Magnetostatic Active Contour Model with Classification...

Research ArticleMagnetostatic Active Contour Model with ClassificationMethod of Sparse Representation

Guoqi Liu 12 Yifei Dong1 Ming Deng1 and Yihang Liu1

1College of Computer and Information Engineering Henan Normal University Xinxiang China2Big Data Engineering Laboratory for Teaching Resources amp Assessment of Education Quality Xinxiang Henan 453007 China

Correspondence should be addressed to Guoqi Liu liuguoqi080408163com

Received 3 November 2019 Revised 16 May 2020 Accepted 2 June 2020 Published 1 July 2020

Academic Editor Jar Ferr Yang

Copyright copy 2020 Guoqi Liu et al -is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

-e active contour model is widely used to segment images For the classical magnetostatic active contour (MAC) model themagnetic field is computed based on the detected points by using an edge detector However noise and nontarget points arealways detected -us MAC is nonrobust to noise and the extracted objects may be deviant from the real objects In this paper amagnetostatic active contour model with a classification method of sparse representation is proposed First rough edge in-formation is obtained with some edge detectors Second the extracted edge contours are divided into two parts by sparseclassification that is the target object part and the redundant part Based on the classified target points a new magnetic field isgenerated and contours evolve with MAC to extract the target objects Experimental results show that the proposed model coulddecrease the influence of noise and robust segmentation results could be obtained

1 Introduction

Image segmentation aims to separate the ldquotargetrdquo area andthe ldquobackgroundrdquo area of the input image and to extract theinteresting part for in-depth understanding and analysis[1 2] Segmented images are the advanced expression of theoriginal pixels to semantic objects -erefore efficient imagesegmentation is a key step from image processing to imageanalysis and also a basic problem in computer vision

-e active contour model (ACM) is one of the main waysto realize image segmentation In recent years many scholarshave conducted in-depth studies on this area and somemodels are widely used in computer vision pattern recog-nition target tracking and other fields Recently with thedevelopment of the neural network some methods thatcombined deep learning with the level set are exerted toresolve complex segmentation and recognition problem In[3] a newmethodology combines deep learning with the levelset for the automated segmentation of the left ventricle of theheart from cardiac cine magnetic resonance (MR) data -iscombination is relevant for segmentation problems where thevisual object of interest presents large shape and appearance

variations but the annotated training set is small which is thecase for various medical image analysis applications

ACM can be usually divided into two types the ACMbased on region information [4ndash10 11] and the ACM basedon edge information [12ndash16] -e region-based ACM hasbeen cited and studied by many scholars because it does notrely on the edge information of the image and can better dealwith the weak edge even the image without edge

-e classic region-based ACM is the CV model [17 18]proposed by Chan and Vese However it is sensitive toinhomogeneous intensity Some methods on the basis of theCV model are proposed to solve the shortcomings Forexample the local binary fitting (LBF) model is proposed byLi [19] and the locally statistical active contour model(LSACM) model is proposed by Zhang [20] To a certainextent the ability of these models to segment inhomoge-neous images is improved However the segmentation ofsome images with serious inhomogeneous intensity is stilldifficult and the high computational complexity is usuallyrequired In [21] the region-based ACM that embeds theimage local information is proposed By defining a localimage fitting (LIF) energy [21] local image information is

HindawiJournal of Electrical and Computer EngineeringVolume 2020 Article ID 5438763 10 pageshttpsdoiorg10115520205438763

extracted and able to segment images with intensityinhomogeneities

-e edge-based ACM mainly uses the gradient infor-mation of the image and pushes the contour to the targetboundary under the action of the defined forces of the curveIt is usually robust to inhomogeneous intensity-e geodesicactive contour (GAC) model [22] comes from the snakemodel [23] which makes the contour smoothly converge toobjects However the evolution of the contour curve in theGAC model is slow and it is sensitive to initialization Inorder to speed the contour evolution a distance regularizedlevel set evolution method (DRLSE) [24] by integrating aregional speeding term is proposed by Li On the other handsome models by defining a new external force field on thebasis of the GAC model are proposed to improve the ro-bustness of initialization For example the gradient vectorflow (GVF) model [25] and vector field convolution (VFC)model [26] are integrated into the GAC model Howeverthere are some saddle points stationary points and otherequilibrium points [27 28] in the vector fields thus thecontour is hard to converge to the concave area

