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Biomedical Signal Processing and Control 52 (2019) 120–127

Contents lists available at ScienceDirect

Biomedical Signal Processing and Control

journa l homepage: www.e lsev ier .com/ locate /bspc

ullback-Leibler distance and graph cuts based active contourodel for local segmentation

enyan Sun a,b, Enqing Dong a,∗

School of Mechanical, Electrical and Information Engineering, Shandong University (Weihai), Weihai 264209, ChinaSchool of Information Engineering, Shandong Youth University of Political Science, Jinan 250103, China

r t i c l e i n f o

rticle history:eceived 19 June 2018eceived in revised form 20 January 2019ccepted 6 April 2019

eywords:

a b s t r a c t

Graph cuts based active contour model can obtain the global optimal solution and run faster. To achieverobust local segmentation of inhomogeneous images and improve operation efficiency, a modifiedKullback-Leibler distance and graph cuts based active contour (KLD-GCBAC) model in the iterative narrowband frame is proposed in this paper. The dynamic narrow band is constructed between the morpholog-ical erosion of evolving curve and the preset outer boundary. In the boundary term of discrete energy

ctive contour modelraph cuts

mage segmentationullback-Leibler distance

formulation, an adaptive coefficient is designed to adjust the weights of edges connecting adjacent pix-els. And the Kullback-Leibler distance between the inner and outer local neighborhoods is introduced tothe region term as the weight of n-links connecting pixels with terminal nodes. Experimental results onsynthetic and medical images with intensity inhomogeneity show that the proposed model can make

f the

full use of local features o

. Introduction

Active contour model (ACM) has been proved to be an effec-ive image segmentation method and widely used, which can getlosed and smooth boundary through the evolution of an initialontour using energy minimization theory. The desired segmenta-ion result is determined by the optimal solution of minimizing thenergy functional which is used to describe the contour and its evo-ution. The total energy functional is generally composed of internalnd external energy, which can include the length, area or curva-ure of the evolving contour and the mean, variance or gradient ofhe image intensity. According to whether the energy functionalontains free parameters, ACMs are divided into parametric mod-ls [1,2] and geometric models [3–6]. After the Snake model [1]roposed in 1985, lots of classic and modified models [7–9] havemerged, which has greatly promoted the development of ACM. Byeans of variation principle and gradient descent flow, the solu-

ion to the minimum of energy functional can be solved. But whenhe energy is not convex, the solution may not be global optimal,nd thus cannot get correct segmentation result.

Graph cuts (GC) [10] is a combinatorial optimization algorithm

or solving the problem of energy minimization, which has beenpplied in image segmentation [11], image matting [12], stereoision [13] and so on. On the basis of graph theory, an image is

∗ Corresponding author.E-mail address: enqdong@sdu.edu.cn (E. Dong).

ttps://doi.org/10.1016/j.bspc.2019.04.008746-8094/© 2019 Published by Elsevier Ltd.

image and achieve local segmentation more efficiently.© 2019 Published by Elsevier Ltd.

mapped to a weighted graph and interactive operations of the userare needed to specify some seed nodes as source node s and sinknode t corresponding to foreground or background respectively,which can be a single pixel or a collection of some pixels. UseG=(V, E) to represent the undirected graph mapping to the image,V = {v} ∪ {s, t} to represent all nodes in G, and E = {e} ∪ {{s, v} , {v, t}}to denote all edges connecting two nodes in G, where {v} is thecollection of pixels to be classified, {e} denotes all edges connect-ing adjacent nodes in the neighborhood system, called n-links, and{{s, v} , {v, t}} represents the edges connecting any node v with thesource node s and sink node t, called t-links. Each edge is assigneda non-negative weight.

