# Unsupervised range-constrained thresholding

**Abstract**

Three range-constrained thresholding methods are proposed in the light of human visual perception. The new methods first implement gray level range-estimation, using image statistical characteristics in the light of human visual perception. An image transformation is followed by virtue of estimated ranges. Criteria of conventional thresholding approaches are then applied to the transformed image for threshold selection. The key issue in the process lies in image transformation which is based on unsupervised estimation for gray level ranges of object and background. The transformation process takes advantage of properties of human visual perception and simplifies an original image, which is helpful for image thresholding. Three new methods were compared with their counterparts on a variety of images including nondestructive testing ones, and the experimental results show its effectiveness.

Unsupervised range-constrained thresholding

Zuoyong Li

a,

⇑

, Jian Yang

b

, Guanghai Liu

c

, Yong Cheng

d

, Chuancai Liu

b

a

Department of Computer Science, Minjiang University, Fuzhou 350108, China

b

School of Computer Science and Technology, Nanjing University of Science and Technology, Nanjing 210094, China

c

School of Computer Science and Information Technology, Guangxi Normal University, Guilin 541004, China

d

School of Communication Engineering, Nanjing Institute of Technology, Nanjing 211167, China

article info

Article history:

Received 5 November 2009

Available online 26 September 2010

Communicated by Y.J. Zhang

Keywords:

Thresholding

Image segmentation

Human visual perception

Standard deviation

Unsupervised estimation

abstract

Three range-constrained thresholding methods are proposed in the light of human visual perception. The

new methods ﬁrst implement gray level range-estimation, using image statistical characteristics in the

light of human visual perception. An image transformation is followed by virtue of estimated ranges. Cri-

teria of conventional thresholding approaches are then applied to the transformed image for threshold

selection. The key issue in the process lies in image transformation which is based on unsupervised esti-

mation for gray level ranges of object and background. The transformation process takes advantage of

properties of human visual perception and simpliﬁes an original image, which is helpful for image thres-

holding. Three new methods were compared with their counterparts on a variety of images including

nondestructive testing ones, and the experimental results show its effectiveness.

Ó 2010 Elsevier B.V. All rights reserved.

1. Introduction

Image segmentation intends to extract an object from a back-

ground based on some pertinent characteristics such as gray level,

color, texture and location (Tao et al., 2008). It is a critical prepro-

cessing step in image analysis and computer vision (Huang and

Wang, 2009; Sen and Pal, 2010). Among the existing segmentation

techniques, thresholding is one of the most popular approaches in

terms of simplicity, robustness and accuracy. Implicit assumption

in image thresholding is that object (foreground) and background

have distinctive gray levels. Thresholding serves a variety of appli-

cations, such as biomedical image analysis (Hu et al., 2006; Min and

Park, 2009), character identiﬁcation (Huang et al., 2008; Nomura

et al., 2009; Pai et al., 2010) and industrial inspection (Ng, 2006).

Thresholding techniques fall into bilevel and multilevel cate-

gory (Coudray et al., 2010; Horng, 2010; Malyszko and Stepaniuk,

2010; Wang et al., 2010) according to the number of segments. The

former assumes an image to be composed of two components (i.e.,

object and background), with an aim of ﬁnding an appropriate

threshold for distinguishing both parts. Thresholding result is a

binary image where all pixels with gray levels higher than

determined threshold are classiﬁed into foreground and the rest

of pixels assigned to background, or vice versa. The latter category

supposes that an image consists of multiple parts, each having

homogeneous gray level. Obviously, multiple thresholds should

be chosen to group pixels with gray level within a speciﬁed range

into one class. It can be regarded as an extension of the bilevel one.

Thresholding can also be classiﬁed into parametric and non-

parametric approaches from another perspective (Bazi et al.,

2007; Sahoo and Arora, 2004; Tizhoosh, 2005). In the parametric

approach, gray level distribution of an image is assumed to obey

a given statistical model, and optimal parameter estimation for

the model is sought by using image histogram. Fitted model is used

to approximate practical distribution. Bottom of valley in the mod-

el is regarded as the appropriate location of the optimal threshold.

This usually involves a nonlinear estimation of intensive computa-

tion. The nonparametric method determines the optimal threshold

by optimizing certain criterion, such as between-class variance

(Otsu, 1979), variance (Hou et al., 2006) and entropy (Kapur

et al., 1985; Pun, 1980). The nonparametric approach is proved

to be more robust and accurate.

Many thresholding approaches have been developed over the

last few years (Albuquerque et al., 2004; Kwon, 2004; Ramesh

et al., 1995; Sahoo et al., 1988; Wang et al., 2008). For example,

Bazi et al. (2007) proposed a parametric method, which ﬁnds the

optimal threshold through parameter estimation based on the

assumption that object and background follow a generalized

Gaussian distribution. Otsu’s method (1979) chooses the threshold

by maximizing the between-class variance of both object and

background. Sahoo et al. (1988) revealed that Otsu’s method is

one of the better threshold selection approaches for general real

world images with regard to uniformity and shape measures.

