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Projectively invariant representations using implicit algebraic curves

  • David Forsyth
  • Joseph L. Mundy
  • Andrew Zisserman
  • Christopher M. Brown
Shape Description
Part of the Lecture Notes in Computer Science book series (LNCS, volume 427)

Keywords

Scatter Matrix Invariant Shape Global Extremum Algebraic Invariant Fitting Ellipse 
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.

References

  1. [1]
    Agin, G.J. “Fitting ellipses and general second order curves,” Carnegie Mellon University CMU-RI-TR-81-5, undated.Google Scholar
  2. [2]
    Bookstein, F. “Fitting conic sections to scattered data,” CVGIP, 9, 56–91, 1979.Google Scholar
  3. [3]
    Canny, J.F. “Finding edges and lines in images,” TR 720, MIT AI Lab, 1983.Google Scholar
  4. [4]
    Forsyth, D.A., Mundy, J.L., Zisserman, A.P. and Brown, C.M. “Projectively invariant data representation by implicit algebraic curves: a detailed discussion,” Internal report 1814/90, Department of Engineering Science, Oxford University, 1990.Google Scholar
  5. [5]
    Forsyth, D.A. “Finding the global extremum of a function with bounded derivative over a compact domain,” Internal report 1815/90, Department of Engineering Science, Oxford University, 1990.Google Scholar
  6. [6]
    Grace, J.H. and Young, A. The algebra of invariants, Cambridge University Press, Cambridge, 1903.Google Scholar
  7. [7]
    Grimson, W.E.L. and T. Lozano-Pérez, “Localizing overlapping parts by searching the interpretation tree,” IEEE T-PAMI, PAMI-9, 4, 469–481, 1987.Google Scholar
  8. [8]
    Kung, J.P.S. and Rota, G.-C. “The invariant theory of binary forms,” Bull. Amer. Math. Soc., 10, 27–85, 1984Google Scholar
  9. [9]
    Lowe, D. Perceptual Organisation and Visual Recognition, Kluwer, Boston, 1985.Google Scholar
  10. [10]
    Nielson, L. “Automated guidance of vehicles using vision and projectively invariant marking,” Automatica, 24, 2, 135–148.Google Scholar
  11. [11]
    Porrill, J. “Fitting ellipses and predicting confidence envelopes using a bias corrected Kalman filter,” Proc. 5'th Alvey vision conference, 1989.Google Scholar
  12. [12]
    Pratt, V. “Direct least-squares fitting of algebraic surfaces”, ACM SIGGRAPH, 21, 145–151, 1987.Google Scholar
  13. [13]
    Sampson, P.W. “Fitting conic sections to “very scattered” data: an iterative refinement of the Bookstein algorithm,” CVGIP, 18, 97–108, 1982.Google Scholar
  14. [14]
    Springer, T.A. Invariant theory, Springer-Verlag lecture notes in Mathematics, 585, 1977.Google Scholar
  15. [15]
    Thompson, D.W. and J.L. Mundy, “3D model matching from an unconstrained viewpoint,” Proc. IEEE Conf. on Robotics and Automation, 1987.Google Scholar
  16. [16]
    Weiss, I. “Projective invariants of shapes,” Proc. DARPA IU workshop, 1125–1134, 1989.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • David Forsyth
    • 1
  • Joseph L. Mundy
    • 1
  • Andrew Zisserman
    • 1
  • Christopher M. Brown
    • 1
  1. 1.Robotics Research Group Department of Engineering ScienceOxford UniversityEngland

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