Image segmentation can be seemed as a problem of binary label-ing via GC, each node in G is set a label indicating whether it belongsto the foreground or background. Any cut of the graph can divideall pixels into two categories, and the sum of weights of all cutedges is called the cost of the cut. The cut with the minimumcost is the optimal segmentation result, which is also equivalentto the maximum flow. At present, the commonly used algorithmsto achieve max-flow/min-cut mainly include Goldberg-Tarjan [14]and Ford-Fulkerson [15]. Then image segmentation is consideredas minimizing the cost function. The prior knowledge, grayscale,and statistical information of the image can be used to define dataterm and smooth term of the energy, which correspond to regional

constraint and boundary constraint, respectively.

ACM and GC are main methods of image segmentation and haveachieved varying degrees of development. In recent years, GC iscombined with ACM to overcome local minimum of traditional

rocess

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W. Sun, E. Dong / Biomedical Signal P

CM, obtain global optimal solution of the energy function, andmprove the operating efficiency, which has attracted extensivettention and become a research direction of image segmenta-ion method. Several typical ACM models have been discretizednd optimized globally using graph cuts. Boykov and Kolmogorov16] used GC to find the global minimum of the energy functionf geodesic active contour (GAC) model [3], which mainly useshe gradient of image and has the risk of falling into weak edges.hen some global or local region-based ACMs [18–20] via GC wereroposed to improve the performance. Different from construct-

ng global graph, Xu et al. [21] proposed a graph cuts based activeontour (GCBAC) model, and then the framework to find the globalinimum within the contour neighborhood was introduced. And

ao [22] generalized the GCBAC model and proposed three algo-ithms based on iterative narrowband and GC to optimize the GACith region forces (GACWRF) model for interactive object segmen-

ation. In Ref. [23], global or local segmentation can be implementedy constructing different network graphs, but the proposed method

s not applicable for inhomogeneous images for making use oflobal intensity information. To reduce the effect of the balanceoefficient between edge term and data term in additive energyunctional, some multiplicative GC based ACMs [24–26] were pro-osed to achieve local segmentation of inhomogeneous images,hich can get better performance than additive models, but the

tability and operational efficiency need to be improved.Kullback-Leibler (KL) distance [27], also called relative entropy,

s a metric to measure the difference between two probability dis-ributions in the same event space. The closer two distributionsre, the smaller the KL distance is. This measure plays an impor-ant role in information theory, and it has been proved that KListance can be introduced to the energy term and used to objectracking [28,29], image segmentation [30–32] and pattern recogni-ion [33]. In Ref. [30], Zheng et al. proposed an improved CV modelsing KL distances as the coefficients of internal and external ener-ies, which can automatically adjust the parameters and get highobustness and efficiency. Cheng et al. [31] also proposed a region-ased multi-phase level set method utilizing the between-clusterL distance to formulate the energy function.

To achieve robust local segmentation of inhomogeneous imagesfficiently, a KL distance and graph cuts based active contour (KLD-CBAC) model is proposed in this paper, which constructs theetwork graph in an iterative narrowband framework, and designshe weights of n-links and t-links using local mean and statisticalnformation.

The rest of this paper is organized as follows: Section 2 presentseveral classic active contour models based on GC. Section 3resents the proposed KLD-GCBAC model in detail. Section 4 takesxperiments to validate the performance of KLD-GCBAC model, andhe paper is summarized in Section 5.

. Related work

.1. Graph cut based active contour without edges

In Ref. [19], a graph cut based Chan-Vese [4] model with relaxedomogeneity constraint was proposed, we name it as GCBCV, inhich the discrete energy formulation of was presented as

= �∑p,q ∈ ek

ωk(xp

(1 − xq

)+ xq

(1 − xp

))+

∑p

∣∣im (p) − mi (p)∣∣2xp

+∑∣∣im (p) − m (p)

∣∣2 (1 − x

)(1)

p

o p

here, im is the image, p denotes any pixel in the image with ainary variable xp, im (p) is the intensity of p, mi(p) and mo(p) are

ing and Control 52 (2019) 120–127 121

the mean intensity in the neighborhood W of the pixel p inside andoutside the contour, respectively, which are defined as

mi(p) =∑

p ∈ Wim(p)xp∑pxp

(2)

mo(p) =∑

p ∈ Wim(p)(1 − xp)∑p(1 − xp)

(3)

In Eq. (1), the first sum is the discrete representation of thelength of the evolving contour, � is the balance coefficient of theedge item, ek represents the edge connecting nodes vp and vq in the

8-neighborhood system, and ωk = ı2��k|ek| is the capacity of the edge

ek. In the construction of the graph, the weights of edges connect-ing each pixel p with terminal node S or T are assigned according

to the difference of∣∣im (p) − mi (p)

∣∣2and

∣∣im (p) − mo(p)∣∣2

.

