## Application of global phase filtering method in multi frequency measurement |

Optics Express, Vol. 22, Issue 11, pp. 13641-13647 (2014)

http://dx.doi.org/10.1364/OE.22.013641

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### Abstract

In reverse engineering, reconstruction of 3D point cloud data is the key step to acquire the final profile of the object. However, the quality of 3D reconstruction is influenced by noise in the three-dimensional measurement. This paper aims to tackle the issue of removing the noisy data from the complex point cloud data. The 3D-GPF (Three Dimensional Global Phase Filtering) global phase filtering method is proposed based on the study of phase filtering method, consisting of the steps below. Firstly, the six-step phase shift profilometry is used to obtain the local phase information, and encoding the obtained phase information. Through the global phase unwrapping method, the global phase can be acquired. Secondly, 3D-GPF method is used for the obtained global phase. Finally, the effect of 3D reconstruction is analyzed after the global phase filtering. Experimental results indicate that the noisy points of three-dimensional graphics is reduced 98.02%, the speed of 3D reconstruction is raised 12%.The effect of the proposed global phase filtering method is better than DCT and GSM methods. It is high precision and fast speed, and can be widely used in other 3D reconstruction application.

© 2014 Optical Society of America

## 1. Introduction

1. X. X. Jiao, X. Zhao, Y. Yang, Z. L. Fang, and X. C. Yuan, “Dual-camera enabled real-time three-dimensional integral imaging pick-up and display,” Opt. Express **20**(25), 27304–27311 (2012). [CrossRef] [PubMed]

5. L. Theis, R. Hosseini, and M. Bethge, “Mixtures of conditional Gaussian scale mixtures applied to multiscale image representations,” PLoS ONE **7**(7), e39857 (2012). [CrossRef] [PubMed]

6. B. Goossens, A. Pizurica, and W. Philips, “Image denoising using mixtures of projected Gaussian Scale Mixtures,” IEEE Trans. Image Process. **18**(8), 1689–1702 (2009). [CrossRef] [PubMed]

7. X. Wu, S. J. Liu, M. Wu, H. Q. Sun, J. L. Zhou, Q. Y. Gong, and Z. H. Ding, “Nonlocal denoising using anisotropic structure tensor for 3D MRI,” Med. Phys. **40**(10), 101904 (2013). [CrossRef] [PubMed]

8. L. Li, W. Hou, X. Zhang, and M. Ding, “GPU-based block-wise nonlocal means denoising for 3D ultrasound images,” Comput. Math. Methods Med. **2013**, 921303 (2013). [CrossRef] [PubMed]

11. L. M. Song, X. X. Dong, J. T. Xi, Y. G. Yu, and C. K. Yang, “A new phase unwrapping algorithm based on Three Wavelength Phase Shift Profilometry method,” Opt. Laser Technol. **45**, 319–329 (2013). [CrossRef]

## 2. The unwrapping principle of multi frequency phase

11. L. M. Song, X. X. Dong, J. T. Xi, Y. G. Yu, and C. K. Yang, “A new phase unwrapping algorithm based on Three Wavelength Phase Shift Profilometry method,” Opt. Laser Technol. **45**, 319–329 (2013). [CrossRef]

## 3. The filtering principle of global phase

*x*is their reflection. According to the continuous conditions and smooth conditions, the slope of two adjacent points (

_{1}、x_{2}、 ……、x_{m}, y_{1}、y_{2}、……、y_{m}*k*and

*j*) must be calculated, it can be written as:

## 4.Experiments

## 5.Conclusions

- 1) Better denoising effect: based on the global phase, the global phase filtering method is proposed in this paper, it has better effect than the local phase filtering method, and it can effectively eliminate the noisy disturbance.
- 2) Effectively retained the available phase information: for the existing phase filtering methods, a lot of useful phase information is also removed in removing noisy points, the method in this paper can retain the phase information effectively when removing all the noisy signals.
- 3) High speed: the number of the noisy points is less than other filtering methods, so the speed of 3D measurement can be improved.
- 4) Suit to different 3D reconstruction methods: the proposed phase filtering method is based on the absolute phase value, so the proposed method is suitable to other 3D reconstruction methods, such as multiple frequency method as well as the gray (code) method.

## Acknowledgments

## References and links

1. | X. X. Jiao, X. Zhao, Y. Yang, Z. L. Fang, and X. C. Yuan, “Dual-camera enabled real-time three-dimensional integral imaging pick-up and display,” Opt. Express |

2. | J. Yang, Z. H. Jia, X. Z. Qin, J. Yang, and Y. J. Hu, “BM3D Image Denoising Based on Shape-adaptive Principal Component Analysis,” Comput. Eng. |

3. | A. Danielyan, Y. W. Wu, P. Y. Shih, Y. Dembitskaya and A. Semyanov, “Denoising of two-photon fluorescence images with Block-Matching 3D filtering,” Methods, Japan, Epub 20 Mar. (2014). |

4. | C. Q. Kang, W. Q. Cao, L. Hua, L. Fang, and H. Chen, “Infrared image denoising algorithm via two-stage 3D filtering,” Laser Infrared. |

5. | L. Theis, R. Hosseini, and M. Bethge, “Mixtures of conditional Gaussian scale mixtures applied to multiscale image representations,” PLoS ONE |