However, Otsu’s method exhibits a weakness of tending to classify

0167-8655/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved.

doi:10.1016/j.patrec.2010.09.020

⇑

Corresponding author. Tel.: +86 13906926400; fax: +86 059183761607.

E-mail addresses: fzulzytdq@126.com, fzulzytdq@yahoo.com.cn (Z. Li).

Pattern Recognition Letters 32 (2011) 392–402

Contents lists available at ScienceDirect

Pattern Recognition Letters

journal homepage: www.elsevier.com/locate/patrec

an image into two parts of similar size regardless of the practical

situation. After exploring the underlying reason for Otsu’s weak-

ness, Hou et al. (2006) presented an approach based on minimum

class variance, which can be regarded as a generalization of Otsu’s.

In image thresholding, one of the most efﬁcient techniques is en-

tropy-based approach, which regards a gray level image histogram

as a probability distribution. In Pun’s method (1980), the threshold

is determined by maximizing the posteriori entropy of object and

background. Kapur et al. (1985) found some ﬂaws in Pun’s deriva-

tions and proposed a corrected version. In 2004, Albuquerque et al.

presented an approach based on Tsallis entropy. Tsallis entropy is

applied as a general entropy form for information theory. In addi-

tion, Ramesh’s method (1995) ﬁnds the threshold by minimizing

function approximation error for image histogram with a bilevel

function. Wang et al. (2008) determined the threshold by optimiz-

ing a criterion function deduced by image histogram and Parzen

window technique. A thorough survey over thresholding is pro-

vided in the literature (Sezgin and Sankur, 2004).

Conventional nonparametric approaches utilize some criteria to

search the optimal threshold from all the gray levels, and neglect

properties of human visual perception. This makes them suffer a

limitation of being unable to obtain satisfactory results when seg-

menting some images. To eliminate the above limitation, three

unsupervised range-constrained thresholding methods are pre-

sented in this paper. Based on properties of human visual percep-

tion, they ﬁrst ﬁnd gray level ranges of object and background in an

unsupervised way by utilizing statistical characteristics of an im-

age. Then, an image transformation is implemented via the above

ranges. The transformation should simplify an original image and

improve segmentation performance. Finally, three existing criteria

are applied to a transformed image for threshold determination.

The performance of range-constrained methods is compared with

their conventional counterparts by testing a variety of images.

Experimental results show their superiority over the counterparts.

The remainder of this paper is organized as follows: Section 2

introduces properties of human visual perception. Three unsuper-

vised range-constrained methods are proposed in Section 3. Their

performance is detailed on a variety of images and compared with

their counterparts in Section 4. Conclusions appear in Section 5.

2. Human visual perception

Human visual perception has the following properties as de-

scribed in the literature (Arora et al., 2008).

(1) Human eye is insensitive to features present at the both

extremes of pixel intensity, whereas sensitive to distinguish-

ing features at the mid-range intensities. This characteristic

suggests a focus upon mid-region of a gray scale image, i.e.,

around the mean, when segmenting images.

(2) A lot of images may have either histograms with high inten-

sity values or more structures near a certain value (usually

the mean) than that farther from the mean. A rough estima-

tion of such a histogram exhibits a Gaussian distribution.

3. Unsupervised range-constrained thresholding methods

Conventional nonparametric thresholding approaches ﬁnd the

optimal threshold via optimizing some criteria. The process ne-

glects the properties of human visual perception, resulting in

unsatisfactory segmentation for some real world images. In an ef-

fort to eliminate the limitation, the authors have tried a new

scheme in the light of human visual perception. The scheme ﬁrst

ﬁnds gray level ranges of object and background via human visual

perception and image statistical characteristics in an unsupervised

way, then simpliﬁes an original image by image transformation

based on the ranges, and ﬁnally applies the criteria of three exist-

ing methods to the transformed image, thus forming range-

constrained approaches with better segmentation performance.

3.1. Gray level ranges of object and background

For the sake of description convenience, we assume that object

(foreground) pixels have higher gray levels than background ones.

In the light of human visual perception, two gray levels should be

chosen as the lower bound for object and the upper bound for

background by using statistical characteristics of an image. After

ﬁnding the lower and upper bounds, gray level ranges of object

and background are accordingly determined, respectively. The

detailed process is as follows:

(1) Without losing generality, Let I be a gray scale image with L

levels [0, 1, ... , L

1]. The number of pixels with gray level i

is denoted by n

i

and the total number of pixels by

N = n

0

+ n

1

+ + nL

1

. The mean and standard deviation of

the image are deﬁned as

l

¼

1

N

X

L1

i¼0

in

i

; ð1Þ

r

¼

1

N 1

X

L1

i¼0

ði

l

Þ

2

n

i

!

1

2

: ð2Þ

(2) Compute two gray levels

T

u

¼

l

b

r

; ð3Þ

T

l

¼

l

þ b

r

; ð4Þ

where b is a parameter and its value can be automatically determined

by optimizing the proposed criterion in Eq. (13). T

u

and T

l

are the

upper and lower bounds for background and object, respectively.