2.2. GCBAC

The GCBAC [21] model regards the ideal segmentation curveas a global optimal solution of the width-known contour neigh-borhood (CN), which is derived from the morphological expansionof initial contour. The inner boundary of CN serves as the sourcepoint s, and the outer boundary corresponds to the sink point t. Thepixels within the CN are mapped into a graph. The multi-sourcemulti-sink problem is converted to single-source single-sink prob-lem, and the graph is cut using the maximum flow/minimum cutalgorithm. By continuously updating the CN and finding the globaloptimal solution within the CN until the algorithm converges, thefinal segmentation result is obtained.

GCBAC is proved to converge after a finite number of iterationsor oscillate back and forth between several cuts with same capacity.In the construction of network graph, GCBAC requires high connec-tivity and edge weight settings for the nodes. The cost function ofGCBAC has not internal energy, and the weight of edge connectingadjacent nodes is assigned as follows:

c (i, j) = (g (i, j) + g(j, i))6 (4)

where g (i, j) = exp(−gradij(i)/maxk(gradij (k))), and gradij (k) is theintensity gradient at location k in the direction of i→j.

2.3. IINBBGC method

In Ref. [22], an improved iterative narrow band based graph cuts(IINBBGC) method to solve the minimization of the GACWRF modelwas proposed, which provides the general framework of iterativegraph cuts based active contour. In IINBBGC method, an iterativenarrowband Rb around the evolving curve is obtained by morpho-logical expansion. The pixels inside Rb are regarded as the nodes ofgraph G, and the nodes with label xp = 1 and xp = 0 correspond to thesource s and sink t, respectively. The weights of n-links connectingadjacent nodes are calculated using Eq. (5), and the weights of t-links of nodes on the inner and outer boundaries are set to infinity,and the weights of other t-links are computed using Eqs. (6) and (7)respectively.

wpq = ωpq

1 + ˇ∣∣I (p) − I(q)

∣∣ (5)

wsp =∣∣Cb (p) − I(p)

∣∣ (6)

wpt =∣∣Cf (p) − I(p)

∣∣ (7)

where I is the image, I (p) and I(q) are intensity values of p and qrespectively, and ̌ > 0 is a weighted coefficient of the differencebetween I (p) and I(q). While ωpq is the weight of vector in the neigh-borhood system, Cb (p) and Cf (p) are the means of inner and outer

122 W. Sun, E. Dong / Biomedical Signal Proces

rsa

w

w

3

3

A{

wEr

mia

E )| · Kp

wIt

8

oTs|t

amta

K

wpf

s

�

Fig. 1. The illustration of 4-neighborhood and 8-neighborhood system.

egions of the closed curve C, respectively. If the probability den-ity functions hf (I(p)) and hb (I(p)) of the inner and outer regionsre used, the weights of t-links also can be assigned as

sp = −log (hb (I(p))) (8)

pt = −log(hf (I(p))

)(9)

. The proposed model

.1. The discrete formulation

From Refs. [24], the general formulation of additive GC basedCMs in a narrow band framework can be written as follows:

E = Eb (p, q) + Er (p)

p, q ∈ RNB(10)

here RNB is the iterative narrow band, p, q indicate pixels in RNB,b (p, q) and Er (p) are the discrete GC formulations of boundary andegion forces respectively.

