Advertisement

Smoothing Range Data for Curvature Estimation

  • Gaile G. Gordon
Part of the NATO ASI Series book series (volume 83)

Abstract

The calculation of curvature plays a crucial role in the recognition of sculptured objects from range data. The smoothing operation which must precede the calculation of curvature should be considered an important part of this process as it has the potential to alter its results. We take as our goal the selection of an effective scale and method for smoothing range data which minimizes changes in the shape of the object. Toward this end we have examined the effect of two aspects of the smoothing process on detection of extremal points of curvature. First, we discuss the use of cross validation as method of scale selection, and second we look at the results of nonlinear smoothing, in particular the use of anisotropic diffusion. Several recommendations are also made regarding the potential usefulness of smoothing methods which take into account the orientation of the surface.

Keywords

Cross Validation Range Data Smoothing Parameter Anisotropic Diffusion Range Image 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    P. F. Besl and R. C. Jain: Invariant Surface Characteristics for 3D Object Recognition in Range Images. In: Computer Vision, Graphics, and Image Processing. 33,33–80 (1986)CrossRefGoogle Scholar
  2. 2.
    M. Brady, J. Ponce, A. Yuille, and H Asada: Describing Surfaces. In: Proceedings of the 2nd International Symposium on Robotics Research. Editted by: H. Hanafusa and H. Inoue. MIT Press: Cambridge, MA, 1985Google Scholar
  3. 3.
    P. Craven and G. Wahba: Smoothing Noisy Data with Spline Functions. In: Numerische Mathematik. 31, 377–403 (1979)CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    T.J. Fan, G. Medioni and R. Nevatia: Description of Surfaces from Range Data Using Curvature Properties. In: Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 86–91, 1986Google Scholar
  5. 5.
    T.J. Fan, G. Medioni and R. Nevatia: Surface Segmentation and Description form Curvature Features. In: Proceedings of DARPA Image Understanding Workshop, pp. 351–359, 1987Google Scholar
  6. 6.
    P. J. Flynn, A. K. Jain: On Reliable Curvature Estimation. In: Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 110–116, 1989Google Scholar
  7. 7.
    Geiger, Poggio: An Optimal Scale for Edge Detection. MIT Artificial Intelligence Laboratory Memo No. 1078, September 1988Google Scholar
  8. 8.
    D.D. Hoffman and Whitman Richards: Parts of Recognition. MIT Artificial Intelligence Laboratory Memo No. 732, December 1983Google Scholar
  9. 9.
    R.L. Hoffman: Object Recognition from Range Images. PhD thesis, Department of Computer Science, Michigan State University, 1986Google Scholar
  10. 10.
    Huisken, G.: Flow by Mean Curvature of Convex Surfaces into Spheres. Journal of Differential Geometry, Vol. 20, 1984Google Scholar
  11. 11.
    R. S. Millman and G. D. Parker.: Elements of Differential Geometry. New York: Prentice- Hall, 1977MATHGoogle Scholar
  12. 12.
    P. Perona, J. Malik: A Network for Multiscale Image Segmentation. In: Proceedings of IEEE International Symposium of Circuits and Systems, pp. 2565–2568, 1988Google Scholar
  13. 13.
    J. Ponce, M. Brady: Toward a Surface Primal Sketch. MIT Artificial Intelligence Laboratory Memo No. 824, April 1985Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Gaile G. Gordon
    • 1
  1. 1.Harvard Robotics LaboratoryHarvard UniversityCambridgeUSA

Personalised recommendations