(3) Determine gray level ranges of object and background via

the following way:

R

F

¼ðT

l

L 1; ð5Þ

R

B

¼½0 T

u

Þ: ð6Þ

Finding the upper and lower bounds needs choosing a reasonable

value for parameter b, which in turn involves a statistical criterion

to be deﬁned.

Assuming that the image I is divided into three portions via two

gray levels t

1

and t

2

, where t

1

< t

2

, with three parts denoted by C

b

, C

f

and C

m

, where C

b

is the background class with gray levels

[0, ... , t

1

1], C

f

the foreground class with levels

[t

2

+1,... , L 1], and C

m

the middle class with levels [t

1

, ... , t

2

].

C

m

is the middle transition region between C

b

and C

f

as described

in (Hu et al., 2008). The mean of each class is deﬁned as

l

b

¼

1

N

b

X

t

1

1

i¼0

in

i

; ð7Þ

l

f

¼

1

N

f

X

L1

i¼t

2

þ1

in

i

; ð8Þ

l

m

¼

1

N

m

X

t

2

i¼t

1

in

i

; ð9Þ

where N

b

, N

f

and N

m

are the numbers of pixels in C

b

, C

f

and C

m

,

respectively. And their respective standard deviation can be given by

Z. Li et al. / Pattern Recognition Letters 32 (2011) 392–402

393

r

b

¼

1

N

b

1

X

t

1

1

i¼0

ði

l

b

Þ

2

n

i

!

1

2

; ð10Þ

r

f

¼

1

N

f

1

X

L1

i¼t

2

þ1

ði

l

f

Þ

2

n

i

!

1

2

; ð11Þ

r

m

¼

1

N

m

1

X

t

2

i¼t

1

ði

l

m

Þ

2

n

i

!

1

2

: ð12Þ

Based on the above standard deviations, the statistical criterion

could be deﬁned as

r

S

¼

a

ð

r

b

þ

r

f

Þþð1

a

Þ

r

m

; ð13Þ

where

a

is a parameter between 0 and 1. The criterion consists of

two terms, the ﬁrst term standing for the sum of standard devia-

tions corresponding to C

b

and C

f

. Standard deviation is a common

statistical measure reﬂecting degree of deviations between mean

and individuals. Hence, the term could represent intra-class similar-

ities of the background and foreground to some extent. The smaller

the term is, the higher the similarities. But it is worth mentioning

that both background and foreground themselves of a practical im-

age usually have some deviations on pixels’ gray levels, especially

for background. So it is unreasonable to determine the value of b

by minimizing only the ﬁrst term. To solve the problem,

r

m

, stan-

dard deviation of the transitional class, C

m

, is introduced into the

criterion as a penalty term. The parameter

a

in Eq. (13) is a weight

balancing the contributions of the two terms.

For the image I, following steps describe the detail about auto-

matic selection of b:

(1) Initialize MVS to be inﬁnite, and i = 1, where MVS is the min-

imum value of

r

S

, i is the temporal number of iterations.

(2) Compute two gray levels t

1

and t

2

via the following

equations:

t

1

¼

l

0:1 i

r

; ð14Þ

t

2

¼

l

þ 0:1 i

r

; ð15Þ

where

l

and

r

are deﬁned in Eqs. (1) and (2), respectively. If t

1

<0or

t

2

> L 1, then break the process; else, continue step 3. Here, the

reason using a constant 0.1 in Eqs. (14) and (15) is as follows: image

thresholding includes an implicit assumption that object and back-

ground have distinctive gray levels, that is, their difference should

be at least several gray levels. Standard deviation of an image is usu-

ally between 20 and 100, with practical values for our sample

images in experiments being as: Cell (24.532), Tile (20.829), PCB

(54.341), Gearwheel (100.05), Potatoes (83.056), Block (73.122),

Lena (47.51), Peppers (53.179), Flower (41.912) and Corn (62.083).

Therefore, 0.1 is basically the minimum coefﬁcient for standard

deviation

r

in Eqs. (14) and (15).

(3) Calculate the value of our statistical criterion

r

S

by Eq. (13).

If

r

S

< MVS, then MVS =

r

S

, b = 0.1 i and i = i + 1; else,

i = i + 1. Subsequently, return to step 2.

Once b is determined, the upper and lower bounds can be calcu-

lated by Eqs. (3) and (4). Take cell image in Fig. 1(a) as an example.

Its foreground, background and middle classes are shown in

Fig. 1(b)–(d), where bright pixels are our focuses. The upper and

lower bounds are 222 and 227, and b is automatically set to 0.1.

Accordingly, gray level ranges of the background and object are

[0 222) and (227 L 1], respectively.