Similar to the discrete representation of GAC in IINBBGCethod, the term Eb (p, q) is used to measure the cost of assign-

ng different labels to adjacent pixels p and q, which can be defineds follows:

b (p, q) =∑

p,q ∈ RNB

∑p ∈ N(q)

ωpq(xp

(1 − xq

)+ xq

(1 − xp

))e−|I(p)−I(q

here xp is the binary label of pixel p, I is the image, I (p) and(q) are the intensity values of pixels p and q respectively, N ishe neighborhood system which is generally 4-neighborhood or

-neighborhood, ωpq = ı2��pq2|epq| , ı is the mesh size,

∣∣epq∣∣ is the length

f edge vector epq, ��pq is the angle between adjacent vectors.he illustration of 4-neighborhood and 8-neighborhood systems ishown in Fig. 1. If ı is set to 1 unit, for 4-neighborhood, ��pq = �/2,e1| = |e2| = 1, ω1 = ω2 = �

4 , and for 8-neighborhood, ��pq = �/4,hen |e1| = |e3| = 1, |e2| = |e4| =

√2, ω1 = ω3 = �

8 , ω2 = ω4 = �8√

2.

The coefficient Kpq in Eq. (11) is an adaptive adjustment used todjust the boundary term in different cases. It is assumed that theore similar p and q are, the larger the weight of edge connecting

hem should be, otherwise the weight is smaller. So Kpq is designeds follows:

pq = e1+sign(s(p))sign(s(q)) · �pq (12)

here sign(·) is the symbolic function, s(·) and �pq are the signedressure function and constraint variable respectively defined as

ollows

(p) = I (p) − fs (p) + ft(p)(13)

2

pq ={min (Lst, Lts) , sign (s (p)) /= sign (s (q))

max (Lss, Ltt) , sign (s (p)) = sign (s (q))(14)

sing and Control 52 (2019) 120–127

q(11)

In Eq. (13), ft(p) and fs (p) are local means of the interior andexterior neighborhoods of pixel p respectively, calculated usingEqs. (15) and (16) in which K� is a Gaussian kernel filter with thevariance of �, �(p) is a binary signed distance function to the evolv-ing curve, H� is a Heaviside function with parameter �, and * is aconvolution operation.

ft (p) = K� (p) *[Hε (�(p)) I(p)]K� (p) *Hε (�(p))

(15)

fs (p) = K� (p) * [1 − Hε (�(p)) I(p)]K� (p) * [1 − Hε (� (p))]

(16)

In Eq. (14), Lst and Lts represent two cost functions of assigningdifferent labels for pixels {p, q} respectively, such as {xp = 0, xq =1} and {xp = 1, xq = 0}, Lss and Ltt indicate two cost functions ofassigning same labels for pixels {p, q}, such as {xp = 0, xq = 0} and{xp = 1, xq = 1} for {p, q} respectively, which are defined as follows:

Lst =∣∣(I (p) − fs(p))2 − (I (q) − ft(q))2

∣∣ (17)

Lts =∣∣(I (p) − ft(p))2 − (I (q) − fs(q))2

∣∣ (18)

Lss = (I (p) − fs(p))2 + (I (q) − fs(q))2 (19)

Ltt = (I (p) − ft(p))2 + (I (q) − ft(q))2 (20)

Based on the KL distance of the inner and outer neighborhoods,the discrete formulation of region term Er (p) used to measure thecost of assigning label to pixel p in a narrow band graph is definedas follows:

Er (p) =∑p ∈ RNB

di (p) log(di(p)do(p)

)xp

+∑p ∈ RNB

do (p) log(do (p)di (p)

)(1 − xp) (21)

where di (p) and do (p) are the probability distribution functionsof the inner and outer neighborhoods of pixel p respectively.Assuming that the intensity of local region obeys the Gaussiandistribution, di (p) and do (p) can be expressed as follows:

di (p) = 1√2��i(p)

exp

(− (I (p) − ft(p))2

2�2i

(p)

)(22)

do (p) = 1√2��o(p)

exp

(− (I (p) − fs(p))2

2�2o (p)

)(23)

where �i(p) and �o(p) corresponding to the standard deviations ofthe inner and outer neighborhoods respectively are calculated asfollows:

