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

Geyou Zhang, Ce Zhu, Kai Liu

TL;DR

A pixel-wise and frame-wise loopable binomial self-compensation (BSC) algorithm to effectively and flexibly eliminate motion error in the four-step phase shifting profilometry, enabling high-accuracy 3D reconstruction with a quasi-single-shot frame rate.

Abstract

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.

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

TL;DR

A pixel-wise and frame-wise loopable binomial self-compensation (BSC) algorithm to effectively and flexibly eliminate motion error in the four-step phase shifting profilometry, enabling high-accuracy 3D reconstruction with a quasi-single-shot frame rate.

Abstract

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.
Paper Structure (11 sections, 15 equations, 10 figures, 1 algorithm)

This paper contains 11 sections, 15 equations, 10 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. System Setup and Frequency Selection
  4. Binomial Self-compensation for Motion Error
  5. Stereo Phase Unwrapping
  6. Experimental Evaluations
  7. Absolute Accuracy of 3D Reconstruction
  8. Robustness on Depth Discontinuous Scenes
  9. Temporal Resolution of 3D Imaging
  10. Generality on Different Dynamic Objects
  11. Limitations and Future Outlook

Figures (10)

  • Figure 1: Diagram of our paraxial binocular structured light system.
  • Figure 2: Binomial self-compensation for motion error.
  • Figure 3: Motion error converges as $K$ increases: (a) three-step VS four-step phase shifting, and (b) visualization of motion error in four-step phase shifting, the mean absolute error of phase exponentially diminishes as $K$ increases.
  • Figure 4: Experimental setup.
  • Figure 5: Measurement error VS motion speed of a periodically waving plate by traditional four-step phase shifting, HTC wang2018motion, $\mu$-FTP zuo2018micro, PFD liu2019real, PFS guo2021real, and our BSC, the value in parentheses represents the mean error. Note the y-axis is in logarithmic scale.
  • ...and 5 more figures