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Using uncertainty to link 3D edge detection and local surface modelling

  • O Monga
  • N Ayache
  • P Sander
5. Segmentation: Multi-Scale, Surfaces And Topology
Part of the Lecture Notes in Computer Science book series (LNCS, volume 511)

Abstract

We establish a theoretical link between the 3D edge detection and the local surface approximation using uncertainty. As a practical application of the theory, we present a method for computing typical curvature features from 3D medical images. We use the uncertainties inherent in edge (and surface) detection in 2- and 3-dimensional images determined by quantitatively analyzing the uncertainty in edge position, orientation and magnitude produced by the multidimensional (2-D and 3-D) versions of the Monga-Deriche-Canny recursive separable edge-detector. These uncertainties allow to compute local geometric models (quadric surface patches) of the surface, which are suitable for reliably estimating local surface characteristics, for example, Gaussian and Mean curvature. We demonstrate the effectiveness of our methods compared to previous techniques. These curvatures are then used to obtain more structured features such as curvature extrema and lines of curvature extrema. The final goal is to extract robust geometric features on which registration and/or tracking procedures can rely.

Key words

Typical surface features local curvature extrema mean and Gaussian curvature local surface modelling uncertainty 3D edge detection 

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References

  1. [AB90]
    N. Ayache, J.D. Boissonnat,, L. Cohen,, B. Geiger, J. Levy-Vehel, O. Monga, and P. Sander. Steps toward the automatic interpretation of 3d images. In Proceedings of the NATO Advanced Research Workshop on 3D Imaging in Medicine, Travemünde, June 1990. NATO ASI Series, Springer-Verlag.Google Scholar
  2. [Aya91]
    N. Ayache. Artificial Vision for Mobile Robots — Stereo-Vision and Multisensory Perception. MIT Press, Boston, 1991.Google Scholar
  3. [BJ88]
    Paul J. Besl and Ramesh C. Jain. Segmentation through Variable-Order surface fitting. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-10(2):167–192, March 1988.Google Scholar
  4. [Can86]
    John Canny. A computational approach to edge detection. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-8(6):678–698, November 1986.Google Scholar
  5. [dC76]
    Manfredo P. do Carmo. Differential Geometry of Curves and Surfaces. Prentice-Hall, Englewood Cliffs, 1976.Google Scholar
  6. [Der87]
    Rachid Deriche. Using Canny's criteria to derive a recursively implemented optimal edge detector. International Journal of Computer Vision, pages 167–187, 1987.Google Scholar
  7. [Koe90]
    Jan J. Koenderink. Solid Shape. MIT Press, Boston, 1990.Google Scholar
  8. [Lue69]
    David G. Luenberger. Optimization by Vector Space Methods. Wiley, New York, 1969.Google Scholar
  9. [MAS91]
    Olivier Monga, Nicholas Ayache, and Peter Sander. From voxel to curvature. Technical report, INRIA, 1991. No 1356.Google Scholar
  10. [MD89]
    Olivier Monga and Rachid Deriche. 3d edge detection using recursive filtering. In Conference on Vision and Patern Recognition, San Diego, June 1989. IEEE.Google Scholar
  11. [MDMC]
    Olivier Monga, Rachid Deriche, Gregoire Malandain, and Jean-Pierre Cocquerez. Recursive filtering and edge closing: two primary tools for 3d edge detection.Google Scholar
  12. [MDR91]
    Olivier Monga, Rachid Deriche, and Jean-Marie Rocchisani. 3d edge detection using recursive filtering: Application to scanner images. Computer Vision Graphic and Image Processing, Vol. 53, No 1, pp. 76–87, January 1991.Google Scholar
  13. [SZ]
    Peter T. Sander and Steven W. Zucker. Singularities of principal direction fields from 3-D images. IEEE Transactions on Pattern Analysis and Machine Intelligence. To appear. Available as Technical Report CIM-88-7, McGill Research Center for Intelligent Machines, McGill University, Montréal.Google Scholar
  14. [SZ87]
    Peter T. Sander and Steven W. Zucker. Tracing surfaces for surfacing traces. In Proceedings of the First International Conference on Computer Vision, pages 241–249, London, June 1987.Google Scholar
  15. [SZ90]
    Peter T. Sander and Steven W. Zucker. Inferring surface trace and differential structure from 3-D images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12(9), September 1990.Google Scholar
  16. [ZH81]
    S.W. Zucker and R.M. Hummel. A three-dimensional edge operator. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-3(3):324–331, May 1981.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • O Monga
    • 1
  • N Ayache
    • 1
  • P Sander
    • 1
  1. 1.INRIA Domaine de Voluceau-RocquencourtChesnay CedexFrance

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