## Human face measurement by projecting bandlimited random patterns

Optics Express, Vol. 14, Issue 17, pp. 7692-7698 (2006)

http://dx.doi.org/10.1364/OE.14.007692

Acrobat PDF (1156 KB)

### Abstract

This article presents a fast and accurate method to measure human faces for medical applications. To encode an object point, several random patterns are projected. A correlation technique, which takes only the area of one pixel into account, is used to locate the homologous points. It could be shown that band limited random patterns are helpful for noise reduction. The comparison of the point cloud of a measured plane with an ideal one showed a standard deviation less then 50*μ*m. Furthermore a depth difference of 20*μ*m is detectable.

© 2006 Optical Society of America

## 1. Introduction

*s*and the measurement accuracy better than 100μmm. Furthermore a cost-saving measuring setup is desired.

## 2. Method

*x→*and x→

_{cl}_{cr}) in the corresponding image plane. In addition to the pinhole model, anisotropy and shear have been taken into account, distortion is not yet included. The extrinsic six camera parameters (3 for the centre of projection and 3 for the angles of rotation) describe the position of the camera in an external world coordinate system by a simple Euclidian transformation. To reduce the number of parameters, the world coordinate system is identified with the system of the left camera. Actually, the intrinsic parameters of both cameras are determined by a previously calibration procedure using a planar calibration pattern [1].

*l*is the intensity at the current position in picture

_{i}*i*of the left camera, and

*l→*the average intensity of the pixel over all

*N*images. The terms for the right camera are analogous. This implies that the transformation between the intensity of homologous points is only linear. Therefore nonlinearities, for example the gain of the cameras or angle dependent scattering may lead to systematic measurement errors. A point is accepted as a homologous one if

*ρ*exceeds a certain threshold (e.g.

*ρ*= 0.9). This threshold is essential to suppress remaining outliers, which mainly occur if an object point is only visible in one camera.

_{th}## 3. Experimental setup

*μ*m,) and a commercially available XGA-projector (1024×768). The focal length of the camera lenses is 25mm and therefore a camera has a diagonally angle of view of about 2

*θ*= 17°. The lateral resolution, caused by pixel size and focal length, is about 0.4mm whereas the longitudinal resolution covers a range of 0.4mm to 0.8mm, depending on the angle between optical axes of the cameras. In this setup the maximum allowed angle between the optical axes is limited by the nose of the person, because both sides of the nose need to be visible as well as possible in both cameras. We used an angle of 20° which leads to a longitudinal resolution of 0.8mm. The distance between one camera and the measured person is about 1.1m. The measurement volume is about 250×200×180 (H×W×D/mm).

## 4. Data processing and optimization

### 4.1. Subpixel interpolation

*ρ*for this position. The position is shifted till

*ρ*reaches a maximum. Figure 2 shows an example of a bilinear computed subpixel correlation function in a 2×2 sensor field. The central value (u = v = 100) corresponds to the maximum of the integer value based search. This example shows that a maximum can occur in any of the four quadrants. Therefore, four search algorithms are required. The function displayed in Fig. 3 is computed with a bicubic algorithm [6].

### 4.2. Pattern structures

## 5. Results

### 5.1. Evaluation of the measurement method

*μ*m to 160

*μ*m was used. To separate this feature of interest from deficiencies caused by imperfect calibration a two-dimensional polynomial fit of fourth order was subtracted. As a result, Fig. 5 shows both the resolved step height of 20

*μ*m and the improved quality of measurement with the optimized illumination structures. No additional filtering of the data has been carried out.

*μ*m. The ratio of rms error to the realized measurement field height of 250mm is better than 2∗10

^{-4}.

## 6. Conclusion

*μ*m and 50

*μ*m (rms) respectively, whereas the absolute error is less than 0.3mm. The accuracy with respect to the lateral measuring range is about 2 ∗ 10

^{-4}. The realized accuracy is sufficient for medical measurements of human faces. The short period of image acquisition (< 3 seconds), the low hardware requirements and the self calibration of the extrinsic parameters are additional advantages of this method. Until now the in the beginning mentioned assumption of a linear intensity transformation between homologous points does not lead to noticeable measurement errors.

## Acknowledgments

## References and links

1. | Y. Ma, S. Soatto, and J. Kosecka, |

2. | R. I. Hartley, “In Defense of the Eight-Point Algorithm,” in |

3. | O. Faugeras, |

4. | F. Devernay, O. Bantiche, and E. Coste-Manire, “Structured light on dynamic scenes using standard stereoscopy algorithms,” in |

5. | P. Albrecht and B. Michaelis, “Stereo Photogrammetry with Improved Spatial Resolution,” |

6. | I. E. Abdou and K. Y. Wong, “Analysis of Linear Interpolation Schemes for Bi-Level Image Applications” in |

**OCIS Codes**

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

(150.6910) Machine vision : Three-dimensional sensing

(170.1850) Medical optics and biotechnology : Dentistry

(170.3890) Medical optics and biotechnology : Medical optics instrumentation

**ToC Category:**

Instrumentation, Measurement, and Metrology

**History**

Original Manuscript: March 27, 2006

Revised Manuscript: July 12, 2006

Manuscript Accepted: July 14, 2006

Published: August 21, 2006

**Virtual Issues**

Vol. 1, Iss. 9 *Virtual Journal for Biomedical Optics*

**Citation**

Axel Wiegmann, Holger Wagner, and Richard Kowarschik, "Human face measurement by projecting bandlimited random patterns," Opt. Express **14**, 7692-7698 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-17-7692

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### References

- Y. Ma, S. Soatto and J. Kosecka, An Invitation to 3-D Vision (Springer, 2003)
- R. I. Hartley, "In Defense of the Eight-Point Algorithm," inIEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 19, No. 6, pp. 580-593, (1997)
- O. Faugeras, Three-Dimensional Computer Vision (Artificial Intelligence) (MIT Press, 1993)
- F. Devernay, O. Bantiche and E. Coste-Manire, "Structured light on dynamic scenes using standard stereoscopy algorithms," in Rapport de recherche de l’INRIA, No. 4477, (June 2002), http://www.inria.fr/rrrt/rr-4477.html
- P. Albrecht and B. Michaelis, "Stereo Photogrammetry with Improved Spatial Resolution," in 14th International Conference on Pattern Recognition, pp. 845-849, (1998)
- I. E. Abdou and K. Y. Wong, "Analysis of Linear Interpolation Schemes for Bi-Level Image Applications" in IBM Journal of Research and Development, Vol. 26, No. 6, pp. 667-680, (1982)

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