6. | B. Goossens, A. Pizurica, and W. Philips, “Image denoising using mixtures of projected Gaussian Scale Mixtures,” IEEE Trans. Image Process. |

7. | X. Wu, S. J. Liu, M. Wu, H. Q. Sun, J. L. Zhou, Q. Y. Gong, and Z. H. Ding, “Nonlocal denoising using anisotropic structure tensor for 3D MRI,” Med. Phys. |

8. | L. Li, W. Hou, X. Zhang, and M. Ding, “GPU-based block-wise nonlocal means denoising for 3D ultrasound images,” Comput. Math. Methods Med. |

9. | X. M. Chen, L. T. Jiang, and R. D. Ying, “Research of 3D reconstruction and filtering algorithm based on depth information of Kinect,” Appl. Res. Comput. |

10. | H. B. Yu, D. Z. Feng, Y. Cao, and X. K. Yao, “Three-dimensional Space-time Nonadaptive Pre-filtering Approach in Airborne Radar,” J. Electron. Inf. Technol. |

11. | L. M. Song, X. X. Dong, J. T. Xi, Y. G. Yu, and C. K. Yang, “A new phase unwrapping algorithm based on Three Wavelength Phase Shift Profilometry method,” Opt. Laser Technol. |

12. | L. M. Song, C. M. Chen, L. Zhang, and X. X. Dong, “High Precision Global Phase Unwrapping Method Used in the Multi-frequency 3D Measurement,” Opt. Electron Eng. |

**OCIS Codes**

(100.0100) Image processing : Image processing

(100.2980) Image processing : Image enhancement

(100.6890) Image processing : Three-dimensional image processing

(110.0110) Imaging systems : Imaging systems

(110.6880) Imaging systems : Three-dimensional image acquisition

**ToC Category:**

Image Processing

**History**

Original Manuscript: April 17, 2014

Revised Manuscript: May 23, 2014

Manuscript Accepted: May 23, 2014

Published: May 29, 2014

**Citation**

Limei Song, Yulan Chang, Zongyan Li, Pengqiang Wang, Guangxin Xing, and Jiangtao Xi, "Application of global phase filtering method in multi frequency measurement," Opt. Express **22**, 13641-13647 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-11-13641

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### References

- X. X. Jiao, X. Zhao, Y. Yang, Z. L. Fang, X. C. Yuan, “Dual-camera enabled real-time three-dimensional integral imaging pick-up and display,” Opt. Express 20(25), 27304–27311 (2012). [CrossRef] [PubMed]
- J. Yang, Z. H. Jia, X. Z. Qin, J. Yang, Y. J. Hu, “BM3D Image Denoising Based on Shape-adaptive Principal Component Analysis,” Comput. Eng. 39(3), 241–244 (2013).
- A. Danielyan, Y. W. Wu, P. Y. Shih, Y. Dembitskaya and A. Semyanov, “Denoising of two-photon fluorescence images with Block-Matching 3D filtering,” Methods, Japan, Epub 20 Mar. (2014).
- C. Q. Kang, W. Q. Cao, L. Hua, L. Fang, H. Chen, “Infrared image denoising algorithm via two-stage 3D filtering,” Laser Infrared. 43(3), 261–264 (2013).
- L. Theis, R. Hosseini, M. Bethge, “Mixtures of conditional Gaussian scale mixtures applied to multiscale image representations,” PLoS ONE 7(7), e39857 (2012). [CrossRef] [PubMed]
- B. Goossens, A. Pizurica, W. Philips, “Image denoising using mixtures of projected Gaussian Scale Mixtures,” IEEE Trans. Image Process. 18(8), 1689–1702 (2009). [CrossRef] [PubMed]
- X. Wu, S. J. Liu, M. Wu, H. Q. Sun, J. L. Zhou, Q. Y. Gong, Z. H. Ding, “Nonlocal denoising using anisotropic structure tensor for 3D MRI,” Med. Phys. 40(10), 101904 (2013). [CrossRef] [PubMed]
- L. Li, W. Hou, X. Zhang, M. Ding, “GPU-based block-wise nonlocal means denoising for 3D ultrasound images,” Comput. Math. Methods Med. 2013, 921303 (2013). [CrossRef] [PubMed]
- X. M. Chen, L. T. Jiang, R. D. Ying, “Research of 3D reconstruction and filtering algorithm based on depth information of Kinect,” Appl. Res. Comput. 30(4), 1216–1218 (2013).
- H. B. Yu, D. Z. Feng, Y. Cao, X. K. Yao, “Three-dimensional Space-time Nonadaptive Pre-filtering Approach in Airborne Radar,” J. Electron. Inf. Technol. 36(1), 215–219 (2014).
- L. M. Song, X. X. Dong, J. T. Xi, Y. G. Yu, C. K. Yang, “A new phase unwrapping algorithm based on Three Wavelength Phase Shift Profilometry method,” Opt. Laser Technol. 45, 319–329 (2013). [CrossRef]
- L. M. Song, C. M. Chen, L. Zhang, X. X. Dong, “High Precision Global Phase Unwrapping Method Used in the Multi-frequency 3D Measurement,” Opt. Electron Eng. 39(12), 18–25 (2012).

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