3.2. Image transformation

In order to implement image transformation, gray level ranges

of object and background must ﬁrst be obtained as described in

Section 3.1. The ranges can be treated as gray level constrains on

object and background. For the image I, the process of image trans-

formation is as follows:

(1) Calculate the upper and lower bounds by Eqs. (3) and (4).

(2) Obtain gray level ranges of object and background, i.e., R

F

and R

B

, by Eqs. (5) and (6).

(3) Implement image transformation via the following way:

f

tr

ði; jÞ¼

T

u

if f ði; jÞ2R

B

;

T

l

if f ði; jÞ2R

F

;

f ði; jÞ otherwise;

8

>

<

>

:

ð16Þ

where f(i, j) and f

tr

(i, j) are gray levels at pixel (i, j) of the original im-

age and the transformed form, respectively.

The transformation weakens gray level changes in both object

and background simultaneously, thus simplifying the original im-

age. The weakening effect is favorable to subsequent image seg-

mentation. Take transformed form Fig. 2(b) for the cell image as

an example. Their respective histogram is displayed in Fig. 2(c)

and (d). From Fig. 2, one can conclude that gray level changes of

object and background have been weakened dramatically, and

the transformed image becomes much simpler than the original.

Furthermore, one can observe that the transformation turns a his-

togram of unimodal distribution into an apparent bimodal one, the

latter being preferable when detecting the valley in a histogram,

for valley is usually regarded as the appropriate location of the

optimal threshold.

3.3. Method 1: Range-Constrained Ramesh’s method (RCramesh)

RCramesh recursively approximates the histogram of a given

transformed image with a bilevel function, and ﬁnds the optimal

threshold by minimizing approximation error. Here, the error is

represented by the variance of the approximated histogram. It is

worth mentioning that gray level range of the transformed image

Fig. 1. Cell image and its classes: (a) original, (b) foreground class, (c) background class, (d) middle class.

394 Z. Li et al. / Pattern Recognition Letters 32 (2011) 392–402

should be [T

u

T

l

], where T

u

and T

l

are the upper and lower bounds.

For a given gray level T

u

6 t 6 T

l

, the approximation error in RCra-

mesh can be formulated as

EðtÞ¼

1

N

1

1

X

t

i¼T

u

ði

l

1

Þ

2

þ

1

N

2

1

X

T

l

i¼tþ1

ði

l

2

Þ

2

; ð17Þ

where

l

1

¼

1

N

1

X

t

i¼T

u

in

i

; ð18Þ

l

2

¼

1

N

2

X

T

l

i¼tþ1

in

i

; ð19Þ

where N

1

is the number of pixels with levels [T

u

, ..., t], and N

2

the

number of pixels with levels [t +1,... , T

l

]. The optimal threshold t

*

can be determined by RCramesh,

T

¼ Arg min

T

u

6t6T

l

fEðtÞg: ð20Þ

3.4. Method 2: Range-Constrained Tsallis method (RCtsallis)

For a transformed image, let p

i

be the probability of gray level i

appeared in the image, where T

u

6 i 6 T

l

. Assuming that the pixels

in the image are classiﬁed into two classes, A and B, by a gray level

t, where T

u

6 t 6 T

l

. Class A corresponds to the foreground and class

B to the background, or vice versa. Cumulative probability of each

class can be deﬁned as

x

A

¼

X

t

i¼T

u

p

i

; ð21Þ

x

B

¼

X

T

l

i¼tþ1

p

i

: ð22Þ

A priori Tsallis entropy for each class is deﬁned as

S

A

q

ðtÞ¼

1

P

t

i¼T

u

p

i

=

x

A

ðÞ

q

q 1

; ð23Þ

S

B

q

ðtÞ¼

1

P

T

l

i¼tþ1

p

i

=

x

B

ðÞ

q

q 1

: ð24Þ

And the optimal threshold t

*

can be determined by RCtsallis,

T

¼ Arg max

T

u

6t6T

l

fS

A

q

ðtÞþS

B

q

ðtÞþð1 qÞS

A

q

ðtÞS

B

q

ðtÞg: ð25Þ

3.5. Method 3: Range-Constrained Wang’s method (RCwang)

For a transformed image with gray levels [T

u

, T

u

+1,..., T

l

], the

number of pixels with level i (T

u

6 i 6 T

l

) is denoted by n

i

and the

total number of pixels by N ¼ N

T

u

þ N

T

u

þ1

þþN

T

l

. Suppose that

the pixels in the transformed image are divided into two classes, A

and B, by a level t (T

u

6 t 6 T

l

). A is the set of pixels with levels

[T

u

, ... , t], and B the set of pixels with levels [t +1,... , T

l

]. The

two sets constitute the corresponding probability spaces, and their

probability density function, p

A

(x, y) and p

B

(x, y), can be formulated

as follows by using Parzen window estimation:

p

A

ðx; yÞ¼

1

N

X

t

i¼T

u

X

N

i

j¼1

1

h

2

N

i

u

ðx; y; x

j

; y

j

; h

2

N

i

Þ; ð26Þ

p

B

ðx; yÞ¼

1

N

X

T

l

i¼tþ1

X

N

i

j¼1

1

h

2

N

i

u

ðx; y; x

j

; y

j

; h

2

N

i

Þ; ð27Þ

where

u

ðx; y; x

j

; y

j

; h

2

N

i

Þ¼

1

2

p

exp

ðx x

j

Þ

2

þðy y

j

Þ

2

2h

2

N

i

!