In [29] a variational approach for simultaneous estimationof bias field and segmentation of images with intensity in-homogeneity is presented where the model intensity of in-homogeneous objects is Gaussian distributed with differentmeans and variances -en a sliding window to map theoriginal image intensity onto another domain is introducedwhere the intensity distribution of each object is still Gaussianbut can be better separated In [30] a novel ACM driven byregularized gradient flux flows is presented for image seg-mentation which achieves an accurate result since the zerocrossings of the image Laplacian are reached at the objectboundary when minimizing the gradient flux flows Mean-while the Laplacian of the image is regularized with an an-isotropic diffusion term which can not only reduce noise butalso preserve edge information In [31] the method namedselective binary and Gaussian filtering regularized level set(SBGFRLS) is proposed which selectively penalizes the level setfunction to be binary and then uses a Gaussian smoothingkernel to regularize it Zhi and Shen [32] proposed a saliencydriven region-edge-based top-down level set (SDREL) by usingboth saliencymap and color intensity as region external energyto motivate an initial evolution of level set function (LSF) -issaliency map term improves the performance of extractingobjects from a complicated background and also enhances theasynchronous evolution of single LSF results

-e magnetostatic active contour (MAC) model [33] isproposed by Xie and it utilizes the edge information to realizethe segmentation of objects Different from the ACMs basedon traditional vector fields the problem of equilibrium pointsdoes not exist in MAC and it can effectively extract objectswith a concave region By combining the level set method thechange of topology structure is permitted to extract multipleobjects But there are two main problems with MAC (1)robustness to noise should be improved (2) the detected edgeis sometimes deviant from the real target edge which leads tothe inaccuracy of the segmented result In order to solve thesetwo problems an improved MAC model with a classificationmethod of sparse representation is proposed

2 Background

21 MACModel -e edge information of the image is usedin the MAC model It takes the force of the magnetic field tothe current as the original force to move the contour to theedge of the target

In theMACmodel the direction of current for the objectboundary can be computed using boundary orientationestimation And the boundary orientation O(x) can beobtained by

O(x) (minus 1)λ

minus Iy(x) Ix(x)1113872 1113873 (1)

-at is a 90∘ rotation of the normalized gradient vector(Ix(x) Iy(x))Ix(x) and Iy(x) are the partial derivatives inx and y of image I

λ 1 anticlockwise rotation

2 clockwise rotation1113896 (2)

Next the magnetic flux density B(x) at each pixel po-sition x due to the electric current applied to the objectboundary is computed Given a current If(s) B(x) is definedas

B(x) μ04π

1113944sisinS

If(s)Γ(s) times1113954Rxs

R2xs

(3)

μ0 and π are constants S is a set of some pixels and s

denotes a boundary pixel Γ(s) is an electric current vector ats and proportional to the edge strength andΓ(s) f(s)O(s) f is the gradient magnitude of image IF(c) ICΥ(c) times B(c) is the unit vector from x to s and Rxs

is the distance between them -en given the current IC

applied to the active contour C its magnetic field F(c) iscomputed as

F(c) ICΥ(c) times B(c) (4)

Υ(c) represents the current vector at each point F(c) isreplaced by F(x) and the evolution equation of the MACmodel is defined as follows

Ct αg(x)κ 1113954N +(1 minus α)(F(x) middot 1113954N) 1113954N (5)

α is a real constant κ denotes the curvature and 1113954N is theunit normal of the evolving contour g(x) is a stoppingfunction which is defined as

g(x) 1

1 +|nablaI|p(p 1 2) (6)

-en the evolution equation of the MAC model withrespect to level set function Φ is as follows

Φt αg(x)nabla middotnablaΦ

|nablaΦ|1113888 1113889|nablaΦ| minus (1 minus α)F(x) middot nablaΦ (7)

22 Classification Method of Sparse Representation -e twomain tasks of signal sparse representation are the gener-ation of dictionaries and the sparse decomposition ofsignals

