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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 40, Iss. 29 — Oct. 10, 2001
  • pp: 5206–5216

Localization and registration of three-dimensional objects in space—where are the limits?

Xavier Laboureux and Gerd Häusler  »View Author Affiliations


Applied Optics, Vol. 40, Issue 29, pp. 5206-5216 (2001)
http://dx.doi.org/10.1364/AO.40.005206


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Abstract

We discuss the accuracy limits for the localization of surfaces in three-dimensional (3-D) space. Such a localization is necessary for the registration of different views of an object, taken by 3-D sensors from several directions. A quantitative analysis shows that the lateral localization accuracy of a small surface area is proportional to the local curvature of the surface. This confirms the intuitive conjecture that our visual system performs localization of 3-D objects via sharp features. The longitudinal localization accuracy depends only on the noise of the data and is usually much better than the lateral localization accuracy, suggesting that surfaces are to be registered only along the longitudinal directions.

© 2001 Optical Society of America

OCIS Codes
(100.2960) Image processing : Image analysis
(100.5010) Image processing : Pattern recognition
(100.6890) Image processing : Three-dimensional image processing
(200.3050) Optics in computing : Information processing

History
Original Manuscript: February 19, 2001
Revised Manuscript: July 3, 2001
Published: October 10, 2001

Citation
Xavier Laboureux and Gerd Häusler, "Localization and registration of three-dimensional objects in space—where are the limits?," Appl. Opt. 40, 5206-5216 (2001)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-40-29-5206


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References

  1. L. P. Yaroslavsky, “The theory of optimal methods for localization of objects in picture,” Prog. Opt. 32, 145–201 (1993). [CrossRef]
  2. H. Baher, Analog and Digital Signal Analysis (Wiley, Chichester, UK, 1994).
  3. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996).
  4. A. Papoulis, Signal Analysis (McGraw-Hill, New York, 1991).
  5. L. P. Yaroslavsky, Digital Picture Processing (Springer-Verlag, Berlin, 1985). [CrossRef]
  6. Y. Chen, G. Medioni, “Object modeling by registration of multiple range images,” Image Vision Comput. 10, 145–155 (1992). [CrossRef]
  7. J. Feldmar, N. Ayache, “Rigid, local and locally affine registration of free-form surfaces,” Int. J. Comput. Vision 18, 99–119 (1996). [CrossRef]
  8. S. Karbacher, G. Häusler, H. Schönfeld, “Reverse engineering using optical range sensors,” in Handbook of Computer Vision and Applications, Vol. 3: Systems and Applications, B. Jähne, H. Haussecker, P. Geissler, eds. (Academic Press, Boston, 1999).
  9. Features should be here understood as both specific points of the object surface and certain properties assigned to these points.
  10. G. Häusler, D. Ritter, “Feature-based object recognition and localization in 3D-space using a single video image,” Comput. Vision Image Understand. 73, 64–81 (1999). [CrossRef]
  11. M. P. do Carmo, Differential Geometry of Curves and Surfaces (Prentice-Hall, Englewood Cliffs, N.J., 1976).
  12. C. S. Chua, R. Jarvis, “Point signatures: a new representation for 3D object recognition,” Int. J. Comput. Vision 25, 63–85 (1997). [CrossRef]
  13. J. Canny, “A computational approach to edge detection,” IEEE Trans. Pattern Anal. Mach. Intell. 8, 679–698 (1986). [CrossRef] [PubMed]
  14. A. Gueziec, “Large deformable splines, crest lines and matching,” Proceedings of the Fourth International Conference on Computer Vision (IEEE Computer Society, Los Alamitos, Calif., 1993), pp. 650–657.
  15. J. P. Thirion, “New feature points based on geometric invariants for 3D image registration,” Int. J. Comput. Vision 18, 121–137 (1996). [CrossRef]
  16. P. J. Besl, N. D. McKay, “A method for registration of 3D shapes,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 239–256 (1992). [CrossRef]
  17. Z. Zhang, “Iterative point matching for registration of free-form curves and surfaces,” Int. J. Comput. Vision 13, 119–152 (1994). [CrossRef]
  18. T. Masuda, K. Sakaue, N. Yokoya, “Registration and integration of multiple range images for 3-D model construction,” Proceedings of the 13th International Conference on Pattern Recognition (IEEE Computer Society, Los Alamitos, Calif., 1996), Vol. 1, pp. 879–883. [CrossRef]
  19. K. S. Arun, T. S. Huang, S. D. Blostein, “Least-squares fitting of two 3D point sets,” IEEE Trans. Pattern Anal. Mach. Intell. 9, 698–700 (1987). [CrossRef] [PubMed]
  20. B. K. Horn, “Closed-form solution of absolute orientation using unit quaternions,” J. Opt. Soc. Am. A 4, 629–642 (1987). [CrossRef]
  21. B. K. Horn, H. M. Hilden, S. Negahdaripour, “Closed-form solution of absolute orientation using orthonormal matrices,” J. Opt. Soc. Am. A 5, 1127–1135 (1988). [CrossRef]
  22. J. B. A. Maintz, M. A. Viergever, “A survey of medical image registration,” Med. Image Anal. 2, 1–36 (1998). [CrossRef]
  23. M. A. Audette, F. P. Ferrie, T. M. Peters, “An algorithmic overview of surface registration techniques for medical imaging,” Med. Image Anal. 4, 201–217 (2000). [CrossRef]
  24. S. Seeger, X. Laboureux, “Feature extraction and registration,” in Principles of 3D Image Analysis and Synthesis, B. Girod, G. Greiner, H. Niemann, eds. (Kluwer Academic, Boston, 2000).
  25. R. J. Campbell, P. J. Flynn, “A survey of free-form object representation and recognition techniques,” Comput. Vision Image Understand. 81, 166–210 (2001). [CrossRef]
  26. The analysis is done in one dimension to simplify the formulation. The extension to two variables would be straightforward.
  27. Another advantage of this approach is that R(ε) does not need to be normalized through the support width.
  28. The proof can be done analytically or verified by simple numerical simulations.
  29. Because we consider the two signals only within their overlapping domain, the Gaussian white-noise assumption over this domain is a justified restriction.
  30. I. N. Bronstein, K. A. Semendjajew, G. Musiol, H. Mühlig, Taschenbuch der Mathematik (Verlag Harri Deutsch, Frankfurt am Main, Germany, 2000).
  31. From now on “localization error” designates the “standard deviation of the localization error” as well, and the localization accuracy is defined as the inverse of the localization error.
  32. Actually 2Mx + 1 (Mx + 12) is the total (half) number of points. Here and in future developments of this paper they are approximated through 2Mx and Mx, respectively.

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