: ð28Þ

In Eqs. (26)–(28), h

N

i

denotes the window width of the set com-

posed of those pixels with gray level i,(x

j

, y

j

) is the coordinate of

the jth pixel in the set. And the optimal threshold t

*

can be deter-

mined by RCwang,

t

¼ Arg min

T

u

6t6T

i

ZZ

X

p

2

A

ðx; yÞdx dy þ

ZZ

X

p

2

B

ðx; yÞdx dy

2

ZZ

X

p

A

ðx; yÞp

B

ðx; yÞdx dy

; ð29Þ

where

X

= [1, m] [1, n], m and n are the height and width of the

image, respectively. And the following equations hold:

ZZ

X

p

2

A

ðx; yÞdx dy ¼

1

N

2

X

t

i¼T

u

X

N

i

j¼1

X

t

k¼T

u

X

N

k

r¼1

Gðx

j

; y

j

; x

r

; y

r

; h

2

N

i

þ h

2

N

k

Þ;

ð30Þ

ZZ

X

p

2

B

ðx; yÞdx dy ¼

1

N

2

X

T

l

i¼tþ1

X

N

i

j¼1

X

T

l

k¼tþ1

X

N

k

r¼1

Gðx

j

; y

j

; x

r

; y

r

; h

2

N

i

þ h

2

N

k

Þ;

ð31Þ

ZZ

X

p

A

ðx;yÞp

B

ðx;yÞdxdy ¼

1

N

2

X

t

i¼T

u

X

N

i

j¼1

X

T

l

k¼tþ1

X

N

k

r¼1

Gðx

j

;y

j

; x

r

;y

r

; h

2

N

i

þ h

2

N

k

Þ;

ð32Þ

where

Gðx

j

; y

j

; x

r

; y

r

; h

2

N

i

þ h

2

N

k

Þ¼

1

h

2

N

i

þ h

2

N

k

u

ðx

j

; y

j

; x

r

; y

r

; h

2

N

i

þ h

2

N

k

Þ; ð33Þ

and the deﬁnition of function

u

can refer to Eq. (28).

The advantages of RCramesh, RCtsallis and RCwang over their

counterparts are as follows: (1) a transformed image is used in-

stead of the original one during thresholding, which transfers

Fig. 2. Images and histograms: (a) original cell image, (b) the transformed image, (c) histogram of (a), (d) histogram of (b).

Z. Li et al. / Pattern Recognition Letters 32 (2011) 392–402

395

Table 1

Thresholds, numbers of misclassiﬁed pixels, ME values and running times obtained by applying various methods to the NDT images.

NDT images Thresholding methods

Ramesh’s method RCramesh Tsallis RCtsallis Wang’s method RCwang

Cell

Threshold 241 222 171 226 171 225

Misclassiﬁed pixels 53,861 2634 7375 4172 7375 3780

ME 0.82185 0.040192 0.11253 0.06366 0.11253 0.057678

Running times (s) 1.641 1.844 3.469 3.672 281.27 281.47

Tile

Threshold 213 197 149 200 149 199

Misclassiﬁed pixels 46,719 1711 10229 2703 10229 2257

ME 0.71288 0.026108 0.15608 0.041245 0.15608 0.034439

Running times (s) 1.375 1.563 3.406 3.594 265.69 265.88

PCB

Threshold 173 79 161 80 161 80

Misclassiﬁed pixels 15,707 2655 14,426 2501 14,426 2501

ME 0.23967 0.040512 0.22012 0.038162 0.22012 0.038162

Running times (s) 0.359 0.625 0.375 0.641 203.59 203.86

Fig. 3. Thresholding results of cell image: (a) original, (b) ground truth image, (c) Ramesh’s method (t = 241), (d) RCramesh (t = 222), (e) Tsallis (t = 171), (f) RCtsallis (t = 226),

(g) Wang’s method (t = 171), (h) RCwang (t = 225).

Fig. 4. Thresholding results of tile image: (a) original, (b) ground truth image, (c) Ramesh’s method (t = 213), (d) RCramesh (t = 197), (e) Tsallis (t = 149), (f) RCtsallis (t = 200),

(g) Wang’s method (t = 149), (h) RCwang (t = 199).

396 Z. Li et al. / Pattern Recognition Letters 32 (2011) 392–402

Fig. 5. Thresholding results of PCB image: (a) original, (b) ground truth image, (c) Ramesh’s method (t = 173), (d) RCramesh (t = 79), (e) Tsallis (t = 161), (f) RCtsallis (t = 80),

(g) Wang’s method (t = 161), (h) RCwang (t = 80).