�2i (p) =

∫k�(y − p)(I (y) − ft(p))2Hε (�(y))dy∫

k�(y − p)Hε (�(y))dy(24)

�2o (p) =

∫k�(y − p)(I (y) − fs(p))2 (1 − Hε (�(y)))dy∫

k�(y − p) (1 − Hε (�(y)))dy(25)

3.2. The construction of the narrow band graph

For local segmentation, a narrow band graph should be con-structed and the narrow band should contain the desired boundary.The construction of the network graph G is shown in Fig. 2. The redcurve in Fig. 2 is the evolving curve C, the inner green curve Cin isobtained using morphological erosion, and the outer green Cout is

near the image boundary. The region between Cin and Cout is thenarrow band RNB. Each pixel in the graph G is assigned a binarylabel. The pixels outside Cout with label xp = 0 are regarded as back-ground (¨B)̈ corresponding to the source node set S, and the pixels

W. Sun, E. Dong / Biomedical Signal Process

Fig. 2. The construction of the network graph.

Table 1The corresponding relationship of the graph.

S/T xp (0/1) B/O

it

tbodns

w

w

3m

m

(

(

(

(segmentation results with highest accuracy. For case 1, case 2 and

S 0 BT 1 O

nside Cin with xp = 1 are regarded as object (¨O)̈ corresponding tohe sink set T. The corresponding relationship is shown in Table 1.

Using the 8-neighborhood system of the nodes in the graph G,he weights of n-links connecting adjacent nodes are set as theoundary term Eb (p, q). The weights of t-links connecting the nodesn curve Cin and Cout with terminal nodes are set to infinity, anderived from region term Er (p), the weights of others t-links con-ecting the pixels in the narrow band with terminal set S and Thould be assigned as follows:

pt = di (p) log(di(p)do(p)

)(26)

sp = do (p) log(do(p)di(p)

)(27)

.3. Implementation steps of the proposed local segmentationodel

The main steps of the proposed KLD-GCBAC model for local seg-entation can be summarized as follows:

1) Place initial closed curve C inside the object to be segmented.The binary label xp = 1 if the pixel is inside C, otherwise xp = 0.The boundary of the image or any closed curve containing theobject boundary is selected as the fixed outer boundary Cout ofthe narrow band.

2) Carry out the morphological erosion of curve C to obtain theinner boundary Cin of the narrowband. The region between Cinand Cout is taken as the narrow band, as shown in Fig. 2.

3) Calculate ft(p), fs (p) using Eqs. (15),(16) and �2i

(p), �2o (p) using

Eqs. (24),(25), respectively.

4) Map the image to a network graph according to previously

methods described in Section 3.2, and assign weights for n-linksand t-links.

ing and Control 52 (2019) 120–127 123

(5) Use the max-flow/min-cut algorithm [15] to realize the mini-mum cut of the network graph, and update the labels of pixelsin the narrowband to obtain current segmentation result.

(6) Smooth the curve using morphological closing operation.(7) Repeat steps (2)-(6) until convergence.

4. Experimental results

We apply the proposed KLD-GCBAC model on several syntheticand medical images to validate its local segmentation effective-ness, comparing with GCBAC [21], GCBCV [19], IINBBGC [22] andMLM-GCACM [26] models. For GCBAC model, the size of radius ofdisk-type structure element for morphological expansion opera-tions is 2. For GCBCV model, the size of rectangular window is31*31, � = 0.2 ∗ 255 ∗ 255. For IINBBGC model, the weights of t-links are set using Eqs. (6),(7) and � is generally set to 0.1. Andfor MLM-GCACM model, the standard deviation � of Gaussian fil-ter is 10. Other parameters need to be set respectively for differentimages. All models use 8-neighborhood system, and these experi-ments are implemented using Matlab R2015b on a PC of 3.4 GHzIntel (R) Core (TM) CPU. In all experimental results, the greencurves are initial contours and the red curves are final segmentationresults.