2 Journal of Electrical and Computer Engineering

-e sparse decomposition algorithm is proposed byMallat [34] which is a very famous matching tracking (MP)algorithm -e basis function used to represent the signalcan be selected flexibly according to the characteristics of thesignal itself [35] -e algorithm is easy to implement sothere are a lot of applications in many different fields such asimage and signal processing [36] Sparse representationmodel is represented as follows

Y DL 1113944N

i1DiLi

D D1 DN1113858 1113859

L L1 LN1113858 1113859 sim is sim sparse

(8)

where Y is a signal D is a dictionary and L is the coefficientmatrix -en Y can be divided into two parts and theformula is

Y 1113957Y + Y (9)

where 1113957Y is the object part and Y is regarded as the redundantpart -e formula for extracting 1113957Y is

1113957Y 1113944M

i1DiLi MleN (10)

In order to clearly explain the proposed method atypical example is shown in Figure 1 An image with noiseis shown in Figure 1(a) First some contour points areobtained by using an edge detection operator (the Sobeldetector is used) which is shown in Figure 1(b) Secondthe dictionary is obtained by labeling for the detectedcontour points It is assumed that the number of labeledconnect contours is N and the basis function in the dic-tionary is written as Di(i 1 N) -erefore the con-tour points Y are decomposed into several components Itis shown as follows

Y 1113944N

i1Di (11)

Because some basis functions are redundant in equa-tion (11) the sparse coefficients are finally to be determinedby solving the similar equation (8) with OMP algorithm-emain principle behind the OMP is simple and intuitivein each iteration the coefficients maximally correlated withthe residual are chosen In OMP the contour length ofbasis function or prior information can be used as themeasure of maximum correlation -rough OMP algo-rithm the corresponding basis functions are obtainedwhich are shown in Figure 1 When extracting a singleobject with contour length correlation of OMP the ob-tained result is shown in Figure 1(d) With prior infor-mation of triangle area of OMP the result is shown inFigure 1(d) By setting M 4 of OMP the first fourmaximum correlation basis functions are obtained and 1113957Y isobtained which is shown in Figure 1(e) -e redundantpart Y Y minus 1113957Y is shown in Figure 1(f ) which always in-cludes noise and nontarget objects -e detected points Y

are classed into two parts 1113957Y and Y

3 Proposed Method

31 Problem Analysis -e MAC is a segmentation modelbased on the edge information In this model there are twomajor problems when extracting the target object -esegmentation result of Figure 2(a) shows that the MACmodel extracts some nontarget regions (including somenoises) and the final extracted contour is inaccurate

-e reasons for these problems lie in the MAC modelitself -e magnetic field is used to extract the target objectwhile the magnetic field depends on the edge informationwhich is obtained by some detection operators -e de-tection result is shown in Figure 2(b) Some noise points andother nontarget objects are obtained in the process of de-tection -erefore the segmentation results with MAC willbe influenced

32 MAC Model with the Classification Method of SparseRepresentation In view of the shortcomings of the MACmodel the evolution equation (5) is improved in this paper-e force field is computed with the classified edge pointsTwo images in Figure 3 are taken as examples -eimplementation process of the improved model is as follows

First the rough edge points are obtained by using theoriginal edge detection operator and the detected results areeasily affected by noise and nontarget objects -us it di-rectly leads to a result that the model cannot accuratelyextract the edge information of the target object -e seg-mentation results are not ideal In this paper the extractedresult is denoted by e which can be expressed as follows

e e1 + e2 + middot middot middot + eN

E e1 e2 eN1113858 1113859(12)

where e represents the detected result and it contains somenoise points and edges of nontarget objects and the resultsare shown in Figures 3(a) and 3(b)

Second the edge points obtained by using the edgedetection operator form the contour curve-e preconditionis that the edge contours e are divided into two types bysparse classification that is the formula is expressed as

e 1113957e + e (13)

Some edge contours for describing the target objects arerepresented as 1113957e e1 + e2 + middot middot middot + eM MleN -e otheredge contours are represented as e and they are viewed asredundant In general for an image with a single target asshown in Figure 3(a) the target object can be determinedaccording to edge feature (such as edge length) -e longestedge contour is extracted by using the edge length and theedge contour of the obtained target object is shown by thered line in Figure 3(c) the green contour curves representthe part that is considered redundant On the other handfor an image with multiple targets in Figure 3(b) targetobjects can be determined according to the following stepsFirstly the contours in the detected result are marked asbasis functions -en the OMP algorithm is used to selectthe coefficient that is most correlated with the residual in

