Skip to main content
SpringerLink
Log in

Efficiently Locating Objects Using the Hausdorff Distance

  • Published:
International Journal of Computer Vision Aims and scope Submit manuscript

Abstract

The Hausdorff distance is a measure defined between two point sets, here representing a model and an image. The Hausdorff distance is reliable even when the image contains multiple objects, noise, spurious features, and occlusions. In the past, it has been used to search images for instances of a model that has been translated, or translated and scaled, by finding transformations that bring a large number of model features close to image features, and vice versa. In this paper, we apply it to the task of locating an affine transformation of a model in an image; this corresponds to determining the pose of a planar object that has undergone weak-perspective projection. We develop a rasterised approach to the search and a number of techniques that allow us to locate quickly all transformations of the model that satisfy two quality criteria; we can also efficiently locate only the best transformation. We discuss an implementation of this approach, and present some examples of its use.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Ayache, N. and Faugeras, O. 1986. HYPER: A new approach for the recognition and positioning of two-dimensional objects. IEEE Transactions on Pattern Analysis and Machine Intelligence, 8(1):44-54.

    Google Scholar 

  • Barrow, H. G., Tenenbaum, J. M., Bolles, R. C., and Wolf, H. C. 1977. Parametric correspondence and chamfer matching: Two new techniques for image matching. In Proc. Fifth International Joint Conference on Artificial Intelligence, Cambridge, MA, pp. 659- 663.

  • Borgefors, G. 1988. Hierarchical chamfer matching: A parametric edge matching algorithm. IEEE Transactions on Pattern Analysis and Machine Intelligence, 10(6):849-865.

    Google Scholar 

  • Breu, H., Gil, J., Kirkpatrick, D., and Werman, M. 1995. Linear time Euclidean distance transform algorithms. IEEE Transactions on Pattern Analysis and Machine Intelligence, 17(5):529-533.

    Google Scholar 

  • Bruel, T. M. 1992. Fast recognition using adaptive subdivision of transformation space. In Proc. Computer Vision and Pattern Recognition, Champaign-Urbana, Illinois, pp. 445-451.

    Google Scholar 

  • Cass, T. A. 1990. Feature matching for object localization in the presence of uncertainty. In Proc. Third International Conference on Computer Vision, Osaka, Japan, pp. 360-364.

  • Danielsson, P. E. 1980. Euclidean distance mapping. Computer Graphics and Image Processing, 14:227-248.

    Google Scholar 

  • Huttenlocher, D. P. and Ullman, S. 1990. Recognizing solid objects by alignment with an image. International Journal of Computer Vision, 5(2):195-212.

    Google Scholar 

  • Huttenlocher, D. P. and Rucklidge, W. J. 1993. A multi-resolution technique for comparing images using the Hausdorff distance. In Proc. Computer Vision and Pattern Recognition, New York, NY, pp. 705-706.

  • Huttenlocher, D. P., Klanderman, G. A., and Rucklidge, W. J. 1993. Comparing images using the Hausdorff distance. IEEE Transactions on Pattern Analysis and Machine Intelligence, 15(9):850- 863.

    Google Scholar 

  • Olson, C. F. 1994. Time and space efficient pose clustering. In Proc. Computer Vision and Pattern Recognition, Seattle, Washington, pp. 251-258.

  • Paglieroni, D. W. 1992. Distance transforms: Properties and machine vision applications. Computer Vision, Graphics and Image Proc.: Graphical Models and Image Processing, 54(1):56-74.

    Google Scholar 

  • Paglieroni, D. W., Ford, G. E., and Tsujimoto, E. M. 1994. The position-orientation masking approach to parametric search for template matching. IEEE Transactions on Pattern Analysis and Machine Intelligence, 16(7):740-747.

    Google Scholar 

  • Rucklidge, W. J. 1995a. Efficient Computation of the Minimum Hausdorff Distance for Visual Recognition. Ph. D. thesis, Cornell University.

  • Rucklidge, W. J. 1995b. Locating objects using the Hausdorff distance. In Proc. Fifth International Conference on Computer Vision, Cambridge, MA, pp. 457-464.

Download references

Author information

Authors and Affiliations

  1. Xerox Palo Alto Research Center, 3333 Coyote Hill Road, Palo Alto, CA, 94304

    William J. Rucklidge

Authors
  1. William J. Rucklidge
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rucklidge, W.J. Efficiently Locating Objects Using the Hausdorff Distance. International Journal of Computer Vision 24, 251–270 (1997). https://doi.org/10.1023/A:1007975324482

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1007975324482

Search

Navigation