Narrow Band Active Contour Model for Local Segmentation ...narrow band is built, and the curve evolution precision (CEP) can change from one to inﬁnity ﬂexibly. Considering that

Narrow Band Active Contour Model for Local

Segmentation of Medical and Texture Images

Qiang ZHENG1 En-Qing DONG1

Abstract: A new narrow band active contour model based on binary level set function (LSF) for local segmentation

is proposed in this paper. By taking morphological dilation and erosion operations on the binary LSF, a stable and flexible

narrow band is built, and the curve evolution precision (CEP) can change from one to infinity flexibly. Considering that the

contour will be initialized inside the target object and inflated afterwards in local segmentation, morphological closing operation

is utilized to smooth the binary LSF. Comparing with Gaussian filtering and curvature term, morphological closing operation

will not only facilitate curve inflation more effectively, but also maintain the binary property of LSF. Moreover, the proposed

model is a local segmentation framework, so different speed functions can be designed for different kinds of images. In order to

demonstrate the effectiveness and robustness of the framework, we choose medical and texture images as examples. Meanwhile,

two speed functions are designed respectively. One is for subcortical brain structures segmentation in MR brain images fused

with the non-strict symmetric information, and the other is for texture segmentation combined local entropy and local gradient

operators. Experiments on some synthetic, medical and texture images demonstrate the effectiveness and robustness of the

proposed method in object segmentation.

Keywords: Active contour, image segmentation, medical images, texture images

Image segmentation plays a very important role in com-

puter vision and artificial intelligence. Its goal is to extract

regions of interest (ROI) from a given image. Until now, nu-

merous image segmentation methods have been proposed,

and many efforts have also been made to improve the seg-

mentation performance.

Active contour model (ACM) is one of the most successful

segmentation methods, which has been proved to be an effi-

cient framework for image segmentation[1]. The basic idea

is to minimize a given energy functional according to an

iterative algorithm. The current ACMs can be categorized

into two classes: edge-based ACMs[2−6] and region-based

ACMs[7−18].

Edge-based ACMs utilize image gradient to attract the

contour toward object boundaries, which is usually sensi-

tive to noise and weak edges. Region-based ACMs utilize

global statistical information to identify object boundaries,

and have been proved to have many advantages over edge-

based ACMs, such as insensitivity to image noise, robust-

ness against initial curve location, and better segmentation

performance for images with weak edges or without edges.

Therefore, region-based ACMs are more widely applied to

image segmentation than edge-based ACMs, especially for

images with intensity inhomogeneity[12−18]. In the devel-

Manuscript received January 17, 2012; accepted June 7, 2012Supported by Natural Science Foundation of Shandong Province

(2009ZRB01661), Independent Innovation Foundation of ShandongUniversity, Graduate Independent Innovation Foundation of Shan-dong University, and Research Fund for the Doctoral Program ofHigher Education of China (20120131110062)Recommended by Associate Editor Yi-Jun LIUCitation: Qiang Zheng, En-Qing Dong. Narrow Band Active Con-

tour Model for Local Segmentation of Medical and Texture Images.Acta Automatica Sinica, 2013, 39(1): 21−301. School of Mechanical, Electrical and Information Engineering,

Shandong University at Weihai, Weihai 264209, China

opment process, a large number of classical models are pro-

posed: Chan-Vese (CV) model[8], piecewise constant (PC)

model[9], piecewise smooth (PS) model[9], local binary fit-

ting (LBF) model[12−13] and so on.

In practical applications, local segmentation is often re-

quired to segment the target object, such as putamen, cau-

date nucleus and globus pallidus segmentation in MR brain

images. However, no matter where the initial contour lo-

cates in an image, most region-based ACMs have global seg-

mentation property to segment all objects from the image.

An effective approach to achieve local segmentation is to

reformulate region-based ACMs in a narrow band way. So

far, many methods have been proposed for local segmenta-

tion. According to the kind of level set function (LSF), the

current local segmentation models (LSM) can be divided

into two categories: signed distance function (SDF)-based

LSMs[19−21] and local approximated SDF (LASDF)-based

LSMs[22−26].