Journal of Electrical and Computer Engineering 3

each iteration Because the target contour occupies a largeproportion in the foreground the contour length is usuallyused as the maximum correlation measure without otherprior information In the end the target objects areextracted and the target objects are distinguished from theredundancy -e result after classification is shown inFigures 3(c) and 3(d) -e red contour curves represent thetarget part

For an image with multiple objects of Figure 3(b) wedetermine the M 2 through the OMP algorithm and theformula can be written as

1113957e e1 + e2 (14)

Finally a new magnetic field is generated for the evo-lution of the contour according to the edge information 1113957e ofthe target object extracted from the classification

(a) (b)

Figure 2 Segmentation results with the MACmodel (a) -e segmentation result of the image with MAC (b)-e results of edge detection

(a) (b) (c)

(d) (e) (f )

Figure 1 An example of the OMP algorithm (a) An image with noise (b)-e result with the Sobel detector (c)-e obtained basis functionwith the contour length measure of OMP (d) Another basis function (e) -e union 1113957Y of several basis functions (f ) -e redundant part Y


4 Experiment and Analysis

-ese experiments are simulated mainly in the MATLABR2010a with Intel Core 320GHZ and 4GB of memoryenvironment -e proposed model is compared with someadvanced models -e compared models include the clas-sical CV model the SBGFRLS model the LIF model theSDREL model and the MAC model Not only the realimages but also the medical images are tested and thesegmentation performance of the proposed model is eval-uated objectively by calculating the Jaccard similarity co-efficient [37] and F-score [38]

41 Segmentation of Images with a Single Target -e imagesin this section are the real images published in the Weiz-mann database [39] for testing for example the six imagesin Figure 4 Label images for quantitative evaluation are alsoprovided in this database -e remaining images are medicalimages and other images and these images are also used fortesting Among them the segmentation results of imageswith a single target are shown in Figure 4

From these images the region-based CVmodel and theSBGFRLS model are easily affected by the complexbackground when extracting the target objects As shownin the segmentation results of Figures 4(a) and 4(b) thesemodels not only extract noise points but also extract someother unnecessary objects -us the segmentation resultsare not ideal -e MAC model based on the edge infor-mation has the same disadvantages as the two modelsmentioned above and the segmentation results are shownin Figure 4(e) -e segmentation results of the LIF modeland the SDREL model are shown in Figures 4(c) and 4(d)respectively -e LIF model is easy to be affected by thenoise and inhomogeneous intensity regions the extractedcontour curves are disordered which are sensitive toinitialization and the segmentation results are inaccurateAs shown in the segmentation result of the fourth image ofthe SDREL model the saliency feature is utilized to acquirean object However some nontargets are not detected assaliency areas so that some oversegmentation regionsappear

-e segmentation results of the proposed model areshown in Figure 4(f ) Since the edge contour is classified bythe classification method based on sparse representationand only the edge contour of the target object is utilized togenerate a newmagnetic field therefore the proposedmodel

can robustly extract the object contour and the segmen-tation results are better

42 Segmentation of Images with Multiple Targets In thissection several advanced models are used to test the seg-mentation performance of images with multiple targets andthe segmentation results of various models are shown inFigure 5 It can be seen that the segmentation results of theproposed model are significantly better than other modelsparticipating in the comparison During the segmentation ofthese images the parameters in each model are set to defaultvalues without any changes Both CV and SBGFRLS modelsutilize the region information to evolve the contour andthey are robust to noise compared with the ACMs based onedge information As shown in Figures 5(a) and 5(b) theresults are less affected by noise but they are affected bynontarget objects For example the first row segmentationresults of Figures 5(a) and 5(b) show that the segmentationresults of these models include some nonobjects

-e ACMs based on local information are always sen-sitive to noise such as LIF and MAC models -e corre-sponding segmentation results shown Figures 5(c) and 5(e)are greatly affected by the noise

