Efficient Polynomial Implementation of Several Multithresholding Methods for Gray-Level Image Segmentation

  • David MenottiEmail author
  • Laurent Najman
  • Arnaldo de A. Araújo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9423)


Multithresholding consists of segmenting a histogram of image in classes by using thresholds. Many researchers avoid the exponential space problem of possible thresholds combinations of a given criteria function. In this work, we present a polynomial easy-to-implement dynamic programming algorithm to find the exact optimum thresholds of three well-known criteria functions for multithresholding: the maximum of histogram between class-variance (Otsu’s method); the maximum histogram entropy (Kapur et al.’s method), and minimum histogram error (Kittler and Illingworth’s method). The algorithm, that has been used to optimum quantization, has \(O((K-1)L^2)\) time complexity, where K and L stand for the number of desired classes and the number of gray levels in the image, respectively. Experiments showed that the exact optimum thresholds for gray-level image segmentation can be found in less than 160 milliseconds in a Pentium 4-2GHz, in whatever the number of classes.


Segmentation Multithresholding Dynamic programming 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • David Menotti
    • 1
    Email author
  • Laurent Najman
    • 2
  • Arnaldo de A. Araújo
    • 3
  1. 1.Federal University of ParanáCuritibaBrazil
  2. 2.Groupe ESIEE ParisUniversité Paris-EstNoisy-le-GrandFrance
  3. 3.Federal University of Minas GeraisBelo HorizonteBrazil

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