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# 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

EI

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.
- J. S. Weszka and A. Rosenfeld, Histogram modification for threshold selection, IEEE Trans. Swt. Man Cvhern. SMC-9, 1979, 38-52.
- 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.
- R. L. Kirby and A. Rosenfeld, A note on the use of (gray level, local average gray level) space as an aid in threshold selection, IEEE Trans. Syst. Man Cybern. SMC-9, 1979, 860-864.
- L. S. Davis, A. Rosenfeld, and J. S. Weszka, Region extraction by averaging and thresholding. IEEE Truns. Syst. Man Cybern. SMCB, 1975, 383-388.
- N. Ostu, A threshold selection method from gray-level histograms, IEEE Trans. Sj~st. Mun Cvhern. SMC-9, 1979, 62-66.
- T. W. Ridler and S. Calvard, Picture thresholding using an iterative selection method, IEEE Trans. Cyst. Man Cybern. SMC-8, 1978, 630-632.
- A. Y. Wu, T. Hong, and A. Rosenfeld, Threshold selection using quadtrees, IEEE Truns. Puttern Anul. Mach. Intel/. PAM1-4,1982, 90-93.
- A. Rosenfeld and R. C. Smith, Thresholding using relaxation. IEEE Trans. Pattern Anal. Much. Intel/. PAMl-3, 1981, 598-606.
- J. S. We&a, A survey of threshold selection techniques, Comput. Graphics Image Process. 7. 1978, 259-265.
- K. S. Fu and J. K. Mui, A survey on image segmentation, Pattern Recognition 13, 1980, 3-16.
- T. Pun, A new method for gray-level picture thresholding using the entropy of the histogram, Signal Process. 2, 1980, 223-231.
- T. Pun, Entropic thresholding: A new approach, Comput. Graphics Imuge Process. 16,1981, 210-239.
- A. Rosenfeld and A. Kak, Digital Picture Processing, Academic Press, New York, 1916.
- Y. Nakagawa and A. Rosenfeld, Some experiments on variable thresholding, Pattern Recognitron 11, 1979, 191-204.
- CJ. Johannsen and J. Bille, A threshold selection method using information measures, in Proc. 6th Inc. Conf. on Pattern Recognition, Oct. 1982.
- P. K. Sahoo, Y. C. Chan, and A. K. C. Wong, A survey of thresholding methods, submitted.
- 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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