In SDF-based LSMs, the LSF is initialized to be an SDF,

and the re-initialization with high computation complex-

ity is required in the evolution. With the increasing iter-

ations, the error caused by re-initialization becomes large,

and the narrow band may become unstable. In LASDF-

based LSMs, a limited set of integers such as {−3,−1, 1, 3}or {−1, 1} is utilized to initialize the LSF, which can lo-

cally approximate the SDF. In LASDF-based LSMs, the

segmentation procedure is generally decomposed into two

parts: data dependent term and curve smoothing term,

where the curve smoothing term is a Gaussian filtering

processing generally. However, it is difficult to determine

how to use the Gaussian filtering to regularize LSF. In

[22], Shi et al. put the Gaussian filtering term and the

data dependent term into two cycles. In the two-cycle

22 Acta Automatica Sinica, 2013, Vol. 39, No. 1

scheme, the segmentation results are determined mainly

by the data dependent term, and the Gaussian filtering

term is only used to smooth the curve. But the two-cycle

scheme does not make good use of the facilitation of curve

smoothing term in curve evolution. Zhang et al.[24] put

the two terms into one cycle, however, the Gaussian fil-

tering term will destroy the property of the limited set of

integers such as the binary property of {−1, 1}, and will

enlarge the narrow band, which may lead to failed local

segmentation.

In this paper, we propose a new narrow band ACM for

local segmentation, in which the binary property of LSF is

the fundamental premise. In the proposed model, we make

three main contributions:

Firstly, we build a new stable and flexible narrow band

scheme based on binary LSF and morphological methods

for local segmentation.

Secondly, since the contour will be initialized as a small

shape inside the target object and inflated afterwards in

local segmentation, morphological closing operation is uti-

lized to smooth the binary LSF, which not only can facili-

tate curve inflating more effectively than Gaussian filtering

and curvature term, but also can retain the binary prop-

erty of the LSF. The binary property of the LSF is neces-

sary for building a stable and flexible narrow band in our

model.

Thirdly, the proposed model is a natural framework, so

the speed function can be chosen arbitrarily for different

requirements, such as gradient, the global statistical infor-

mation based speed function, the local statistical informa-

tion based speed function and other speed functions derived

from ACMs. As applications of our proposed model, the

speed function for medical and texture image segmentation

is proposed in this paper respectively.

It should be pointed out that in all figures except Fig. 11,

white curves represent initial contour while black curves

represent results. In Fig. 11, black curves represent initial

contour while white curves represent results.

The rest of the paper is organized as follows. In Section

1, we review some classical models of SDF-based LSMs and

LASDF-based LSMs. Our proposed narrow band ACM for

local segmentation is presented in Section 2. In Section 3,

we validate the proposed method by various experiments

on synthetic, medical and texture images. This paper is

summarized in Section 4.

1 Background

1.1 SDF-based LSMs

1.1.1 Localizing region-based active contours

Localizing region-based active contours (LR-AC) pro-

posed by Lankton et al.[19] is one of the most popular SDF-

based LSMs. In LR-AC, a natural framework that allows

any region-based segmentation energy to be formulated in

a narrow band way is proposed. Let I(x) : Ω → R be a

given image, and C be a closed curve represented as the ze-

ros level set of SDF, i.e., C = {x|φ(x) = 0}. We use Dirac

function δ(φ(x)) to speicfy the area around the curve C:

δ(φ(x)) =

⎧⎪⎨⎪⎩1, φ(x) = 0,12ε

{1 + cos(πφ(x)

ε)}

, 0 < |φ(x)| ≤ ε,

0, |φ(x)| > ε.

(1)

We now define a characteristic function B(x, y) to mask

local regions:

B(x, y) =

{1, ‖x − y‖ < r,

0, otherwise.(2)

The function B(x, y) will be 1 when the point y is in a circle

of radius r centered at x.

Using δ(φ(x)) and B(x, y), the LR-AC energy functional

in terms of a generic segmentation energy F is defined as

follows:

E =

∫Ωx

δ(φ(x))

∫Ωy

B(x, y) · F (I(y), φ(y))dydx, (3)

where the function F can be uniform modeling (UM) en-

ergy, mean separation (MS) energy or histogram separation

(HS) energy.

