## High-resolution, real-time 3D absolute coordinate measurement based on a phase-shifting method

Optics Express, Vol. 14, Issue 7, pp. 2644-2649 (2006)

http://dx.doi.org/10.1364/OE.14.002644

Acrobat PDF (814 KB)

### Abstract

We describe a high-resolution, real-time 3D absolute coordinate measurement system based on a phase-shifting method. It acquires 3D shape at 30 frames per second (fps), with 266K points per frame. A tiny marker is encoded in the projected fringe pattern, and detected by software from the texture image and the gamma map. Absolute 3D coordinates are obtained from the detected marker position and the calibrated system parameters. To demonstrate the performance of the system, we measure a hand moving over a depth distance of approximately 700 mm, and human faces with expressions. Applications of such a system include manufacturing, inspection, entertainment, security, medical imaging.

© 2006 Optical Society of America

## 1. Introduction

1. J. Salvi, J. Pages, and J. Batlle, “Pattern codification strategies in structured light systems,” Pattern Recogn. **37**, 827–849 (2004). [CrossRef]

3. K. G. Harding, “Phase Grating Use for Slop Discrimination in Moiré Contouring,” in *Proc. SPIE* , vol. **1614**, pp. 265–270 (1991). [CrossRef]

4. Z. J. Geng, “Rainbow 3D Camera: New Concept of High-Speed Three Vision System,” Opt. Eng. **35**, 376–383 (1996). [CrossRef]

5. P. S. Huang, Q. Hu, F. Jin, and F. P. Chiang, “Color-Encoded Digital Fringe Projection Technique for High-Speed Three-Dimensional Surface Contouring,” Opt. Eng. **38**, 1065–1071 (1999). [CrossRef]

6. C. Guan, L. G. Hassebrook, and D. L. Lau, “Composite Structured Light Pattern for Three-Dimensional Video,” Opt. Express **11**, 406–417 (2003). [CrossRef] [PubMed]

8. P. S. Huang, C. Zhang, and F. P. Chiang, “High-Speed 3D Shape Measurement Based on Digital Fringe Projection,” Opt. Eng. **42**, 163–168 (2003). [CrossRef]

9. P. S. Huang and S. Zhang, “A Fast Three-Step Phase Shifting Algorithm,” Appl. Opt. (under press) (2006). [CrossRef] [PubMed]

10. Q. Hu, P. S. Huang, Q. Fu, and F. P. Chiang, “Calibration of a 3D Shape Measurement System,” Opt. Eng. **42**, 487–493 (2003). [CrossRef]

11. S. Zhang and P. S. Huang, “A Novel Structured Light System Calibration,” Opt. Eng. (under press) (2006). [CrossRef]

## 2. Principle

### 2.1. Three-step phase-shifting algorithm

*I*′(

*x*,

*y*) is the average intensity,

*I*′′(

*x,y*) the intensity modulation, and ϕ(

*x,y*) the phase. Solving Eqs. (1)-(3) simultaneously, we can obtain phase and data modulation,

*x,y*) in Eq. (4) is the so-called modulo 2π at each pixel, whose value ranges from 0 to 2π. If the fringe patterns contain multiple fringes, phase unwrapping is necessary to remove the sawtooth-like discontinuities and obtain a continuous phase map [13]. Once the continuous phase map is obtained, the phase at each pixel can be converted to

*xyz*coordinates of the corresponding point on the object surface through calibration [14

14. R. Legarda-Sáenz, T. Bothe, and W. P. Jüptner, “Accurate Procedure for the Calibration of a Structured Light System,” Opt. Eng. **43**, 464–471 (2004). [CrossRef]

10. Q. Hu, P. S. Huang, Q. Fu, and F. P. Chiang, “Calibration of a 3D Shape Measurement System,” Opt. Eng. **42**, 487–493 (2003). [CrossRef]

11. S. Zhang and P. S. Huang, “A Novel Structured Light System Calibration,” Opt. Eng. (under press) (2006). [CrossRef]

*I*′(

*x,y*) represents a flat image of the measured object and can be used for texture mapping. Data modulation η(

*x,y*) in Eq. (5) has a value between 0 and 1 and can be used to determine the quality of the phase data at each pixel with 1 being the best.

### 2.2. Marker detection

*y*=

*h*(

*x*) for

*x*∈ [1,

*w*], where

*w*is image width. Functional

*g*(

*x,h*(

*x*)) reaches the maximum. Here,

*I*

_{g}is the inverted gamma map,

*I*

_{t}is the texture image,

*w*

_{g}is the weight for the gamma map, and

*w*

_{t}is the weight for the texture image. We consider both the texture and the gamma map to minimize the effect of noise and background. Our experiments show that more than 99% markers can be correctly detected using this method.