Using the same initial contour, the comparison of local segmen-tation results using those five models on two single-object images,two multi-object synthetic images and four medical images areshown in Figs. 3–5, respectively. It can be seen that, for the weightsof edges are inversely proportional to the gradient of the image,GCBAC can easily capture the edges with large gradient, but fallsinto the weak boundary. GCBCV model uses neighborhood win-dow to extract local gray information of the image and has certainability to handle inhomogeneous image, but the network graphis constructed based on the entire image, so GCBCV model withglobal segmentation characteristics cannot realize local segmenta-tion from multi-object images. IINBBGC and MLM-GCACM based oniterative narrowband and graph cuts can obtain local segmentationresults, however, the weights of t-links in IINBBGC model cannotdescribe the local features of the image well, which makes somesegmentation results unsatisfactory; and the narrow band in MLM-GCACM model is constructed between the evolving contour and theouter boundary, so the inner boundary of the ring object cannot beextracted. The proposed KLD-GCBAC model making full use of localgray and statistical information of the image to design the weightsof n-links and t-links can obtain good local segmentation results,especially for medical images with complex background and weakedges in Fig. 5.

There is a common indicator to measure the segmentation accu-racy, i.e., the Jaccard similarity (JS), which is defined as follows:

JS =∣∣Vgold ∩ Valgorithm

∣∣∣∣Vgold ∪ Valgorithm∣∣ (28)

where Vgold and Valgorithm indicate the manually segmented “goldstandard” by experts and actual segmentation result respectively,and |·| is the operator for calculating the number of pixels withinthe conditional region. Then, the bigger JS is, the more accurate thesegmentation result is. The comparison of JS coefficients between“gold standards” and segmentation results in Fig. 5 is shown inTable 2, and the comparison of required iterations number and run-ning time is shown in Table 3, in which case 1 to case 4 correspondto from the first to fourth image in Fig. 5, respectively. It can beseen that except for case 4, the proposed KLD-GCBAC has better

case 4, the iterations number and running time required of GCBACis the least, which is mainly due to the stopping of curve evolutionin advance resulting in rapid convergence. For the iterative con-

124 W. Sun, E. Dong / Biomedical Signal Processing and Control 52 (2019) 120–127

Fig. 3. Comparison of segmentation results of single-object images. (a) GCBAC; (b) GCBCV; (c) IINBBGC; (d) MLM-GCACM; (e) KLD-GCBAC.

Fig. 4. Comparison of local segmentation results of multi-object images.

Table 2Comparison of JS coefficients between “gold standards” and segmentation resultsfor experiments in Fig. 5.

GCBAC GCBCV IINBBGC MLM-GCACM KLD-GCBAC

case 1 0.0578 0.3658 0.1374 0.8658 0.9065case 2 0.2588 0.6408 0.0514 0.8489 0.8645case 3 0.1444 0.9373 0.9252 0.9469 0.9505case 4 0.0202 0.0084 0.7532 0.9861 0.9763

Table 3Comparison of required iterations number/ running time (s) for experiments in Fig. 5.

GCBAC GCBCV IINBBGC MLM-GCACM KLD-GCBAC

case 1 1 / 0.41 14 / 1.26 40 / 4.11 8 / 1.37 6 / 1.02case 2 1 / 0.28 4 / 0.64 38 / 4.19 8 / 1.42 5 / 0.94

sIndiGo

case 3 12 / 1.33 9 / 1.02 136 / 45.71 17 / 2.94 2 / 0.87case 4 1 / 0.33 14 / 1.25 112 / 23.05 17 / 2.75 2 / 0.57

truction of narrowband using morphological dilation operations,INBBGC requires the largest iterations number and the longest run-ing time. The segmentation accuracy of MLM-GCACM is not much

ifferent from that of KLD-GCBAC, but the operating efficiency

s lower than that of KLD-GCBAC. Therefore, the proposed MLM-CACM can achieve better segmentation results and has higherperating efficiency.

(a) GCBAC; (b) GCBCV; (c) IINBBGC; (d) MLM-GCACM; (e) KLD-GCBAC.