-e SDRELmodel has the disadvantage of easily crossingweak boundaries as shown in the first image of Figure 5(d)-e proposed model utilizes the classification method ofsparse representation In the proposed modelM 2 is set inthe simulations and noise and nontarget objects are viewedas redundancy thus it improves the segmentation accuracy

43 Quantitative Assessment

431 Jaccard Similarity Coefficient In order to objectivelyreflect the good segmentation performance of the proposedmodel the Jaccard similarity coefficient (JS) is used forquantitative evaluation in this section -at is the labelimages published in [39] are compared with the segmen-tation results of several advanced models mentioned inFigures 4 and 5 Jaccard similarity coefficient formula [37] is

JS(A B) |AcapB|

|AcupB| (15)

where A is the segmentation result and B is the groundtruth of the original image When the JS value is largerindicating higher similarity the segmentation results arerelatively accurate -e JS values of each model are shown

(a) (b) (c) (d)

Figure 3 Segmentation results with the proposed model (a b) -e segmentation results of the MAC model (c d) Classification results ofthe edge contours


in Tables 1 and 2 More segmentation results with ourmodel are shown in Figure 6 and the assessment results areshown in Table 3 Because the edge contours are classifiedin the proposed method the edge contour of the desiredtarget is extracted and the new magnetic field is generatedConsequently compared with the other models the seg-mentation results of the proposed model are the best Forexample it can be seen from Table 1 that the LIF model isgreatly influenced by the noise and the segmentation effectis always not ideal Compare the JS values of the firstcolumn and the sixth column in Table 1 CV model andSBGFRLS model are having better segmentation results inFigure 5 compared with the models based on local infor-mation such as LIF

Table 2 shows the segmentation performance of themodels -ey represent the Jaccard similarity coefficients of

the four images with multiple targets in Figure 5 Because ofthe influence of nonobjects the accuracy with the modelsbased on region information is not ideal as shown inFigure 2(a) and the Jaccard similarity coefficient of theproposed model is higher than that of the other models Itverifies again that the segmentation results of the proposedmodel are ideal -e averaged JS is shown in Table 3 FromTable 3 the proposed method obtains the averaged JS intested images which show the robustness of the proposedmethod More results with the proposed method are shownin Figure 6 and the corresponding JS is shown in Table 4which verifies the robust performances of the proposedmethod

Since the proposed method is integrated into the MACmodel in order to evaluate the upgrade rate with theproposed method the results in Figure 4 with MAC and the

(a) (b) (c) (d) (e) (f )

Figure 4 Segmentation results with models (a) CV model (b) SBGFRLS model (c) LIF model (d) SDREL (e) MAC model (f ) Proposedmodel


proposed method for quantitative analysis are compared-e F-score algorithm [38] is used as a standard -e for-mula of the algorithm is as follows

P TP

(TP + FP)

R TP

(TP + FN)

F 2lowastPR

(P + R)

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(16)

Among them TP is the correct segmentation sample ofthe target foreground FP is a sample that divides the targetbackground error into the foreground FN is a sample thatdivides the target foreground error into the background P isthe precision rate representing the proportion of the correctsegmentation foreground to the total segmentation fore-ground R is the recall rate representing the proportion ofthe correct segmentation foreground to the standard sampleof the target foreground F is the accuracy rate and it is theoverall evaluation index to judge whether the segmentationresult is accurate -e results obtained by the F-score al-gorithm are shown in Table 5

It can be seen from Table 4 that the segmentation resultsof the proposed model are more ideal and more suitable forthe desired target -e specific performance is that theprecision rate recall rate and accuracy rate of segmentationresults of the proposed model are relatively high there is nolarger oversegmentation or leakage segmentation and the

(a) (b) (c) (d) (e) (f )

Figure 5 Segmentation results of tested models (a) CV model (b) SBGFRLS model (c) LIF model (d) SDREL model (e) MAC model (f )Proposed model

Table 1 -e JS values of each model

A B C D E FCV 09108 09008 08933 07325 04587 08700SBGFRLS 08117 06441 02494 09595 00927 07456LIF 03961 04383 03635 04335 00455 03678SDREL 07916 08732 04915 08855 01819 08500MAC 07333 07150 08089 05538 03979 09230OURS 09814 09702 09529 09602 09043 09676AndashF represent the six original images with a single target in Figure 4respectively the top results are indicated by