1.1.2 Narrow band region-based active contours

Narrow band region-based active contour (NBR-AC)[20]

is a regional energy which is reformulated in a fixed-width

band. Let I(x) : Ω → R be a given image, the closed curve

C is represented as the zeros level set of SDF, i.e., C =

{x|φ(x) = 0}. The curvature based narrow band region

energy can be rewritten as:

E = Eregion1(x) + Eregion2(x). (4)

In (4),

Eregion1(x) =∫Ω

H̃(φ + M)(1 − H̃(φ))(I − kin(x))2dx +∫Ω

H̃(φ)(1 − H̃(φ) − M)(I − kout(x))2dx, (5)

and

Eregion2(x) =∫Ω

H̃(φ + M)(1 − H̃(φ))(I − kin(x))2dx +∫Ω

δ̃(φ))

∫ M

0

(I(x + mnnnφ) − hout(x))2 ×(1 + mκκκφ)dmdx, (6)

where M is a real constant, which is used to control the

width of the narrow band. κκκφ(x) is curvature and nnnφ(x) =

∇φ(x)/|∇φ(x)|. H̃(φ(x)) and δ̃(φ(x)) are approximated by

(7) and (8):

H̃(φ(x)) =1

2

[1 +

2

πarctan(

φ(x)

ε)

], (7)

Qiang ZHENG et al./ Narrow Band Active Contour Model for Local Segmentation of Medical and Texture Images 23

δ̃(φ(x)) =1

π

ε

ε2 + φ(x)2. (8)

In (5) and (6), kin(x) and kout(x) are average intensities

of global interior and exterior regions in the narrow band

around the curve C respectively, and hout(x) is the average

intensity along the outward normal line nnnφ(x) of length M .

1.2 LASDF-based LSMs

1.2.1 Fast two-cycle algorithm

In [22], Shi and Karl proposed a fast two-cycle (FTC) al-

gorithm for real-time tracking, which can approximate level

set based curve evolution without solving partial differential

equations (PDEs). Before we present the FTC algorithm,

we firstly give the function φ(x) which can locally approxi-

mate the SDF:

φ(x) =

⎧⎪⎪⎪⎨⎪⎪⎪⎩3, if x is an exterior point,

1, if x ∈ Lout,

−1, if x ∈ Lin,

−3, if x is an interior point,

(9)

where interior points are the points inside curve C but not

in Lin, exterior points are the points outside curve C but

not in Lout. And the two lists Lout and Lin are given as:

Lout = {x|φ(x) > 0 and ∃y ∈ N4(x) s.t. φ(y) < 0}, (10)

Lin = {x|φ(x) < 0 and ∃y ∈ N4(x) s.t. φ(y) > 0}. (11)

And then, in [22], they define two basic procedures

switch−in(x) and switch−out(x). By applying the

switch−in(x) procedure to points in Lout, the boundary

can be moved outward by one-point width. Similarly, the

procedure switch−out(x) can move the boundary inward

by one-point width.

Based on the definition above, the FTC algorithm can

be rewritten as follows:

1) Initialize the LSF φ(x).

2) Cycle 1: data dependent evolution (for details see

[22]).

3) Cycle 2: smoothing via Gaussian filtering (for details

see [22]).

4) If stopping condition is not satisfied in cycle one, go

to step 2), otherwise, stop the algorithm.

1.2.2 Active contours with selective local or global

segmentation

Selective binary and Gaussian filtering regularized level

set (SB-GFRLS) method[24] is a binary level set based local

segmentation model. Let I(x) denotes a given image defined

on the domain Ω, and C be a closed curve, the SB-GFRLS

method can be summarized as follows:

1) Initialize the LSF φ(x) as

φ(x) =

⎧⎪⎨⎪⎩−ρ, x ∈ Ω0 − ∂Ω0,

0, x ∈ ∂Ω0,

ρ, x ∈ Ω − Ω0,

(12)

where ρ > 0, Ω0 is a subset of the image domain Ω, ∂Ω0 is

the boundary of the subset Ω0.

2) Evolve the LSF according to the formulation below

∂φ

∂t= α · F (I(x)) · |∇φ|. (13)

The function F is a generic segmentation energy, which is

used to stop the contour at boundaries.

3) Let φ(x) = 1 if φ(x) > 0, otherwise, φ(x) = −1.

4) Regularize the LSF with Gaussian filter, i.e., φ(x) =

φ(x) ∗ G, where G is the Gausian filter.