5. Discussion

In the proposed KLD-GCBAC model, the standard deviation �of Gaussian kernel function is an important parameter. Since theconvolution has a certain smoothing effect, its value determinesthe size of local neighborhood, and has an effect on the extractionof local features and the weights of n-links.

Keeping other parameters remain unchanged, the segmentationresults of KLD-GCBAC on a synthesis image and a MR brain imagewith different � are shown in Figs. 6 and 7 respectively. It can beseen that if � is too small, the evolving curve easily falls into theminimum within the object; and when � is too large, the smoothingeffect can easily make the curve cross the real boundary. In Fig. 6,the suitable value of � in which the correct segmentation resultcan be obtained is 0.5 < � < 2, while in Fig. 7, the result shown as inFig. 7(d) can be obtained if � is 0.78 < � < 1.4. Thus, medical imageswith complex background and weak edges are more sensitive to �than synthetic images.

KLD-GCBAC model uses morphological closing operation toeliminate small voids within the evolution curve during the iter-ation process and smooth the curve boundary. The radius r of the

disk structure element also has an effect on the local segmentationresult. Fig. 8 shows the comparison of local segmentation resultsof a MR left ventricular image and a real image with different r in

W. Sun, E. Dong / Biomedical Signal Processing and Control 52 (2019) 120–127 125

Fig. 5. Comparison of local segmentation results of medical images. (a) GCBAC; (b) GCBCV; (c) IINBBGC; (d) MLM-GCACM; (e) KLD-GCBAC.

Fig. 6. Comparison of segmentation results using different � on a synthetic image. (a) � = 0.5; (b) � = 0.6; (c) � = 1; (d) � = 2.

on a M

wtmtfa

Fig. 7. Comparison of putamen segmentation results using different �

hich r = 0 corresponds to the situation without smoothing opera-ion. From the first row of Fig. 8, it can be seen that on the absence of

orphological closing operation, the evolving curve may convergeo local weak boundary. Adding morphological operations is helpfulor the evolution of the curve. But in the second row of Fig. 8, therere obvious boundaries outside the object, and the best segmen-

R brain image. (a) � = 0.4; (b) � = 0.5; (c) � = 0.6; (d) � = 0.9.

tation result is obtained without smoothness operation. With thevalue of r increases, error segmentation across the real boundary

becomes more and more serious.

The narrow band of the proposed model is constructed betweenthe erosion curve and the outer boundary of the image, and theevolving curve is placed inside the object to expand outward until

126 W. Sun, E. Dong / Biomedical Signal Processing and Control 52 (2019) 120–127

Fig. 8. Comparison of segmentation results with different radius of structure element. (a) r = 0; (b) r = 1; (c) r = 2; (d) r = 3.

n resu

sirswctoss

6

GIamwiva

A

fFR2

[

[

[

Fig. 9. Comparison of segmentatio

top at the real boundary, then the desired result should be includedn the narrow band. Fig. 9 shows the comparison of segmentationesults of a real image using different initial contours. It can beeen that correct result can be obtained in Fig. 9(b), (c) and (d), inhich the initial contour is inside the object completely or very

lose to the boundary, a rectangle or a pixel. In these situations,he real boundary can be achieved in the narrow band. But partf the inter curve of the narrow band using morphological ero-ion is already outside the object in Fig. 9(a), which leads to erroregmentation.

. Conclusions

The graph cuts and local statistical information based KLD-CBAC model proposed in this paper is a local segmentation model.

t uses the iterative narrowband to construct a network graph,nd designs the weights of n-links and t-links combining the localeans and KL distance of the inner and outer neighborhood regions,hich can better describe the local features of the image. The exper-

mental results on inhomogeneous synthetic and medical imageserify the local segmentation ability of KLD-GCBAC model with highccuracy and operating efficiency.

cknowledgements

This work was supported by the Fundamental Research Funds

or the Central Universities (China), National Natural Scienceoundation of China (Nos. 81671848 and 81371635) and Keyesearch and Development Project of Shandong Province (No.016GGX101017).

[

[

lts with different initial contours.

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