基于中值的阈值，最小误差阈值及其与基于直方图的图像相似性的关系
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Median-based Thresholding, Minimum Error Thresholding,
and Their Relationships with Histogram-based Image Similarity
Yaobin Zou
a,b,c*
, Lulu Fang
a
, Fangmin Dong
a,c
, Bangjun Lei
a,b
, Shuifa Sun
a,b
, Tingyao Jiang
a,b
, Peng Chen
a,b
a
Laboratory of Intelligent Vision Based Monitoring for Hydroelectric Engineering, China Three
Gorges University, Yichang, China
b
Collaborative Innovation Center for Geo-Hazards and Eco-Environment in Three Gorges Area,
Hubei Province, China
c
Collaborative Innovation Center for Key Technology of Smart Irrigation District in Hubei, China
Three Gorges University
Email: [email protected]
ABSTRACT
A popular histogram-based thresholding method is minimum error thresholding (MET) proposed by Kittler and
Illingworth [Minimum error thresholding, Pattern Recognition 19 (1) (1986) 41-47], whereas Xue and Titterington
recently proposed a median-based thresholding (MBT) [Median-based image thresholding, Image and Vision
Computing 29 (9) (2011) 631-637]. Both MET and MBT can be derived from the maximization of log-likelihood. In
this paper, we present a different theoretical interpretation about MBT and MET, from the perspective of minimizing
Kullback-Leibler (KL) divergence. Since the KL divergence is a measure of the difference between two probability
distributions, it is reasonable to regard MET and MBT as the special applications of histogram-based image similarity
(HBIS) in the image thresholding. Further, it is natural to suggest a more universal image thresholding framework based
on image similarity concept, since HBIS is just one of many image similarity methodologies. This thresholding
framework directly transforms the threshold determining problem into an image comparison issue. Its significance is that
it provides a concise and clear theoretical framework for developing potential thresholding methods with the plentiful
image similarity theories.
Keywords:Image thresholding; image similarity; Kullback-Leibler divergence.
1. INTRODUCTION
Image thresholding is one of the most important and effective methods for image segmentation. It is best suited for
images consisting of object and background with different gray level values [1]. Many image thresholding methods
determine the thresholds by analyzing the image histogram. Minimum error thresholding (MET) proposed by Kittler and
Illingworth is one of the most-widely used histogram-based methods [2]. Recently, Xue and Titterington proposed a
median-based thresholding (MBT) [3]. Both MET and MBT can be derived from maximization of log-likelihood [2-4].
This paper presents a different theoretical interpretation about MBT and MET, from the perspective of minimizing
Kullback-Leibler (KL) divergence. The KL divergence is a measure in statistics that quantifies in bits how close a
probability distribution
{}
i
pp= is to a model distribution {}
i
qq
=
[5],
(||) ln( )
K
Liii
i
Dpq p pq=
∑
(1)
K
L
D is non-negative, not symmetric in p and q , zero if the distributions match exactly and can potentially equal
infinity. The KL divergence provides a criterion to estimate the difference between two probability distributions.
2. SYMBOL SPECIFICATIONS
For a given gray level image
χ
with N pixels and largest gray level T , the gray level of the ith pixel is denoted
with
i
x
. A threshold t classifies the image
χ
into two classes
1
()Ct and
2
()Ct, where
1
() {:0 ,1 }
i
Ct i x t i N=≤≤≤≤
Sixth International Conference on Digital Image Processing (ICDIP 2014), edited by Charles M. Falco,
Chin-Chen Chang, Xudong Jiang, Proc. of SPIE Vol. 9159, 915915 · © 2014 SPIE
CCC code: 0277-786X/14/$18 · doi: 10.1117/12.2064335
Proc. of SPIE Vol. 9159 915915-1
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