5) Return to step 2) if the evolution has not converged,

otherwise, stop the evolution.

2 The proposed method

2.1 Narrow band ACM

In this section, we propose a new narrow band ACM for

local segmentation. The main idea of the proposed method

consists of four parts:

1) Image preprocessing

In order to improve image quality and utilize more infor-

mation in speed function, image preprocessing is necessary

sometimes, which contains image denoising, image enhance-

ment, image registration, image fusion and so on.

2) Build narrow band

Different from narrow band scheme mentioned above in

Section 1, we build a stable and flexible narrow band based

on binary LSF and morphological operation. Binary LSF

is a fundamental premise in our local segmentation method

and can only take two values 1 and −1 as

φ(x) =

{1, x ∈ Ω0,

−1, x ∈ Ω \ Ω0,(14)

where Ω0 is a subset of the image domain Ω. After ini-

tialized as a binary LSF in Fig. 1 (a), we use morpholog-

ical dilation operation to dilate the binary LSF, and use

morphological erosion operation to erode the binary LSF.

The region between the dilated boundary (i.e., the outer

boundary in Fig. 1 (b)) and eroded boundary (i.e., the in-

ner boundary in Fig. 1 (b)) is just our narrow band. The

narrow band is easy to build and stable to control.

(a) Initialized binary

LSF

(b) Construction of narrow

band

Fig. 1 The initialized binary LSF and the construction of

narrow band

In general, we assume that the radii of the structuring el-

ement in morphological dilation and erosion operations are


equivalent. Now we give the definition of curve evolution

precision (CEP), which is the radius of the structuring ele-

ment in dilation or erosion operation. Therefore, the CEP

in our method can be changed from one to infinity flexi-

bly by the radius of the structuring element. In addition,

we declare that the smaller the CEP is, the smaller the ra-

dius is, the thinner the narrow band becomes, and the more

helpful it is for local segmentation.

It is important for local segmentation whether the CEP

reaches one-point width. Fig. 2 shows its importance in lo-

cal segmentation. When the objects in images are adjacent

very much, only small CEP can satisfy the local segmenta-

tion in Fig. 2 (a).

(a) CEP = 1 (b) CEP = 2

Fig. 2 The effect of CEP

3) Update points in narrow band with a given speed func-

tion

After building the narrow band, we should update the

points in the narrow band with a given speed function.

Because our proposed method is a natural framework, the

speed function can be chosen arbitrarily. A suitable speed

function can be chosen as gradient, the global statistical

information based speed function, the local statistical in-

formation based speed function and other speed functions

derived from ACMs for different requirements.

4) Smooth the curve

Curve smoothing term is an important term for local

segmentation. Good smoothing scheme may facilitate curve

evolution. In the traditional level set methods, curvature

term is usually used to smooth the curve, which is proved

to have a complex computation. In [22] and [24], Gaussian

filtering is used to replace the curvature term to reduce

the computation, but the replacement brings new problems

such as big CEP and so on. Moreover, Gaussian filtering

and curvature term may restrain curve evolution when the

CEP is small.

Under the consideration of the case that the contour

will be initialized as a small shape inside the target object

and inflated afterwards in local segmentation, morphologi-

cal closing operation is utilized to smooth the binary LSF,

which not only can facilitate curve inflating more effectively

than Gaussian filtering and curvature term, but also can

retain the binary property of LSF. The binary property of

LSF is a fundamental premise for building a stable and flex-

ible narrow band, and we should retain the binary property

of LSF in curve evolution.

Due to the equivalency of curvature term and Gaussian

filtering in smoothing curve, Fig. 3 only shows the restrained

effect of the Gaussian filtering in Fig. 3 (a) with small CEP.

When the CEP becomes big in Fig. 3 (b), the restrained

effect will be reductive. In Fig. 3 (c), our proposed method

with morphological closing operation has facilitating effect

to local segmentation.

(a) CEP = 1 withGaussian

filtering

(b) CEP ≥ 2 withGaussian

filtering

(c) CEP = 1 withmorphological

closing operation

Fig. 3 The effect of curve smoothing scheme

From the analysis mentioned above, the procedures of

our proposed method can be summarized as:

1) Image preprocessing according to practical require-

ments.

