An Efficient Algorithm for Optimal Multilevel Thresholding of Irregularly Sampled Histograms

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.