com/paper/2404.06693/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 37 references that are in the map.
- First posted on arXiv 10 Apr 2024.

## Builds on (most cited first, 3 of 3)

- [Causes and Corrections for Bimodal Multipath Scanning with Structured Light](https://mlsanity.com/paper/1706.02715/) (2017)
- [Micro Fourier Transform Profilometry (μFTP): 3D shape measurement at 10,000 frames per second](https://mlsanity.com/paper/1705.10930/) (2017)
- [Phase Guided Light Field for Spatial-Depth High Resolution 3D Imaging](https://mlsanity.com/paper/2311.10568/) (2023)

## Built on by (most cited first, 1 of 1)

- [Robust Phase-Shifting Profilometry for Arbitrary Motion](https://mlsanity.com/paper/2507.10009/) (2025)

## Abstract (arXiv)

Phase shifting profilometry (PSP) is favored in high-precision 3D scanning due to its high accuracy, robustness, and pixel-wise property. However, a fundamental assumption of PSP that the object should remain static is violated in dynamic measurement, making PSP susceptible to object moving, resulting in ripple-like errors in the point clouds. We propose a pixel-wise and frame-wise loopable binomial self-compensation (BSC) algorithm to effectively and flexibly eliminate motion error in the four-step PSP. Our mathematical model demonstrates that by summing successive motion-affected phase frames weighted by binomial coefficients, motion error exponentially diminishes as the binomial order increases, accomplishing automatic error compensation through the motion-affected phase sequence, without the assistance of any intermediate variable. Extensive experiments show that our BSC outperforms the existing methods in reducing motion error, while achieving a depth map frame rate equal to the camera's acquisition rate (90 fps), enabling high-accuracy 3D reconstruction with a quasi-single-shot frame rate.