2) Locate the initial curve with a small shape inside the

target object, and initialize it to be a binary LSF as (14).

3) Dilate and erode the binary LSF with a special radius

sized structuring element to build a narrow band.

4) Update the speed function F (x).

5) For every point in the narrow band, evolve the LSF

with the speed function F (x) according to the following

iteration equation

φn+1 = φn + t · F. (15)

6) Let φ(x) = 1 if φ(x) ≥ 0, otherwise, φ(x) = −1.

7) Smooth the LSF with morphological closing operation.

8) Return to step 3) if evolution has not converged, oth-

erwise, stop the evolution.

2.2 Application to medical images

In this section, we take local segmentation of subcortical

brain structures in MR brain images, and mainly focus on

local segmentation of putamen, globus pallidus and caudate

nucleus. Riklin-Raviv et al.[27] proposed that symmetric in-

formation may facilitate segmentation in the absence of any

prior shape information. However, the MR brain images

are not strictly symmetric, and many studies have demon-

strated the asymmetry of the gray matter structure in the

brain images. In this paper, we propose to solve the asym-

metry problem as follows: firstly, we use affine transforma-

tion to register the original image and the reflected image

globally, and then we use non-rigid registration algorithm,

i.e., active Demons algorithm[28], to register the original im-

age and the reflected image further locally. Therefore, the

two-step image registration can make us take full advantage

of the non-strict symmetric information without reducing or

even eliminating the natural feature in brain image.

The procedures of subcortical brain structures segmen-

tation according to our framework are:



In order to utilize non-strict symmetric information in

MR brain images, we process the images as the following

steps:

a) Reflect the original image I0(x).

b) Register the original image I0(x) and the reflected

image I1(x) using affine transform, whose transformation

matrix is described in (16). We label the registered image

as I2(x).

T =

⎡⎢⎣ Sx cos θ Sx sin θ 0

−Sy sin θ Sy cos θ 0

x y 1

⎤⎥⎦ (16)

c) Register the original image I0(x) and the registered

image I2(x) using active Demons algorithm, in which, the

estimated displacement is given in (17). We label the reg-

istered image as I3(x).

u =(m − f)∇f

|∇f |2 + α2(m − f)2+

(m − f)∇m

|∇m|2 + α2(m − f)2, (17)

where m is the moving image I2(x), f is the static image

I0(x), and α is the normalization factor.

d) Fuse the original image I0(x) and the registered image

I3(x) with maximum fusion as I4(x) = max(I0(x), I3(x)).

e) Roughly estimate the biased field of the fused image

I4(x) with Gaussian filtering, and subtract the biased field

from the fused image to weaken the impact of intensity

inhomogeneity as

I(x) = I4(x) − I4(x) ∗ Gσ. (18)

Therefore, I(x) can be viewed as a roughly approximated

intensity homogeneous image fused with the asymmetric

information in brain image. Fig. 4 shows related results of

the preprocessing. The images in the second row are the

partial enlarged version of the images in the first row. In

active Demons algorithm, the normalization factor α = 1.6,

the Gaussian filter, which is used to regularize the displace-

ment, is 35 × 35 with variance σ = 4.

(a) The original

image I0(x)

(b) The fused image

I4(x)

(c) The image I(x)

after applying (18)

Fig. 4 Image preprocessing results


target object, and initialize it to be a binary LSF as (14).


sized structuring element to build a narrow band.


Because our proposed method is a natural framework, the

speed function can be chosen arbitrarily. In order to sat-

isfy the requirements of MR brain segmentation, especially

for intensity inhomogeneity, we select the local statistical

information based speed function, and give the representa-

tion with binary LSF.

Assume I(x) is the image computed by step a) of image

preprocessing, and C is a closed curve. Firstly, we define

a characteristic function B(x, y) to mask local regions as

(2). And then, we assume that the initialized binary LSF

has value 1 inside curve C, and −1 outside curve C. The

interior and exterior of curve C can be specified as

Hin =φ(x) + 1

2, (19)

Hout =1 − φ(x)

2. (20)

Therefore, the local versions of the means can be defined as

u(x) =

∫Ωy

B(x, y) · Hin(y) · I(y)dy∫Ωy

·Hin(y)dy, (21)

v(x) =

∫Ωy

B(x, y) · Hout(y) · I(y)dy∫Ωy

·Hout(y)dy. (22)

Based on the definition above, the speed function can be

given as

F (x) = (I(x) − v(x))2 − (I(x) − u(x))2. (23)


with the speed function F (x) according to (15).



