Advertisement

Abstract

The sampling rate for signal reconstruction has been and remains an important and central criterion in numerous applications. We propose, in this paper, a new approach to determining an optimal sampling rate for a 2D-surface reconstruction using the so-called Two-Thirds Power Law. This paper first introduces an algorithm of a 2D surface reconstruction from a 2D image of circular light patterns projected on the surface. Upon defining the Two-Thirds Power Law we show how the extracted spectral information helps define an optimal sampling rate of the surface, reflected in the number of projected circular patterns required for its reconstruction. This result is of interest in a number of applications such as 3D face recognition and development of new efficient 3D cameras. Substantive examples are provided.

Keywords

Sampling rate Reconstruction The Two-Thirds Power Law Structured light patterns 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Faugeras, O., Luong, Q.-T.: The Geometry of Multiple Images (2001)Google Scholar
  2. 2.
    Wei, Z., Zhou, F., Zhang, G.: 3D coordinates measurement based on structured light sensor. Sensors and Actuators A: Physical 120, 527–535 (2005)CrossRefGoogle Scholar
  3. 3.
    Asada, M., Ichikawa, H., Tsuji, S.: Determining of surface properties by projecting a stripe pattern. In: Proc. Int. Conf. on Pattern Recognition, pp. 1162–1164 (1986)Google Scholar
  4. 4.
    Dipanda, A., Woo, S.: Towards a real-time 3D shape reconstruction using a structured light system. Pattern Recognition 38, 1632–1650 (2005)CrossRefGoogle Scholar
  5. 5.
    Batlle, J., Mouaddib, E., Salvi, J.: Recent Progress in Coded Structured Light as a Technique to solve the Correspondence Problem: A Survey. Pattern Recognition 31, 963–982 (1998)CrossRefGoogle Scholar
  6. 6.
    Papoulis, A.: Signal Analysis. McGraw-Hill, New York (1977)zbMATHGoogle Scholar
  7. 7.
    Eldar, Y.C.: Compressed Sensing of Analog Signals in Shift-Invariant Spaces. IEEE Transactions on Signal Processing 57(8) (August 2009)Google Scholar
  8. 8.
    Jerri, A.J.: The Shannon Sampling Theorem - Its Various Extensions and Applications: A Tutorial Review. Proceedings of The IEEE 65(11) (November 1977)Google Scholar
  9. 9.
    Maoz, U., Portugaly, E., Flash, T., Weiss, Y.: Noise and the two-thirds power lawGoogle Scholar
  10. 10.
    de’ Sperati, C., Viviani, P.: The Relationship between Curvature and Velocity in Two-Dimensional Smooth Pursuit Eye Movements. The Journal of Neuroscience 17, 3932–3945 (1997)Google Scholar
  11. 11.
    Schaal, S., Sternad, D.: Origins and violations of the 2/3 power law in rhythmic 3D movements. Experimental. Brain Research,, 60–72 (2001)Google Scholar
  12. 12.
    Lee, D., Krim, H.: 3D surface reconstruction using structured circular light patterns. In: Blanc-Talon, J., Bone, D., Philips, W., Popescu, D., Scheunders, P. (eds.) ACIVS 2010, Part I. LNCS, vol. 6474, pp. 279–289. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  13. 13.
    Lacquaniti, F., Terzuolo, C., Viviani, P.: The law relating the kinematic and figural aspects of drawing movements. Acta Psychologica, 115–130 (1983)Google Scholar
  14. 14.
    Pollefeys, M., Koch, R., Van Gool, L.: Self-Calibration and Metric Reconstruction Inspite of Varying and Known Intrinsic Camera Parameters. International Journal of Computer Vision, 7–25 (1999)Google Scholar
  15. 15.
    Armangue, X., Salvi, J., Batlle, J.: A Comparative Review Of Camera Calibrating Methods with Accuracy Evaluation. Pattern Recognition 35, 1617–1635 (2000)zbMATHGoogle Scholar
  16. 16.
    Sturm, P.: On Focal Length Calibration from Two Views. In: IEEE International Conference on Computer Vision and Pattern Recognition, pp. 145–150 (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Deokwoo Lee
    • 1
  • Hamid Krim
    • 1
  1. 1.Department of Electrical and Computer EngineeringNorth Carolina State UniversityRaleighUSA

Personalised recommendations