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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 17 — Aug. 21, 2006
  • pp: 7692–7698
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Human face measurement by projecting bandlimited random patterns

A. Wiegmann, H. Wagner, and R. Kowarschik  »View Author Affiliations


Optics Express, Vol. 14, Issue 17, pp. 7692-7698 (2006)
http://dx.doi.org/10.1364/OE.14.007692


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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 50μm. Furthermore a depth difference of 20μm is detectable.

© 2006 Optical Society of America

1. Introduction

The advantages of optical measurements like fast data acquisition, non-contact measurement or the possibility of soft tissue measurements are used in a wide range of technical, medical and security applications.

The aim of this work is to achieve a precise 3-D model of a human face for computer aided surgeries in dentistry. Due to the fact that mainly children are the patients, fast data acquisition is essential. The time for measurement should be less than 3s and the measurement accuracy better than 100μmm. Furthermore a cost-saving measuring setup is desired.

2. Method

Like human stereovision, photogrammetric techniques use the same basic principle to get 3-D information of the environment : images of the object are captured from two different perspectives. Pairs of image points resulting from the same object point are called homologous points. These points given, the object can be reconstructed using triangulation methods.

A sketch of the technical realization is given in Fig. 1. For image acquisition a convergent arrangement of two cameras is applied. The camera model which is used to describe the process of image capturing is the pinhole camera. For a precise reconstruction, all parameters of this model have to be known exactly. The parameters can be divided in intrinsic and extrinsic ones. The most important intrinsic parameter is the ratio of the distance projection centre — image plane and the pixel size. Further intrinsic parameters are the coordinates of the principal point, which is the perpendicularly projected projection centre (x→cl and x→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

1. Y. Ma, S. Soatto, and J. Kosecka, An Invitation to 3-D Vision (Springer, 2003)

].

Fig. 1. Schematic arrangement of the measuring setup

From the located homologous points the Essential-Matrix is calculated with the normalized Eight-Point Algorithm [2

2. R. I. Hartley, “In Defense of the Eight-Point Algorithm,” in IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 19 , No. 6, pp. 580–593, (1997)

]. The extrinsic parameters are calculated from this matrix using quaternions [3

3. O. Faugeras, Three-Dimensional Computer Vision (Artificial Intelligence) (MIT Press, 1993)

]. This procedure makes the arrangement insensitive against environmental changes because the relative orientation of the cameras is determined from the homologous points.

ρ=i=1N(lil̅)*(rir̅)i=1N(lil̅)2*i=1N(rir̅)2
(1)

Whereas li is the intensity at the current position in picture 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. ρth = 0.9). This threshold is essential to suppress remaining outliers, which mainly occur if an object point is only visible in one camera.

3. Experimental setup

The previously described stereo-photogrammetrical method is realized by an experimental setup, which uses two Fire-Wire-Cameras with 1.3MP (1280 × 960, pixel size = 4.65μm,) 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 2θ = 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

Fig. 2. Bilinear subpixel correlation function
Fig. 3. Bicubic subpixel correlation function

4.2. Pattern structures

The disadvantages of the faster interpolation algorithms in comparison to the sinc-interpolation are their poorer transfer functions. As a result, the initially used binary patterns yield no reasonable results. Therefore, the patterns should be limited in their spatial frequency. Additionally the minimal frequency of the patterns should also be modified, because low frequencies lead to large homogeneous areas in the patterns, which produce flat correlation functions as shown in Fig. 2 and Fig. 3. The result of such flat correlation functions is higher noise. To avoid the negative influence of the pixelized patterns, the projector was defocused a little bit.

Figure 4 gives an example of a binary pattern, at which every 2×2 pixel block was randomly switched to black or white. The other two patterns are the fourier transformations of random spectrums. For the right image the high and low frequencies had been surpressed, for the middle one only the high frequencies.

Fig. 4. Example parts (75 × 100 pixels) of a binary pattern, one pattern with limited maximum frequency and a bandlimited one

5. Results

5.1. Evaluation of the measurement method

Fig. 5. Evaluation of the step height sensitivity using a plane with milled grooves between 5μm and 160μm, the projected patterns correspond to the ones shown in Fig. 4

To verify the accuracy of the measurement system, two well known objects have been tested. At first for quantification of the minimal resolvable height step a matt finished aluminium plate with milled grooves from 5μm to 160μm 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 20μm and the improved quality of measurement with the optimized illumination structures. No additional filtering of the data has been carried out.

Fig. 6. Deviation from a flat reference in mm

To check the absolute measurement accuracy a matt finished calibrated granite plate was used. Height and width of this plate filled out the full field of view. All influences of imperfect determination of the intrinsic and extrinsic calibration parameters of the cameras, the uncon-sidered distortion and the computation of the coordinates with the subpixel interpolation can be seen. No filtering and no global fitting except of subtracting the best fit plane were applied to the results shown in Fig. 6. The absolute error of the full field is less than 0.3mm whereas the standard deviation (rms) is smaller than 50μm. The ratio of rms error to the realized measurement field height of 250mm is better than 2∗10-4.

5.2. 3-D-Measurements of human faces

Fig. 7. (1.7MB) GIF animation of a rendered point cloud of a human face. The picture shows in addition a detailed view of the eye’s region as a pointcloud and as a rendered image.

6. Conclusion

This article shows that bandlimited projection patterns in combination with subpixel interpolation can improve the capability of 3-D measurements by stereo-photogrammetry. The experimentally determined values for the sensitivity concerning step height detections and the full field uncertainty of measurement are 20μm and 50μm (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.

In further developments the digital projector will be replaced by a cheaper analogue projection unit, which will allow non pixelized projection patterns. Furthermore, the distortion has to be added to the camera model to overcome the main geometry error. Therefore, stable calibration algorithms have to be implemented.

Acknowledgments

This project was supported by the Thuringia ministry of science, research and culture under the topic: ‘3-D shape measurement for function orientated diagnostic and therapy in dentistry’.

References and links

1.

Y. Ma, S. Soatto, and J. Kosecka, An Invitation to 3-D Vision (Springer, 2003)

2.

R. I. Hartley, “In Defense of the Eight-Point Algorithm,” in IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 19 , No. 6, pp. 580–593, (1997)

3.

O. Faugeras, Three-Dimensional Computer Vision (Artificial Intelligence) (MIT Press, 1993)

4.

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

5.

P. Albrecht and B. Michaelis, “Stereo Photogrammetry with Improved Spatial Resolution,” in 14th International Conference on Pattern Recognition, pp. 845–849, (1998)

6.

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)

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

  1. Y. Ma, S. Soatto and J. Kosecka, An Invitation to 3-D Vision (Springer, 2003)
  2. 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)
  3. O. Faugeras, Three-Dimensional Computer Vision (Artificial Intelligence) (MIT Press, 1993)
  4. 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
  5. P. Albrecht and B. Michaelis, "Stereo Photogrammetry with Improved Spatial Resolution," in 14th International Conference on Pattern Recognition, pp. 845-849, (1998)
  6. 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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