8) Return to step 3) if the evolution has not converged,

otherwise, stop the evolution.

2.3 Application to texture images

There are many texture image segmentation methods in

literatures[29−33], and the key step for texture image seg-

mentation is to define a suitable texture descriptor. In this

section, we propose a new speed function with local entropy

and local gradient operator, which are complementary in

texture segmentation.

The local segmentation procedures of texture images ac-

cording to our framework are:


In this section, we use local entropy and local gradient

operator to build the new texture descriptors.

Local entropy is a texture descriptor, which is defined as

Ie = −L−1∑i=0

p(zi) log2 p(zi), (24)

where p(zi) is the histogram of the local region, and L is

the number of gray series.


Local gradient is another texture descriptor, which is de-

fined as

Ig =

r∑z=−r

|∇I(x + τ)|2 (25)

Fig. 5 shows the related results. The images in Fig. 5 (b)

represented by local entropy operator are clear, but they

are easily influenced by backgrounds. This case may lead

to over segmentation of texture images. The images in

Fig. 5 (c) represented by local gradient are not clear enough,

but the backgrounds will not influence the object segmen-

tation. This case may lead to insufficient segmentation. If

we combine the local entropy and the local gradient oper-

ator, the two texture descriptors may be complementary,

and will get better segmentation.


target object, and initialize it to be binary LSF as (14).

(a) The original

image

(b) Local entropy

operator

(c) Local gradient

operator

Fig. 5 Image preprocessing results


sized structuring element to create a narrow band.


As same as the application to medical image, we select

the local statistical information based speed function for

texture segmentation. For a point x in the corresponding

narrow band, the speed function is

Ftexture(x) =

λ1Fentropy + λ2Fgradient =

λ1((Ie(x) − fe2(x))2 − (Ie(x) − fe1(x))2) +

λ2((Ig(x) − fg2(x))2 − (Ig(x) − fg1(x))2), (26)

where Ie(x) and Ig(x) are computed by (24) and (25). And

fe1(x) and fe2(x) are calculated by (21) and (22), in which

the image I(y) should be replaced with Ie(y), fg1(x) and

fg2(x) are also calculated by (21) and (22), in which the im-

age I(y) should be replaced with Ig(y). λ1 and λ2 are used

to balance the Eentropy and Egradient. In general, Egradient

is about an order of magnitude higher than Eentropy, so we

fix λ1 = 1, and adjust λ2 in interval [0, 1] for balance.


with the speed function F (x) according to iteration equa-

tion (15).



8) Return to step (3) if the evolution of the level set has

not converged, otherwise, stop the evolution.

3 Experimental results

In this section, we perform some experiments to evaluate

the proposed method. The simulations are implemented

in Matlab 2010a using PC with a 2.99GHz Intel (R) Core

(TM) 2 Duo CPU. It should be pointed out that in all

figures except Fig. 11, white curves represent initial con-

tour while black curves represent results. In Fig. 11, black

curves represent initial contour while white curves represent

results.

Firstly, we take putamen segmentation as an example to

show how the CEP, curve smoothing scheme and the non-

strict symmetric information influence the local segmenta-

tion. Putamen segmentation is a classical local segmenta-

tion example. In MR brain images, putamen segmentation

is deeply affected by adjacent structures such as claustrum,

insula and so on. Especially, there is only a small amount

of white matter between the lateral aspect of the putamen

and the claustrum, and the region between them may be

one-pixel width in MR brain images.

Fig. 6 shows the influence of CEP on local segmentation.

In Fig. 6 (a)∼ (d), the radii of neighborhood B(x, y) are 2,

the radii of structuring element used for morphological clos-

ing operation are 9, 2, 2 and 2 respectively. Fig. 6 shows

that putamen segmentation requires small CEP which is

equal to 1.