Table 2

Thresholds, numbers of misclassiﬁed pixels, ME values and running times obtained by applying various methods to the simple real world images.

Simple images Thresholding methods

Ramesh’s method RCramesh Tsallis RCtsallis Wang’s method RCwang

Gearwheel

Threshold 228 84 13 85 202 85

Misclassiﬁed pixels 26,829 106 2247 131 12,664 131

ME 0.40938 0.0016174 0.034286 0.0019989 0.19324 0.0019989

Running times (s) 0.5 0.672 1.094 1.266 262.34 262.52

Potatoes

Threshold 143 97 64 98 65 98

Misclassiﬁed pixels 1805 0 1823 38 1593 38

ME 0.027542 0 0.027817 0.00057983 0.024307 0.00057983

Running times (s) 0.609 0.812 0.734 0.937 189.13 189.33

Block

Threshold 126 52 17 53 128 53

Misclassiﬁed pixels 12,554 428 2589 378 13,910 378

ME 0.19156 0.0065308 0.039505 0.0057678 0.21225 0.0057678

Running times (s) 0.437 0.593 0.781 0.937 232.56 232.72

Fig. 6. Thresholding results of gearwheel image: (a) original, (b) ground truth image, (c) Ramesh’s method (t = 228), (d) RCramesh (t = 84), (e) Tsallis (t = 13), (f) RCtsallis

(t = 85), (g) Wang’s method (t = 202), (h) RCwang (t = 85).

Z. Li et al. / Pattern Recognition Letters 32 (2011) 392–402

397

range of threshold selection from [0 L 1] to [T

u

T

l

]. This coincides

with the properties of human visual perception and improves seg-

mentation performance, (2) image transformation in the proposed

approaches weakens gray level changes in object and background,

thus simplifying the original image, which is helpful for subse-

quent image thresholding.

4. Experimental results

To evaluate the performance of our range-constrained methods,

a variety of images have been chosen as testing samples. The re-

sults yielded by our methods were compared with those obtained

by their counterparts, i.e., Ramesh’s method (1995), Tsallis

(Albuquerque et al., 2004) and Wang’s method (2008). The quality

of segmentation result is quantitatively evaluated via misclassiﬁ-

cation error (ME) measure (Yasnoff et al., 1977), which regards im-

age segmentation as a pixel classiﬁcation process. The measure

reﬂects the percentage of background pixels erroneously classiﬁed

into foreground, and conversely, foreground pixels erroneously as-

signed to background. For a two-class segmentation, ME can be

simply formulated as

ME ¼ 1

jB

O

\ B

T

jþjF

O

\ F

T

j

jB

O

jþjF

O

j

; ð34Þ

where B

O

and F

O

are the background and foreground of the ground

truth image, B

T

and F

T

the background and foreground pixels in the

thresholded image, and || the cardinality of a set. The value of ME

varies between 0 for a perfectly classiﬁed image and 1 for a totally

erroneously classiﬁed one. A lower value of ME means better qual-

ity. In Tsallis and RCtsallis, q = 3. In our methods,

a

= 0.4. All exper-

iments are performed on a notebook PC with 2.13G Intel Core 2 Duo

CPU and 3G RAM. All the images used in the experiments are of

256 256 pixels and 8-bit (i.e., 256 gray levels).

4.1. Experiments on NDT images

The range-constrained methods were ﬁrst applied to three NDT

images and compared with their counterparts. NDT means to de-

tect an object and quantify its possible defects without harmful

Fig. 7. Thresholding results of potatoes image: (a) original, (b) ground truth image, (c) Ramesh’s method (t = 143), (d) RCramesh (t = 97), (e) Tsallis (t = 64), (f) RCtsallis

(t = 98), (g) Wang’s method (t = 65), (h) RCwang (t = 98).

Fig. 8. Thresholding results of block image: (a) original, (b) ground truth image, (c) Ramesh’s method (t = 126), (d) RCramesh (t = 52), (e) Tsallis (t = 17), (f) RCtsallis (t = 53),

(g) Wang’s method (t = 128), (h) RCwang (t = 53).

398 Z. Li et al. / Pattern Recognition Letters 32 (2011) 392–402

effects on itself by special equipments and methods. It is used in a

broad variety of applications, such as aeronautics and astronautics,

nuclear industry, chemistry and civil constructions.

The results in terms of thresholds, numbers of misclassiﬁed pix-

els, ME values and running times for various approaches are listed

in Table 1. The table shows that segmentation results obtained by

authors’ methods have less misclassiﬁed pixels and lower ME val-

ues, implying better performance. This could be attributed to the

utilization of human visual perception in ﬁnding ranges of object

and background for subsequent image transformation. The trans-

formation dramatically simpliﬁes the original image by weakening

gray level changes of object and background. The coincidence with

human visual perception and the image simpliﬁcation are helpful

for improving segmentation performance. In addition, one can ob-

serve that conventional methods are only slightly faster than our

approaches with regard to the speed of segmentation. The range-

constrained methods reduce search space during thresholding

from the whole gray levels of an original image to a much smaller

range [T

u

T

l

] and save running time, as compared with conventional

approaches. Nevertheless, the new methods need extra time to

estimate ranges of object and background, with implementing im-

age transformation. Performance judgment over various methods

can also be evidenced by visual segmentation results shown in

Figs. 3–5. From the ﬁgures, one can conclude that the proposed

methods enjoy better visual effects, as they segment the objects

more accurately.

