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What happens if two different pictures have the same gray-level histogram and the same threshold? Will it be suitable for both? A second-order statistic or some local property with our entropic concept of thresholding might give a better insight into these problems

A new method for gray-level picture thresholding using the entropy of the histogram

Computer Vision, Graphics, and Image Processing, no. 3 (1985): 273-285

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摘要

Two methods of entropic thresholding proposed by Pun (Signal Process.,2, 1980, 223–237;Comput. Graphics Image Process.16, 1981, 210–239) have been carefully and critically examined. A new method with a sound theoretical foundation is proposed. Examples are given on a number of real and artifically generated histograms.

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简介
  • The most commonly used method in extracting objects from a picture is “ thresholding.” If the object is clearly distinguishable from the background, the gray-level histogram will be bimodal and the threshold for segmentation can be chosen at the bottom of the valley.
  • Gray-level histograms are not always bimodal.
  • Weszka et al [l] and Weszka and Rosenfeld [2] present methods to overcome the threshold selection problem when the peaks vary significantly in size and the valley is relatively wide.
  • Others try to improve histograms by using second-order gray-level statistics as described in [3].
  • While deriving a lower bound for the a posteriori entropy of the gray-level histogram [12] Pun made a few errors in algebraic manipulations.
重点内容
  • In picture processing, the most commonly used method in extracting objects from a picture is “ thresholding.” If the object is clearly distinguishable from the background, the gray-level histogram will be bimodal and the threshold for segmentation can be chosen at the bottom of the valley
  • The graph of 4(s) may have one of the following shapes (Figs. 2a-e): In Fig. 2a sa is the obvious choice for threshold value
  • If the nuber of black pixels corresponding to the threshold value si is sufficient, we choose si, otherwise we choose to have the threshold value larger than si
  • Because of its general nature, this algorithm can be used for segmentation purposes
  • What happens if two different pictures have the same gray-level histogram and the same threshold? Will it be suitable for both? A second-order statistic or some local property with our entropic concept of thresholding might give a better insight into these problems
结果
  • First the authors will discuss the choice of threshold value and the authors will present the threshold values of some real and artificially generated pictures.
  • 2a-e): In Fig. 2a sa is the obvious choice for threshold value.
  • If the nuber of black pixels corresponding to the threshold value si is sufficient, the authors choose si, otherwise the authors choose to have the threshold value larger than si.
  • 2c-e the authors choose the threshold value (4
  • In Figs. 2c-e the authors choose the threshold value (4
结论
  • An algorithm (i.e., Algorithm 3) for choosing a threshold from the gray-level histogram of a picture has been derived by using the entropy concept from information theory.
  • The advantage of this algorithm is that it uses a global and objective property of the histogram.
  • What happens if two different pictures have the same gray-level histogram and the same threshold? Will it be suitable for both? A second-order statistic or some local property with the entropic concept of thresholding might give a better insight into these problems
引用论文
  • J. S. Weszka, R. N. Nagel, and A. Rosenfeld, A threshold selection technique, IEEE Truns. Comput. C-23, 1914, 1322-1326.
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  • N. Ahuja and A. Rosenfeld, A note on the use of second order gray-level statistics for threshold selection, IEEE Trans. Syst. Man Cybern. SMC-8, 1978, 895-898.
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  • T. Pun, Entropic thresholding: A new approach, Comput. Graphics Imuge Process. 16,1981, 210-239.
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  • P. K. Sahoo, Y. C. Chan, and A. K. C. Wong, A survey of thresholding methods, submitted.
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  • P. K. Sahoo, Y. C. Chart, and A. K. C. Wong, Evaluation of Some Global Thresholding Techniques, Technical Report No. 126-R-110484, Department of Systems Design, University of Waterloo.
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P.K. Sahoo
P.K. Sahoo
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