An Efficient Algorithm for Optimal Multilevel Thresholding of Irregularly Sampled Histograms

  • Authors:
  • Luis Rueda

  • Affiliations:
  • Department of Computer Science, University of Windsor, Windsor, Canada N9B 3P4

  • Venue:
  • SSPR & SPR '08 Proceedings of the 2008 Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
  • Year:
  • 2008

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Abstract

Optimal multilevel thresholding is a quite importantproblem in image segmentation and pattern recognition. Althoughefficient algorithms have been proposed recently, they do notaddress the issue of irregularly sampled histograms. Apolynomial-time algorithm for multilevel thresholding ofirregularly sampled histograms is proposed. The algorithm ispolynomial not just on the number of bins of the histogram,n , but also on the number of thresholds, k , i.e.it runs in θ (kn 2). The proposedalgorithm is general enough for a wide range of thresholding andclustering criteria, and has the capability of dealing withirregularly sampled histograms. This implies important consequenceson pattern recognition, since optimal clustering in theone-dimensional space can be obtained in polynomial time.Experiments on synthetic and real-life histograms show that fortypical cases, the proposed algorithm can find the optimalthresholds in a fraction of a second.