(a) CEP = 1 (b) CEP = 2

(c) CEP = 3 (d) CEP = 4

Fig. 6 The influence of CEP on local segmentation

Fig. 7 shows the influence of curve smoothing scheme


(morphological closing operation) on local segmentation. In

Fig. 7 (a)∼ (d), the CEPs are 1, and the radii of neighbor-

hood B(x, y) are 2, 5, 8, and 2, respectively. In order to

validate the facilitating effect of morphological closing oper-

ation to local segmentation, in Fig. 7(a)∼ (c), we do not use

any curve smoothing scheme, and in Fig. 7 (d), we use mor-

phological closing operation, in which the radius of structur-

ing element is 9. Comparing Fig. 7 (a)∼ (c) and Fig. 7 (d),

we can see that the facilitating effect of our morphological

closing operation is obvious.

(a) No curve smoothing

scheme and r = 2

(b) No curve smoothing

scheme and r = 5

(c) No curve smoothing

scheme and r = 8

(d) Morphological closing

operation and r = 2

Fig. 7 The influence of curve smoothing scheme

(morphological closing operation) on local segmentation

Fig. 8 shows the influence of curve smoothing scheme

(Gaussian filtering) on local segmentation, which is used to

validate the restrained effect of Gaussian filtering to local

segmentation. In Fig. 8 (a)∼ (d), the Gaussian filter is 5×5,

and variance is 1.0. The radii of neighborhood B(x, y) are 5.

When CEP is small like 1 or 2, Fig. 8 (a) and Fig. 8 (b) show

obvious restrained effect to local segmentation. When CEP

becomes big like 3 or 4, the restrained effect in Fig. 8 (c) and

Fig. 8 (d) becomes small, but the local segmentation cannot

be achieved because of big CEP, and the claustrum and

insula have influenced the local segmentation of putamen.

Fig. 9 shows the influence of non-strict symmetric infor-

mation on local segmentation of subcortical brain structures

in MR brain images. In Fig. 9, the radii of neighborhood

B(x, y) are 2, the radii of structuring element used for mor-

phological closing operation are 9, 3 and 9 respectively in

the first, second and third column of Fig. 9. Comparing the

first row of Fig. 9 without using the non-strict symmetric

information with the second row of Fig. 9 using the non-

strict symmetric information, we can see that the non-strict

symmetric information can facilitate local segmentation of

subcortical brain structures in MR brain images.

(a) CEP = 1 (b) CEP = 2

(c) CEP = 3 (d) CEP = 4

Fig. 8 The influence of curve smoothing scheme (Gaussian

filtering) on local segmentation

(a) Putamen

segmentation

(b) Caudate nucleus

segmentation

(c) Globus pallidus

segmentation

Fig. 9 The influence of the non-strict symmetric information

on local segmentation

Secondly, taking putamen segmentation as an example,

we give experimental results of LR-AC, NBR-AC, FTC and

SB-GFRLS in Fig. 10 (a)∼ (d). The result of our proposed

method is given in Fig. 10 (e). In order to ensure a fair

comparability with our proposed method, the five methods

are all performed on images computed by (18) and fused

with the non-strict symmetric information.

Fig. 10 (a) presents the result of LR-AC method, in

which, the narrow band is defined by the Dirac function

δ(φ(x)). For every point x selected by δ(φ(x)), B(x, y) is

masked to ensure that F operates only on local image in-

formation about x. However, with the increasing iterations

and errors caused by re-initialization of SDF, the narrow

band will become unstable, and the curve evolution will be

enforced to stop for one of the following two reasons: 1)

No points can be sought in the narrow band; 2) Only a few

points can be sought in the narrow band, but the points

will be smoothed out by curvature term in curve evolution.

Fig. 10 (b) presents the result of NBR-AC method. NBR-

AC only uses the information in the fixed width narrow

band. Thick narrow band can make use of more infor-

mation of images, but cannot achieve local segmentation


better. Conversely, thin narrow band can achieve local seg-

mentation better, but the information in the narrow band

is not enough to segment images especially for intensity in-

homogeneity. For example, when M equals to 1, hout(x) is

just the intensity value of the current point x, kin(x) and

kout(x) are the average intensities in the corresponding one-

pixel width narrow band. In Fig. 10 (b), we let M equal to

2 for a balance, but still cannot get a satisfying result.

