Advertisement

Visual Form pp 469-477 | Cite as

Estimating Curvature by Kalman Filters

  • Peter T. Sander

Abstract

A problem which occurs frequently in computer vision research is that of determining reasonable curvature estimates, and is especially difficult in applications where noisy or imperfect data are used [1, 2]. Thus, estimating curve or surface points by an “edge detector” is not an end in itself, but only the first step of image understanding. These points are often noisy and the estimate must be improved before proceeding to subsequent stages such as grouping. The problem addressed in this paper is that of refining the estimated points of a smooth curve which have been corrupted by noise. The method presented here is expected to be of general interest for the edge detection problem by delivering a coherent set of putative curve points along with estimates of normals and curvatures. Here, we restrict the discussion to curves, but note that the method generalizes immediately to surfaces [3].

Keywords

State Vector Kalman Filter Neighbourhood Size Local Frame Local Curve 
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]
    Michael Brady, Jean Ponce, Alan Yuille, and Haruo Asada. Describing surfaces. In Hideo Hanafusa and Hirochika Inoue, editors, Proceedings of the Second International Symposium on Robotics Research, pages 5–16, MIT Press, Cambridge, Mass., 1985.Google Scholar
  2. [2]
    Paul Besl and Ramesh Jain. Intrinsic and extrinsic surface characteristics. In IEEE Proceedings on Computer Vision and Pattern Recognition, pages 226-233, June 1985.Google Scholar
  3. [3]
    Pascal Fua and Peter T. Sander. Computing curvature in stereo imagery. To be presented at SPIE Conference on Geometric Methods in Computer Vision, San Diego, July 1991.Google Scholar
  4. [4]
    Michael Kass, Andrew Witkin, and Demetri Terzopoulos. Snakes: active contour models. In Proceedings of the First International Conference on Computer Vision, pages 259-268, London, June 1987.Google Scholar
  5. [5]
    Peter T. Sander. Generic curvature features from 3-D images. IEEE Transactions on Systems, Man, and Cybernetics, 19(6):1623–1635, November 1989.CrossRefGoogle Scholar
  6. [6]
    Jan J. Koenderink. Solid Shape. MIT Press, Cambridge, 1991.Google Scholar
  7. [7]
    Richard James Morris. Symmetry of Curves and the Geometry of Surfaces. PhD thesis, University of Liverpool, May 1990.Google Scholar
  8. [8]
    Olivier Monga, Nicholas Ayache, and Peter T. Sander. From voxel to curvature. Technical Report 1356, INRIA, December 1990.Google Scholar
  9. [9]
    David G. Luenberger. Optimization by Vector Space Methods. Wiley, New York, 1969.Google Scholar
  10. [10]
    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, PAMI-12(9):833–854, September 1990.Google Scholar

Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • Peter T. Sander
    • 1
  1. 1.Sophia-AntipolisINRIAValbonne CedexFrance

Personalised recommendations