Advertisement

The Hough Transform without the Accumulators

  • Atsushi Imiya
  • Tetsu Hada
  • Ken Tatara
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2396)

Abstract

The least-squares method (LSM) efficiently solves the model-fitting problem, if we assume a model equation. For the fitting to a collection of models, the classification of data is required as pre-processing. The Hough transform, achieves both the classification of sample points and the model fitting concurrently. However, as far as adopting the voting process is concerned, the maintenance of the accumulator during the computation cannot be neglected. We propose a Hough transform without the accumulator expressing the classification of data for the model fitting problems as the permutation of matrices which are defined by data.

Keywords

Sample Point Orthogonal Matrix Projection Matrix Hough Transform Moment Matrix 
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.
    Ballard, D. and Brown, Ch. M., Computer Vision, Prentice-Hall; New Jersey, 1982.Google Scholar
  2. 2.
    Deans, S. R., Hough transform from the Radon transform, IEEE Trans. Pattern Analysis and Machine Intelligence, PAMI-3, 185–188, 1981.CrossRefGoogle Scholar
  3. 3.
    Levers, V. F., Which Hough transform? CVGIP: Image Understanding, 58, 250–264, 1993.CrossRefGoogle Scholar
  4. 4.
    Becker, J.-M., Grousson, S., and Guieu, D., Space of circles: its application in image processing, Vision Geometry IX, Proceedings of SPIE, 4117, 243–250, 2000.Google Scholar
  5. 5.
    Cox, D., Little, J., and O’Shea, D., Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, Springer-Verlag; New York, 1992.zbMATHGoogle Scholar
  6. 6.
    Mattavelli, M., Noel, V., and Ammaldi, E., Fast line detection algorithms based on combinatorial optimization, LNCS, 2051, 410–419, 2001.Google Scholar
  7. 7.
    Brockett, R. W., Least square matching problem, Linear Algebra and its Applications, 122/123/124, 1989, 761–777.CrossRefMathSciNetGoogle Scholar
  8. 8.
    Brockett, R. W., Dynamical system that sort list, diagonalize matrices, and solve linear programming problems, Linear Algebra and its Applications, 146, 1991, 79–91.zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Vandenberghe, L. and Boyd, S., Semdefnite programming, SIAM Review, 38, 49–95, 1996.zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Alizaden, F., Interir point methods in semidefinite programming with application to combinatorial optimization, SIAM, Journal on Optimization, 5, 13–51, 1995.CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Atsushi Imiya
    • 1
    • 2
  • Tetsu Hada
    • 2
  • Ken Tatara
    • 2
  1. 1.National Institute of InformaticsTokyo
  2. 2.IMITChiba UniversityChibaJapan

Personalised recommendations