A B C DCV 04564 07835 09363 09573SBGFRLS 00895 07831 08201 09863LIF 00808 01659 05332 04211SDREL 01145 06423 09162 09453MAC 07192 07987 07126 09176OURS 09290 09638 09548 09805AndashD represent the four original images with multiple targets in Figure 5respectively the top results are indicated by


overall precision is better Compared with the original MACmodel the segmentation precision is improved with theproposed model When the segmentation effect is relatively

satisfied the segmentation effect with the proposed model ismore accurate Some more comparisons with MAC areshown in Figure 7 -e object region is prior and the

Figure 6 More segmentation results with our model

Table 3 -e averaged JS values of tested models

ID CV SBGFRLS LIF SDREL MAC OURSJS 07900 06182 03246 06692 07280 09565

Table 4 -e JS values of Figure 6

ID 1 2 3 4 5 6 7 8 9 10JS 08495 08096 09370 08592 08397 09751 09329 09696 09394 09929


proposed method converges to the objects But MAC ex-tracts some noise and nonobjects-e typical result is shownin the second result of Figure 7(a)

5 Conclusion

In this paper a magnetostatic active contour model witha classification method of sparse representation is pro-posed in order to solve the problem that the magne-tostatic active contour model is often affected by thenonobject background and noise in the image segmen-tation In this model the idea of sparse representation isintroduced -e edge contours are divided into twocategories targets and redundancies Only the edgecontours of the target objects are extracted by edgefeature or OMP algorithm and they are recalculated togenerate a new magnetic field -is method could ro-bustly extract the edge contour of the target object It issimple and easy to implement And it can effectivelyavoid the influence of noise points and unnecessaryobjects

Data Availability

Weizmann database is used to support this study which isshown in [39]-ese prior studies are cited at relevant placeswithin the text as [1 2]

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-is work was jointly supported by the National NaturalScience Foundation of China (nos U1404603 and61901160)

References

[1] X Wang Y Wan R Li J Wang and L Fang ldquoA multi-objectimage segmentation C-V model based on region division andgradient guiderdquo Journal of Visual Communication and ImageRepresentation vol 39 pp 100ndash106 2016

[2] Q E Wu Z Chen R Han et al ldquoA palmprint recognitionapproach based on image segmentation of region of interestrdquoInternational Journal of Pattern Recognition and ArtificialIntelligence vol 30 no 2 pp 1656002ndash1656011 2016

[3] T A Ngo Z Lu and G Carneiro ldquoCombining deep learningand level set for the automated segmentation of the leftventricle of the heart from cardiac cine magnetic resonancerdquoMedical Image Analysis vol 35 pp 159ndash171 2017

[4] N Paragios and R Deriche ldquoGeodesic active regions and levelset methods for supervised texture segmentationrdquo Interna-tional Journal of Computer Vision vol 1 no 46 pp 223ndash2472002

Table 5 Comparison of different models

ModelA B C D

P R F P R F P R F P R FMAC 9591 6371 7656 9611 7445 8391 9989 5051 6709 9855 9079 9451Ours 9570 8234 8852 9979 9193 9570 9979 9381 9671 9737 9970 9852AndashD represent the four original images with multiple targets in Figure 4

(a)

(b)

Figure 7 Segmentation results of medical images (a) -e segmentation results of the MAC model (b) -e segmentation results of theproposed model


[5] R Ronfard ldquoRegion-based strategies for active contourmodelsrdquo International Journal of Computer Vision vol 13no 2 pp 229ndash251 1994

[6] S C Zhu and A Yuille ldquoRegion competition unifying snakesregion growing and BayesMDL for multiband image seg-mentationrdquo IEEE Transactions on Pattern Analysis andMachine Intelligence vol 18 no 9 pp 884ndash900 1996

[7] A Pratondo C-K Chui and S-H Ong ldquoIntegratingmachinelearning with region-based active contour models in medicalimage segmentationrdquo Journal of Visual Communication andImage Representation vol 43 pp 1ndash9 2017

[8] S Mukherjee and S T Acton ldquoRegion based segmentation inpresence of intensity inhomogeneity using legendre polyno-mialsrdquo IEEE Signal Processing Letters vol 22 no 3pp 298ndash302 2015

