Advertisement

Optimal Ellipse Based Algorithm as an Approximate and Robust Solution of Minimum Volume Covering Ellipse Problem

  • Krzysztof Misztal
  • Jacek Tabor
  • Jakub Hyła
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9842)

Abstract

We propose a algorithm to give a approximate solution of a minimal covering circle or ellipse of a set of points. The iterative algorithm is based on the optimal ellipse which best describe a given set of points.

Keywords

Smallest ellipse problem Computational geometry Optimal ellipse Online algorithm 

Notes

Acknowledgement

The research of Krzysztof Misztal is supported by the National Science Centre (Poland) [grant no. 2012/07/N/ST6/02192].

References

  1. 1.
    Lin, M., Gottschalk, S.: Collision detection between geometric models: a survey. In: Proceedings of IMA Conference on Mathematics of Surfaces, vol. 1, pp. 602–608 (1998)Google Scholar
  2. 2.
    Jiménez, P., Thomas, F., Torras, C.: 3D collision detection: a survey. Comput. Graph. 25(2), 269–285 (2001)CrossRefGoogle Scholar
  3. 3.
    Ericson, C.: Real-Time Collision Detection. CRC Press, Boca Raton (2004)Google Scholar
  4. 4.
    Croux, C., Haesbroeck, G., Rousseeuw, P.J.: Location adjustment for the minimum volume ellipsoid estimator. Stat. Comput. 12(3), 191–200 (2002)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Knorr, E.M., Ng, R.T., Zamar, R.H.: Robust space transformations for distance-based operations. In: Proceedings of the Seventh ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 126–135. ACM (2001)Google Scholar
  6. 6.
    Mahalanobis, P.C.: On the generalized distance in statistics. Proc. Nat. Inst. Sci. (Calcutta) 2, 49–55 (1936)zbMATHGoogle Scholar
  7. 7.
    Welzl, E.: Smallest enclosing disks (balls and ellipsoids). In: Maurer, H. (ed.) New Results and New Trends in Computer Science. LNCS, vol. 555, pp. 359–370. Springer, Heidelberg (1991)CrossRefGoogle Scholar
  8. 8.
    Gärtner, B., Schönherr, S.: Smallest enclosing circles-an exact and generic implementation in C++ (1998)Google Scholar
  9. 9.
    Tabor, J., Spurek, P.: Cross-entropy clustering. Pattern Recogn. 47(9), 3046–3059 (2014)CrossRefzbMATHGoogle Scholar
  10. 10.
    Misztal, K., Tabor, J.: Mahalanobis distance-based algorithm for ellipse growing in iris preprocessing. In: Saeed, K., Chaki, R., Cortesi, A., Wierzchoń, S. (eds.) CISIM 2013. LNCS, vol. 8104, pp. 158–167. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  11. 11.
    Seidel, R.: Small-dimensional linear programming and convex hulls made easy. Discrete Comput. Geom. 6(3), 423–434 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    The CGAL Project: CGAL, Computational Geometry Algorithms Library. http://www.cgal.org

Copyright information

© IFIP International Federation for Information Processing 2016

Authors and Affiliations

  1. 1.Faculty of Mathematics and Computer ScienceJagiellonian UniversityKrakówPoland
  2. 2.The Faculty of Electrical Engineering, Automatics, Computer Science and Biomedical EngineeringAGH University of Science and TechnologyKrakówPoland

Personalised recommendations