### 2.3. Absolute phase to coordinate conversion

_{0}, to be absolute zero,

11. S. Zhang and P. S. Huang, “A Novel Structured Light System Calibration,” Opt. Eng. (under press) (2006). [CrossRef]

*A*

_{c}and

*A*

_{p}, respectively. The extrinsic parameter matrices for a fixed world coordinate system are

*M*

_{c}and

*M*

_{p}for the camera and the projector, respectively. Once the system is calibrated, the relationships between the world coordinate system and the camera and projector coordinate systems can be established, we obtain,

*s*

_{c},

*s*

_{p}are camera and projector scaling factor, respectively, (

*u*

_{c},

*v*

_{c}) and (

*u*

_{p},

*v*

_{p}) are the camera and projector image coordinates, respectively, and (

*X*

_{w},

*Y*

_{w},

*Z*

_{w}) is the world coordinates.

*X*

_{w},

*Y*

_{w},

*Z*

_{w}),

*s*

_{c},

*s*

_{p}

*u*

_{p}, and

*v*

_{p}are unknowns, since there are seven equations, the world coordinate (

*X*

_{w},

*Y*

_{w},

*Z*

_{w}) can be uniquely determined.

### 2.4. Marker removal

*x,y*) in Eq. (5)) should be always 1. On the other hand, image intensity on cross” is

*I*

_{0}for all images,

*I*

_{1}=

*I*

_{2}=

*I*

_{3}=

*I*

_{0}. Hence γ = 0 for points on marker. Texture images can be obtained by averaging three fringe images,

*I*

_{0}= 2

*I*′, functional

*f*(

*x,y*) is the same across image, and the marker is removed. The intensities of projected fringe images generated by the computer are,

*a*+

*b*=

*I*

_{c}. Here Ic is the intensity value for the markers, which is 255 in our case. Figure 1(d) shows the result after removing the marker. It clearly shows that the marker is removed cleanly.

## 3. Experiments

*absolute*coordinates of the object, namely, it can measure both geometric shapes and positions. It also shows that the feature details are clearly captured once the object is in focus and the fringe images are bright, while noisier when the object is far away from the focal plane, e.g., when the fringe images are defocused and darker. This is because when the fringe images are darker, the signal-to-noise is smaller. These experiments demonstrated that our system can measure both geometric shapes and positions for a relatively large depth range. More data is available at http://math.harvard.edu/˜songzhang. Moreover, we measured a flat white board in focus and well illuminated, the measurement error was found to be RMS 0.10 mm. For a volume of 342(H) × 376(V) × 700(D) mm, the error is RMS 0.10–0.22 mm. It should be noted that we used a 3 × 3 Gaussian filter for all data to smooth the most significantly random noises. If no filter is used, the measurement error is approximately RMS 0.15–0.30 mm over the same volume.

## 4. Conclusion

## Acknowledgement

## References and links

1. | J. Salvi, J. Pages, and J. Batlle, “Pattern codification strategies in structured light systems,” Pattern Recogn. |

2. | S. Zhang and P. Huang, “High-Resolution, Real-time 3D Shape Acquisition,” in |

3. | K. G. Harding, “Phase Grating Use for Slop Discrimination in Moiré Contouring,” in |

4. | Z. J. Geng, “Rainbow 3D Camera: New Concept of High-Speed Three Vision System,” Opt. Eng. |

5. | P. S. Huang, Q. Hu, F. Jin, and F. P. Chiang, “Color-Encoded Digital Fringe Projection Technique for High-Speed Three-Dimensional Surface Contouring,” Opt. Eng. |

6. | C. Guan, L. G. Hassebrook, and D. L. Lau, “Composite Structured Light Pattern for Three-Dimensional Video,” Opt. Express |

7. | S. Rusinkiewicz, O. Hall-Holt, and L. Marc, “Real-Time 3D Model Acquisition,” in |

8. | P. S. Huang, C. Zhang, and F. P. Chiang, “High-Speed 3D Shape Measurement Based on Digital Fringe Projection,” Opt. Eng. |

9. | P. S. Huang and S. Zhang, “A Fast Three-Step Phase Shifting Algorithm,” Appl. Opt. (under press) (2006). [CrossRef] [PubMed] |

10. | Q. Hu, P. S. Huang, Q. Fu, and F. P. Chiang, “Calibration of a 3D Shape Measurement System,” Opt. Eng. |