[9] C Li R Huang Z Ding J C Gatenby D N Metaxas andJ C Gore ldquoA level set method for image segmentation in thepresence of intensity inhomogeneities with application toMRIrdquo IEEE Transactions on Image Processing A Publicationof the IEEE Signal Processing Society vol 20 no 7pp 2007ndash2016 2011

[10] S Niu Q Chen L de Sisternes Z Ji Z Zhou andD L Rubin ldquoRobust noise region-based active contour modelvia local similarity factor for image segmentationrdquo PatternRecognition vol 61 pp 104ndash119 2017

[11] C Li C Y Kao J Gore and ZDing ldquoMinimization of region-scalable fitting energy for image segmentationrdquo IEEETransactions on Image Processing A Publication of the IEEESignal Processing Society vol 17 no 10 pp 1940ndash1949 2008

[12] X Liao Z Yuan Q Tong J Zhao and Q Wang ldquoAdaptivelocalised region and edge-based active contour model usingshape constraint and sub-global information for uterine fi-broid segmentation in ultrasound-guided HIFU therapyrdquo IETImage Processing vol 11 no 12 pp 1142ndash1151 2017

[13] L D Cohen ldquoOn active contour models and balloonsrdquo CVGIPImage Understanding vol 53 no 2 pp 211ndash218 1991

[14] C Xu and J L Prince ldquoSnakes shapes and gradient vectorflowrdquo IEEE Transactions on Image Processing A Publication ofthe IEEE Signal Processing Society vol 7 no 3 pp 359ndash3691998

[15] M Ciecholewski ldquoAn edge-based active contour model usingan inflationdeflation force with a damping coefficientrdquo Ex-pert Systems with Applications vol 44 pp 22ndash36 2016

[16] B Zhou C J He and Y Yuan ldquoEdge-based active contourmodel with adaptive varying stopping functionrdquo ApplicationResearch of Computers vol 29 no 1 pp 366ndash368 2012

[17] T F Chan B Y Sandberg and L A Vese ldquoActive Contourswithout edges for vector-valued imagesrdquo Journal of VisualCommunication and Image Representation vol 11 no 2pp 130ndash141 2000

[18] T Chan and L Vese ldquoAn active contour model withoutedgesrdquo Scale-Space gteories in Computer Vision pp 141ndash151Springer-Verlag Berlin Germany 1999

[19] C Li C Y Kao J C Gore et al ldquoImplicit active contoursdriven by local binary fitting energyrdquo in Proceedings of the 2007IEEE Conference on Computer Vision and Pattern Recognitionpp 1ndash7 IEEE Minneapolis MN USA June 2007

[20] K Zhang L Zhang K-M Lam and D Zhang ldquoA level setapproach to image segmentation with intensity inhomoge-neityrdquo IEEE Transactions on Cybernetics vol 46 no 2pp 546ndash557 2016

[21] K Zhang H Song and L Zhang ldquoActive contours driven bylocal image fitting energyrdquo Pattern Recognition vol 43 no 4pp 1199ndash1206 2010

[22] V Caselles R Kimmel and G Sapiro ldquoGeodesic activecontoursrdquo International Journal of Computer Vision vol 22no 1 pp 61ndash79 1997

[23] M Kass A Witkin and D Terzopoulos ldquoSnakes activecontour modelsrdquo International Journal of Computer Visionvol 1 no 4 pp 321ndash331 1988

[24] C M Li C Y Xu C F Gui et al ldquoDistance regularized level setevolution and its application to image segmentationrdquo IEEETransaction on Image Processing vol 19 no12 pp154ndash164 2010

[25] C Xu and J L Prince ldquoGradient vector flow a new externalforce for snakesrdquo in Proceedings of the IEEE Computer SocietyConference on Computer Vision and Pattern Recognitionpp 66ndash71 IEEE San Juan Puerto Rico USA June 1997

[26] B Li and S T Acton ldquoActive contour external force usingvector field convolution for image segmentationrdquo IEEETransactions on Image Processing vol 16 no 8 pp 2096ndash2106 2007

