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Conformal Hough Transform for 2D and 3D Cloud Points

  • Gehová López-González
  • Nancy Arana-Daniel
  • Eduardo Bayro-Corrochano
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8258)

Abstract

This work presents a new method to apply the Hough Transform to 2D and 3D cloud points using the conformal geometric algebra framework. The objective is to detect geometric entities, with the use of simple parametric equations and the properties of the geometric algebra. We show with real images and RGB-D data that this new method is very useful to detect lines and circles in 2D and planes and spheres in 3D.

Keywords

Cloud Point Conformal Space Geometric Algebra Wedge Product Geometric Entity 
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.
    Hough, P.V.C.: Machine Analysis of Bubble Chamber Pictures. In: Proc. Int. Conf. High Energy Accelerators and Instrumentation (1959)Google Scholar
  2. 2.
    Duda, R.O., Hart, P.E.: Use of the Hough Transformation to Detect Lines and Curves in Pictures. Comm. ACM 15, 11–15 (1972)CrossRefGoogle Scholar
  3. 3.
    Ballard, D.H.: Generalizing the Hough transform to detect arbitrary shapes. Pattern Recognition 13(2), 111–122 (1981)CrossRefzbMATHGoogle Scholar
  4. 4.
    Shapiro, L., Stockman, G.: Computer Vision. Prentice-Hall, Inc. (2001)Google Scholar
  5. 5.
    Hestenes, D., Sobczyk, G.: Clifford Algebra to Geometric Calculus: A Unified Language for Mathematics and Physics. D. Reidel, Dordrecht (1984)CrossRefzbMATHGoogle Scholar
  6. 6.
    Bayro-Corrochano, E.: Geometric Computing: For Wavelet Transforms, Robot Vision, Learning, Control and Action. Springer, London (2010)CrossRefGoogle Scholar
  7. 7.
    Perwass, C.: Geometric Algebra with Applications in Engineering. Springer, Heidelberg (2009)zbMATHGoogle Scholar
  8. 8.
    Li, H., Hestenes, D., Rockwood, A.: Generalized homogeneous coordinates for computational geometry. In: Sommer, G. (ed.) Geometric Computing with Clifford Algebra, pp. 27–52. Springer (2001)Google Scholar
  9. 9.
    Kultanen, P., Xu, L., Oja, E.: Randomized Hough transform (RHT). In: Proceedings of the 10th International Conference on Pattern Recognition, ICPR 1990, Atlantic City, USA, June 16-21, vol. 1, pp. 631–635 (1990)Google Scholar
  10. 10.
    Li, Z., Hong, X., Liu, Y.: Detection Geometric Object in the Conformal Geometric Algebra Framework. In: Proceedings of the 2011 12th International Conference on Computer-Aided Design and Computer Graphics, CADGRAPHICS 2011, pp. 198–201. IEEE Computer Society, Washington, DC (2011)CrossRefGoogle Scholar
  11. 11.
    Hildenbrand, D., Pitt, J., Koch, A.: Gaalop High Performance Parallel Computing based on Conformal Geometric Algebra. In: Bayro-Corrochano, E., Sheuermann, G. (eds.) Geometric Algebra Computing for Engineering and Computer Science, ch. 22, pp. 477–494 (2010)Google Scholar
  12. 12.
    Canny, J.: A Computational Approach to Edge Detection. IEEE Transactions on Pattern Analysis and Machine Intelligence PAMI-8(6), 679–698 (1986)CrossRefGoogle Scholar
  13. 13.
    Michel, O.: Webots: Professional Mobile Robot Simulation. International Journal of Advanced Robotic Systems 1(1), 39–42 (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Gehová López-González
    • 1
  • Nancy Arana-Daniel
    • 2
  • Eduardo Bayro-Corrochano
    • 1
  1. 1.Department of Electrical Engineering and Computer ScienceCINVESTAVGuadalajaraMéxico
  2. 2.CUCEIUniversity of GuadalajaraGuadalajaraMéxico

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