11. | S. Zhang and P. S. Huang, “A Novel Structured Light System Calibration,” Opt. Eng. (under press) (2006). [CrossRef] |

12. | D. Malacara, ed., |

13. | D. C. Ghiglia and M. D. Pritt, |

14. | R. Legarda-Sáenz, T. Bothe, and W. P. Jüptner, “Accurate Procedure for the Calibration of a Structured Light System,” Opt. Eng. |

15. | D. A. Forsyth and J. Ponce, |

16. | S. Zhang, “High-Resolution, Real-Time 3D Shape Measurement,” Ph.D. thesis, Stony Brook University, State University of New York, (2005). |

**OCIS Codes**

(100.2650) Image processing : Fringe analysis

(110.6880) Imaging systems : Three-dimensional image acquisition

(120.3940) Instrumentation, measurement, and metrology : Metrology

(120.5050) Instrumentation, measurement, and metrology : Phase measurement

(120.5800) Instrumentation, measurement, and metrology : Scanners

(120.6650) Instrumentation, measurement, and metrology : Surface measurements, figure

(150.6910) Machine vision : Three-dimensional sensing

**ToC Category:**

Imaging Systems

**History**

Original Manuscript: January 31, 2006

Revised Manuscript: March 16, 2006

Manuscript Accepted: March 16, 2006

Published: April 3, 2006

**Virtual Issues**

Vol. 1, Iss. 5 *Virtual Journal for Biomedical Optics*

**Citation**

Song Zhang and Shing-Tung Yau, "High-resolution, real-time 3D absolute coordinate measurement based on a phase-shifting method," Opt. Express **14**, 2644-2649 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-7-2644

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### References

- J. Salvi, J. Pages, and J. Batlle, "Pattern codification strategies in structured light systems," Pattern Recogn. 37, 827-849 (2004). [CrossRef]
- S. Zhang and P. Huang, "High-Resolution, Real-time 3D Shape Acquisition," in IEEE Computer Vision and Pattern Recognition Workshop on Realtime 3D Sensors and Their Uses, vol. 3, pp. 28-37 (2004).
- K. G. Harding, "Phase Grating Use for Slop Discrimination in Moir´e Contouring," inProc. SPIE, vol. 1614, pp. 265-270 (1991). [CrossRef]
- Z. J. Geng, "Rainbow 3D Camera: New Concept of High-Speed Three Vision System," Opt. Eng. 35, 376-383 (1996). [CrossRef]
- P. S. Huang, Q. Hu, F. Jin, and F. P. Chiang, "Color-Encoded Digital Fringe Projection Technique for High-Speed Three-Dimensional Surface Contouring," Opt. Eng. 38, 1065-1071 (1999). [CrossRef]
- C. Guan, L. G. Hassebrook, and D. L. Lau, "Composite Structured Light Pattern for Three-Dimensional Video," Opt. Express 11, 406-417 (2003). [CrossRef] [PubMed]
- S. Rusinkiewicz, O. Hall-Holt, and L. Marc, "Real-Time 3D Model Acquisition," in SIGGRAPH, pp. 438 - 446 (2002).
- P. S. Huang, C. Zhang, and F. P. Chiang, "High-Speed 3D Shape Measurement Based on Digital Fringe Projection," Opt. Eng. 42, 163-168 (2003). [CrossRef]
- P. S. Huang and S. Zhang, "A Fast Three-Step Phase Shifting Algorithm," Appl. Opt. (under press) (2006). [CrossRef] [PubMed]
- Q. Hu, P. S. Huang, Q. Fu, and F. P. Chiang, "Calibration of a 3D Shape Measurement System," Opt. Eng. 42, 487-493 (2003). [CrossRef]
- S. Zhang and P. S. Huang, "A Novel Structured Light System Calibration," Opt. Eng. (under press) (2006). [CrossRef]
- D. Malacara, ed., Optical Shop Testing (John Wiley and Songs, NY, 1992).
- D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (John Wiley and Sons, Inc, 1998).
- R. Legarda-S´aenz, T. Bothe, and W. P. Jüptner, "Accurate Procedure for the Calibration of a Structured Light System," Opt. Eng. 43, 464-471 (2004). [CrossRef]
- D. A. Forsyth and J. Ponce, Computer Visoin-A Modern Approach (Prentice-Hall, Inc., New Jersey, 2002).
- S. Zhang, "High-Resolution, Real-Time 3D Shape Measurement," Ph.D. thesis, Stony Brook University, State University of New York, (2005).

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