4.2. Experiments on other images

In this section, seven general real world images were chosen as

test specimen. These images fall into two groups. The ﬁrst is for

simple images, and the second for complex ones. Table 2 lists

quantitative comparison of segmentation results for the ﬁrst

group. The data show that the proposed methods achieve better

segmentations with less misclassiﬁed pixels and lower ME values.

Visual thresholding results are displayed in Figs. 6–8. The ﬁgures

indicate, in addition to a completely segmenting for objects, the

new approaches exhibit less background noise.

Segmentation results for the complex images are in Figs. 9–12.

The ﬁrst two are classic gray level types, and the rest come from

Fig. 9. Thresholding results of Lena image: (a) original, (b) histogram, (c) Ramesh’s method (t = 107), (d) RCramesh (t = 119), (e) Tsallis (t = 161), (f) RCtsallis (t = 127),

(g) Wang’s method (t = 122), (h) RCwang (t = 126).

Fig. 10. Thresholding results of peppers image: (a) original, (b) histogram, (c) Ramesh’s method (t = 131), (d) RCramesh (t = 124), (e) Tsallis (t = 70), (f) RCtsallis (t = 128),

(g) Wang’s method (t = 95), (h) RCwang (t = 128).

Z. Li et al. / Pattern Recognition Letters 32 (2011) 392–402

399

famous Berkeley image database. Due to their complex structures,

quantitative measurement of segmentation quality experiences

serious difﬁculty at present. Only visual perception of subjective

nature is applicable to the judgment of segmentation quality.

Figs. 9–12 show range-constrained methods preserving more de-

tails of the objects, implying better results. More details relating

ranges of object and background for all the images in our experi-

ments are provided in Table 3.

4.3. Parameter selection

The range-constrained methods involve two parameters

a

and

b, and b is determined by our proposed statistical criterion with

a

. Hence, only one parameter

a

is left uncertain. The parameter

is used to balance the contributions of the two terms in our crite-

rion, and smaller value implies larger contribution of the transi-

tional class. To ﬁnd the reasonable value for

a

, a series of

Fig. 11. Thresholding results of ﬂower image: (a) original, (b) histogram, (c) Ramesh’s method (t = 225), (d) RCramesh (t = 54), (e) Tsallis (t = 123), (f) RCtsallis (t = 55),

(g) Wang’s method (t = 122), (h) RCwang (t = 55).

Fig. 12. Thresholding results of corn image: (a) original, (b) histogram, (c) Ramesh’s method (t = 155), (d) RCramesh (t = 100), (e) Tsallis (t = 138), (f) RCtsallis (t = 101),

(g) Wang’s method (t = 131), (h) RCwang (t = 101).

Table 3

Ranges of object and background obtained by the proposed methods for image transformation under the assumption that object pixels have higher gray levels than background

ones.

Images Range of object Range of background Images Range of object Range of background

Cell (227 255] [0 222) Block (67 255] [0 52)

Tile (201 255] [0 197) Lena (128 255] [0 119)

PCB (90 255] [0 79) Peppers (135 255] [0 124)

Gearwheel (104 255] [0 84) Flower (63 255] [0 54)

Potatoes (113 255] [0 97) Corn (112 255] [0 100)

400 Z. Li et al. / Pattern Recognition Letters 32 (2011) 392–402

experiments on six images with different

a

have been carried out.

Experimental results are listed in Table 4. The table indicates that:

(1) ME values of images usually vary from small to big. The reason

is that a big

a

determines an unreasonable value for b, which in

turn leads to inaccurate gray level ranges of object and back-

ground. Such inaccuracy in ranges will signiﬁcantly affect image

transformation and subsequent image thresholding, (2) with refer-

ence to MME values of six images, three range-constrained meth-

ods have different optimal values for

a

. For example, in RCtsallis

and RCwang, the optimal value for positions somewhere between

0.1 and 0.4, whereas in RCramesh, the optimal value is 0.5. How-

ever, it is worth mentioning that the difference of MME values ob-

tained by RCramesh is small when

a

varies between 0.1 and 0.5.

Therefore, as a general guide, the parameter ranges between 0.1

and 0.4, a 0.4 being selected for our proposed methods. Experimen-

tal data reveal

a

= 0.4 usually yield lowest average MME value for

the proposed methods, while

a

varying between 0.1 and 0.4 leads

to the same b as well as transformed image, which brings about

segmentation result with the same average MME value. When

a

higher than 0.4, however, average MME value becomes larger, thus

indicating

a

= 0.4 acting as a turning point.

