README.md

Combined-frequency Phase Extraction (CFPE)

This repository contains code for the paper A fast combined-frequency phase extraction for phase shifting profilometry. In this work, we formulate the phase extraction problem with high-order harmonic as a maximum likelihood estimation (MLE), and our CFPE is an efficient optimization method by introducing a latent phase map and incorporating the expectation-maximization (EM) framework. Compared to the only high-order baseline (LLS), our CFPE method only needs ** about 5% execution time ** to achieve high-order accuracy.

Motivation

As a special curve fitting problem, our CFPE utilizes more data points (cross-frequency images) to solve a high-order harmonic model. That says, ${\theta }^{\ast }=\arg min{\mathrm{\Sigma }}_i{\mathrm{\Sigma }}_j(I_{i,j}-h_{i,j}{)}^2$.

Our CFPE reports an efficient iterative solution to this problem ${\varphi }_1^{new}=update({\varphi }_1^{old})$, and each iteration is computed with closed-form solution. More info is referred to the paper.

Install dependencies

conda install numpy matplotlib opencv seaborn
conda install -c anaconda pathlib

The experiments

• Exp1.ipynb: Test on several synthetic PSP images;
• Exp2.ipynb: Test on 4 real PSP cases;
• Exp3.ipynb: Compare the two interesting cases, with the same gamma distortion ($\gamma$=1.3),
  1. Our CFPE method with 3-frequency 3-step images (periods T1=33, T2=36, T3=39);
  2. Standard PE method with 1-frequency 9-step images (T=1920);

More results about the real cases

• Plate
• Altman cloak
• David
• Pigeon bottle

BibTeX

@article{lee2022cfpe,
  author={Lee, Yong and Mao, Ya and Chen, Zuobing},  
  journal={Optics Express},  
  title={Fast combined-frequency phase extraction for phase shifting profilometry},  
  year={2022},
  volume={30},
  number={25},
  pages={45288--45300},
  doi={https://doi.org/10.1364/OE.473513}}

Questions?

For any questions regarding this work, please email me at [email protected], [email protected].

Acknowledgements

These works are contributed to our CFPE project,

• LLS
• Industrial Camera from hikrobotics
• XGIMI Home projector