narrow band active contour model for local segmentation ...narrow band is built, and the curve...
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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
24 Acta Automatica Sinica, 2013, Vol. 39, No. 1
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:
Qiang ZHENG et al./ Narrow Band Active Contour Model for Local Segmentation of Medical and Texture Images 25
1) Image preprocessing
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
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).
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)
5) For every point in the narrow band, evolve the LSF
with the speed function F (x) according to (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 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:
1) Image preprocessing
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.
26 Acta Automatica Sinica, 2013, Vol. 39, No. 1
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.
2) Locate the initial curve with a small shape inside the
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
3) Dilate and erode the binary LSF with a special radius
sized structuring element to create a narrow band.
4) Update the speed function F (x).
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.
5) For every point in the narrow band, evolve the LSF
with the speed function F (x) according to iteration equa-
tion (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 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
Qiang ZHENG et al./ Narrow Band Active Contour Model for Local Segmentation of Medical and Texture Images 27
(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
28 Acta Automatica Sinica, 2013, Vol. 39, No. 1
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
Qiang ZHENG et al./ Narrow Band Active Contour Model for Local Segmentation of Medical and Texture Images 29
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]