5. Conclusions

Three novel range-constrained thresholding methods are pro-

posed in this paper. In the light of human visual perception, the

methods ﬁrst use statistical characteristics of an image to estimate

gray level ranges of object and background. At this stage, a new

statistical criterion for automatic selection of the parameter b is

developed. Subsequently, the gray level ranges are accordingly

determined. Automatic choice of b enhances the universality of

our methods. Then, range-constrained methods utilize the above

ranges to implement image transformation. Finally, criteria of

three existing thresholding methods are applied to the trans-

formed image for threshold selection. Image transformation by

conﬁning gray level ranges of object and background coincides

with human visual perception and simpliﬁes an original image,

which beneﬁts image segmentation. In addition, experimental re-

sults show that running times of the proposed methods are com-

parative with those of their counterparts, and the reason has

been interpreted in Section 4.1. Experimental results on a variety

of real world images including NDT images show the effectiveness

of the proposed range-constrained methods.

Acknowledgements

This work is supported by National Natural Science Founda-

tion of China (Grant Nos. 60472061, 60632050, 90820004,

60875010), National 863 Project (Grant Nos. 2006AA04Z238,

2006AA01Z119), Technology Project of Provincial University of

Fujian Province (JK2010046) and Technology Project of Education

Department of Fujian Province (JA10226).

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RCwang

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Potatoes 0.00058 0.00058 0.00058 0.00058 0.00058 0.33977 0.38225 0.38225 0.38225 0.38225

Block 0.00577 0.00577 0.00577 0.00577 0.00577 0.00577 0.02237 0.09178 0.09178 0.09178

MME 0.02310 0.02310 0.02310 0.02310 0.03456 0.11848 0.13342 0.14597 0.14597 0.14597

Average MME for three methods

0.02250 0.02250 0.02250 0.02250 0.06735 0.22325 0.24778 0.30912 0.30912 0.30912

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- CitationsCitations12
- ReferencesReferences33

- "In the proposed method, there are four parameters: ˛, ˇ, and neighborhood size. However, ˛ can be automatically determined by the statistical criterion in the literature [24]. Hence, onlyˇ,onlyˇ, and neighborhood size are left uncertain. "

[Show abstract] [Hide abstract]**ABSTRACT:**Transition region-based thresholding is a newly developed image binarization technique. Transition region descriptor plays a key role in the process, which greatly affects accuracy of transition region extraction and subsequent thresholding. Local entropy (LE), a classic descriptor, considers only frequency of gray level changes, easily causing those non-transition regions with frequent yet slight gray level changes to be misclassified into transition regions. To eliminate the above limitation, a modified descriptor taking both frequency and degree of gray level changes into account is developed. In addition, in the light of human visual perception, a preprocessing step named image transformation is proposed to simplify original images and further enhance segmentation performance. The proposed algorithm was compared with LE, local fuzzy entropy-based method (LFE) and four other thresholding ones on a variety of images including some NDT images, and the experimental results show its superiority.- "The main weak point of the these techniques is that they critically rely on the input binarization step performed by thresholding the grayscale input. However, estimating appropriate global or local thresholds may be difficult, as well as due to contrast defects and slight illumination variations, the separation of CEs from the background can be imperfect [5]. In the recent years, Marked Point Processes (MPP) [6, 7, 8] have become popular in 2D and 3D object detection, since they can efficiently model a population of an unknown number of entities, and consider the geometry of the objects. "

[Show abstract] [Hide abstract]**ABSTRACT:**In this paper we introduce a probabilistic approach for optical quality checking of Solder Pastes (SP) in Printed Circuit Boards (PCB). Dealing with unregistered image inputs, the task is to address at the same time SP identification, and detecting special soldering errors, called scooping. For this reason we introduce a novel Hierarchical Marked Point Process (HMPP) framework, which is able to handle the paste and scooping extraction problems simultaneously, so that the SPs and the included scoops have a parent-child relationship. A global optimization process attempts to find the optimal configuration of entities, considering the observed data, prior knowledge, and interactions between the neighboring circuit elements. The proposed method is evaluated on a real PCB image set containing more than 3000 SPs and 600 scooping artifacts- [Show abstract] [Hide abstract]
**ABSTRACT:**In this paper we introduce a probabilistic approach for optical quality checking of solder pastes (SP) in Printed Circuit Boards (PCB). Dealing with unregistered image inputs, our task is to address at the same time SP identification, and detection of special soldering errors, called scooping. For this reason we introduce a novel Hierarchical Marked Point Process (HMPP) framework, which is able to handle the paste and scooping extraction problems simultaneously, so that the SPs and included scoops have a parent–child relationship. A global optimization process attempts to find the optimal configuration of entities, considering the observed data, prior knowledge, and interactions between the neighboring circuit elements. The proposed method is evaluated on a real PCB image set containing more than 3000 SPs and 600 scooping artifacts. A morphology-based baseline method is also introduced for the problem and used as reference for qualitative and quantitative comparison against the proposed model.

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