Skip to main content
SpringerLink
Log in

Recognizing 3-D Curves from a Stereo Pair of Images: a Semi-differential Approach

  • Conference paper
Shape in Picture

Part of the book series: NATO ASI Series ((NATO ASI F,volume 126))

  • 185 Accesses

Abstract

This study investigates how the stereo view of a 3-D curve can be characterized in a way that is invariant under 3-D Euclidean motions of the curve. Depending on the knowledge about and the variability of the parameters of the stereo-setup, several transformation groups are identified as the framework relevant to the extraction of invariants. The point-derivative exchange principle can be used to construct a new set of semi-differential invariants for stereo pairs. The resulting invariants range from the quite simple to the rather complicated, but the information needed for their computation remains limited at all times. Finally, invariants from motion sequences as well as surface shape descriptors are proposed as special cases.

The support of ESPRIT Basic Research Action EP 6448 ‘VIVA’ and the Post-Doctoral Research Grants (T. Moons and E. Pauwels) of the Katholieke Universiteit Leuven are gratefully acknowledged.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Brill, M.H., Barrett, E.B., Payton, P.M. (1992). Projective invariants for curves in two and three dimensions. In: Mundy, J., Zisserman, A. (eds.), Geometric Invariance in Computer Vision, MIT Press, Cambridge, Massachusetts, pp. 193–214.

    Google Scholar 

  2. Kishon, E., Hastie, T., Wolfson, H. (1991). 3-D curve matching using splines, Journal of Robotic Systems 8(6), pp. 723–743.

    Google Scholar 

  3. Sagle, A.A., Walde, R.E. (1973). Introduction to Lie Groups and Lie Algebras, Pure and Applied Mathematics, Vol. 51, Academic Press, New York.

    Google Scholar 

  4. Van Gool, L., Moons, T., Pauwels, E.J., Oosterlinck, A., (1992). Semi-differential invariants. In: Mundy, J., Zisserman, A. (eds.), Geometric Invariance in Computer Vision, MIT Press, Cambridge, Massachusetts, pp. 193–214.

    Google Scholar 

  5. Van Gool, L.J., Brill, M.H., Barrett, E.B., Moons, T., Pauwels, E.J. (1992). Semi-differential invariants for nonplanar curves. In: Mundy, J., Zisserman, A. (eds.), Geometric Invariance in Computer Vision, MIT Press, Cambridge, Massachusetts, pp. 293–309.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Katholieke Univ. Leuven, ESAT-MI2, K. Mercierlaan 94, 3001, Leuven, Belgium

    Theo Moons, Eric J. Pauwels & Luc J. Van Gool

  2. Science Appl. Int. Corp., 1710 Goodridge Drive, 1-11-1, McLean, VA, 22102, USA

    Michael H. Brill

  3. Space Systems Div., Lockheed Missiles and Space Co., 1111 Lockheed Way, Sunnyvale, CA, 94089-3504, USA

    Eamon B. Barrett

Authors
  1. Theo Moons
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Eric J. Pauwels
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Luc J. Van Gool
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Michael H. Brill
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Eamon B. Barrett
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Centre for Mathematics and Computer Science (CWI), Kruislaan 413, 1098 SJ, Amsterdam, The Netherlands

    Ying-Lie O  & Henk J. A. M. Heijmans  & 

  2. Institute for Human Factors (TNO-IZF), Netherlands Organization for Applied Scientific Research, Kampweg 5, 3769 DE, Soesterberg, The Netherlands

    Alexander Toet

  3. Department of Communication and Neuroscience, University of Keele, ST5 5BG, Keele, Staffordshire, UK

    David Foster

  4. Department of Electrical and Computer Engineering, Rutgers University, 08855-0909, Piscataway, NJ, USA

    Peter Meer

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Moons, T., Pauwels, E.J., Van Gool, L.J., Brill, M.H., Barrett, E.B. (1994). Recognizing 3-D Curves from a Stereo Pair of Images: a Semi-differential Approach. In: O, YL., Toet, A., Foster, D., Heijmans, H.J.A.M., Meer, P. (eds) Shape in Picture. NATO ASI Series, vol 126. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03039-4_30

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-03039-4_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-08188-0

  • Online ISBN: 978-3-662-03039-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation