Abstract
The problem of finding elliptical shapes in an image will be considered. We discuss the new solution which uses cross-entropy clustering, providing the theoretical background of this approach. The proposed algorithm allows search for ellipses with predefined sizes and position in the space. Moreover, it works well in higher dimensions.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
References
Celeux, G., Govaert, G.: Gaussian parsimonious clustering models. Pattern Recognition 28(5), 781–793 (1995)
Cover, T.M., Thomas, J.A., Wiley, J., et al.: Elements of information theory, vol. 6. Wiley Online Library (1991)
Davies, E.R.: Finding ellipses using the generalised Hough transform. Pattern Recognition Letters 9(2), 87–96 (1989)
Fitzgibbon, A., Pilu, M., Fisher, R.B.: Direct least square fitting of ellipses. IEEE Trans. Pattern Anal. Mach. Intell. 21(5), 476–480 (1999)
Fraley, C.: Algorithms for model-based Gaussian hierarchical clustering. SIAM Journal on Scientific Computing 20(1), 270–281 (1998)
Free Stock Images, http://www.stockfreeimages.com/
Grünwald, P.D., Myung, I.J., Pitt, M.A.: Advances in minimum description length: Theory and applications. The MIT Press (2005)
Illingworth, J., Kittler, J.: A survey of the Hough transform Computer vision, graphics, and image processing 44(1), 87–116 (1988)
Lehmann, E.L., Casella, G.: Theory of point estimation, vol. 31. Springer (1998)
McLachlan, G.J., Krishnan, T.: The EM algorithm and extensions, p. 274. Wiley, New York (1997)
Mcnicholas, P.D., Murphy, T.B.: Parsimonious gaussian mixture models. Statistics and Computing 18(3), 285–296 (2008)
Mirsky, L.: A trace inequality of John von Neumann. Monatsh. Math. 79(4), 303–306 (1975)
Samé, A., Ambroise, C., Govaert, G.: An online classification em algorithm based on the mixture model. Statistics and Computing 17(3), 209–218 (2007)
Saeed, K., AlBakoor, M.: Region Growing Based Segmentation Algorithm for Typewritten, and Handwritten Text Recognition. Applied Soft Computing 9(2), 608–617 (2009)
Tabor, J., Spurek, P.: Cross-entropy clustering (2012), http://arxiv.org/pdf/1210.5594.pdf
Tsuji, S., Matsumoto, F.: Detection of ellipses by a modified Hough transformation. IEEE Trans. Comput. C-27, 777–781 (1978)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Tabor, J., Misztal, K. (2013). Detection of Elliptical Shapes via Cross-Entropy Clustering. In: Sanches, J.M., Micó, L., Cardoso, J.S. (eds) Pattern Recognition and Image Analysis. IbPRIA 2013. Lecture Notes in Computer Science, vol 7887. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38628-2_78
Download citation
DOI: https://doi.org/10.1007/978-3-642-38628-2_78
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-38627-5
Online ISBN: 978-3-642-38628-2
eBook Packages: Computer ScienceComputer Science (R0)