Fig. 10 (c) presents the result of FTC method. In FTC al-

gorithm, the narrow band is controlled by the two data lists

Lout and Lin, and the two data lists Lout and Lin are limited

to one-pixel width. However, by applying switch−in(x) and

switch−out(x) procedure, the contour can only be moved

by one pixel, which is inflexible in the curve evolution. In

addition, the FTC algorithm is a two-cycle scheme, in which

the segmentation results are mainly determined by the data

dependent term, and the Gaussian filtering term is only

used to smooth the curve. Therefore, in Fig. 10 (c), though

the one-pixel width CEP is small enough to segment puta-

men, the two-cycle scheme does not make good use of the

facilitation of curve smoothing term in curve evolution, and

lead to an undesirable result.

(a) LR-AC (b) NBR-AC (c) FTC

(d) SB-GFRLS (e) Proposed

Fig. 10 Experimental results with different models

Fig. 10 (d) presents the result of SB-GFRLS method. In

the SB-GFRLS method, the key to guarantee the local seg-

mentation property is step 3) in Section 1.2.2, and the nar-

row band is defined by gradient function |∇φ(x)| of bi-

nary LSF. However, the Gaussian filtering in SB-GFRLS

destroys the binary property of LSF, and the SB-GFRLS

cannot obtain one-pixel width narrow band because of the

Gaussian filtering procedure.

Fig. 10 (e) presents the result of the proposed method.

In Fig. 10 (e), the CEP is 1, the radius of neighborhood

B(x, y) is 2, and the radius of structuring element used for

morphological closing operation is 9. It is obvious that the

proposed method is more effective than LR-AC, NBR-AC,

FTC and SB-GFRLS in local segmentation.

Finally, we perform experiments on texture images, and

we only compare the experiments of different texture de-

scriptors mentioned above using our proposed framework.

Fig. 11 shows related results for texture segmentation. In

the first row of Fig. 11, λ1=1, λ2=0.5. Local entropy op-

erator is 5 × 5, and local gradient operator is 7 × 7. The

CEP is 2. The radius of the neighborhood B(x, y) is 45.

The radius of structuring element used for morphological

closing operation is 5. In the second row of Fig. 11, λ1=1,

λ2=1. Other parameters are the same as the first row of

Fig. 11. In the third row of Fig. 11, the radius of the neigh-

borhood B(x, y) is 15, and the radius of structuring element

used for morphological closing operation is 7. Other param-

eters are the same as the first row of Fig. 11. The results in

Fig. 11 (a) show the over-segmentation with local entropy,

but the results in Fig. 11 (b) show the insufficient segmen-

tation with local gradient. By combining local entropy and

local gradient operator in Fig. 11 (c), the two texture de-

scriptors can be complementary to segmentation, and we

can get successful local segmentation of texture images.

(a) Local entropy

Operator

(b) Local gradient

operator

(c) Combined local

operator

Fig. 11 Texture segmentation

4 Conclusions

In this paper, we propose a narrow band active contour

for local segmentation. In this model, we build a new stable

and flexible narrow band based on binary LSF and mor-

phological dilation and erosion operation, and use morpho-

logical closing operation for curve smoothing scheme. In

addition, our model is a natural framework, so a suitable

speed function can be arbitrarily selected for different re-

quirements. Applying the proposed model to medical and

texture image segmentation, the corresponding speed func-

tions are proposed in this paper respectively. Experiments

on some synthetic, medical and texture images demonstrate

the effectiveness and robustness of the proposed method in

local segmentation.

As future work, we would like to extend our method to

3D segmentation combining with 3D registration for med-

ical images, in which case, other than the non-strict sym-

metric information in one slice, we can further utilize the

information in the neighbor slices. In the future work, we


will focus on two aspects for 3D segmentation: 1) exten-

sion of 2D ACMs to 3D segmentation; 2) 3D registration

and fusion of the non-strict symmetric information in brain

images.

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Qiang ZHENG Ph. D. candidate at theSchool of Mechanical, Electrical and Infor-mation Engineering, Shandong Universityat Weihai. His current research interest issignal processing with applications in MRIimage processing.E-mail: [email protected]

En-Qing DONG Professor at theSchool of Mechanical, Electrical and Infor-mation Engineering, Shandong Universityat Weihai. His current research interestsare signal processing with applications inwireless sensor networks and MRI imageprocessing. Corresponding author of thispaper. E-mail: [email protected]

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