[27] D L Zeng Z H Zhou and S L Xie ldquoImage segmentationbased on the poincare map methodrdquo IEEE Transactions onImage Processing vol 21 no 3 pp 946ndash957 2012

[28] G Liu and M Deng ldquoParametric active contour based onsparse decomposition for multi-objects extractionrdquo SignalProcessing vol 148 pp 314ndash321 2018

[29] K Zhang Q Liu H Song and X Li ldquoA variational approachto simultaneous image segmentation and bias correctionrdquoIEEE Transactions on Cybernetics vol 45 no 8 pp 1426ndash1437 2015

[30] H Song ldquoActive contours driven by regularised gradient fluxflows for image segmentationrdquo Electronics Letters vol 50no 14 pp 992ndash994 2014

[31] K Zhang L Zhang H Song and W Zhou ldquoActive contourswith selective local or global segmentation a new formulationand level set methodrdquo Image and Vision Computing vol 28no 4 pp 668ndash676 2010

[32] X-H Zhi and H-B Shen ldquoSaliency driven region-edge-basedtop down level set evolution reveals the asynchronous focus inimage segmentationrdquo Pattern Recognition vol 80 pp 241ndash255 2018

[33] X Xie and M Mirmehdi ldquoMAC magnetostatic active con-tour modelrdquo IEEE Transactions on Pattern Analysis andMachine Intelligence vol 30 no 4 pp 632ndash646 2008

[34] S G Mallat and Z Zhifeng Zhang ldquoMatching pursuits withtime-frequency dictionariesrdquo IEEE Transactions on SignalProcessing vol 41 no 12 pp 3397ndash3415 1993

[35] J Wright Y Ma J Mairal G Sapiro T S Huang and S YanldquoSparse representation for computer vision and patternrecognitionrdquo Proceedings of the IEEE vol 98 no 6pp 1031ndash1044 2010

[36] G Liu and J Zou ldquoLevel set evolution with sparsity constraintfor object extractionrdquo IET Image Processing vol 12 no 8pp 1413ndash1422 2018

[37] H-H Chang A H Zhuang D J Valentino and W-C ChuldquoPerformance measure characterization for evaluating neu-roimage segmentation algorithmsrdquo NeuroImage vol 47no 1 pp 122ndash135 2009

[38] C Goutte and E Gaussier ldquoA probabilistic interpretation ofprecision recall and f-score with implication for evaluationrdquoin Lecture Notes in Computer Science pp 345ndash359 2005

[39] S Alpert M Galun R Basri and A Basri ldquoImage seg-mentation by probabilistic bottom-up aggregation and cueintegrationrdquo in Proceedings of the IEEE Conference onComputer Vision and Pattern Recognition pp 1ndash8 Minne-apolis MN USA June 2007


extracted and able to segment images with intensityinhomogeneities

-e edge-based ACM mainly uses the gradient infor-mation of the image and pushes the contour to the targetboundary under the action of the defined forces of the curveIt is usually robust to inhomogeneous intensity-e geodesicactive contour (GAC) model [22] comes from the snakemodel [23] which makes the contour smoothly converge toobjects However the evolution of the contour curve in theGAC model is slow and it is sensitive to initialization Inorder to speed the contour evolution a distance regularizedlevel set evolution method (DRLSE) [24] by integrating aregional speeding term is proposed by Li On the other handsome models by defining a new external force field on thebasis of the GAC model are proposed to improve the ro-bustness of initialization For example the gradient vectorflow (GVF) model [25] and vector field convolution (VFC)model [26] are integrated into the GAC model Howeverthere are some saddle points stationary points and otherequilibrium points [27 28] in the vector fields thus thecontour is hard to converge to the concave area

In [29] a variational approach for simultaneous estimationof bias field and segmentation of images with intensity in-homogeneity is presented where the model intensity of in-homogeneous objects is Gaussian distributed with differentmeans and variances -en a sliding window to map theoriginal image intensity onto another domain is introducedwhere the intensity distribution of each object is still Gaussianbut can be better separated In [30] a novel ACM driven byregularized gradient flux flows is presented for image seg-mentation which achieves an accurate result since the zerocrossings of the image Laplacian are reached at the objectboundary when minimizing the gradient flux flows Mean-while the Laplacian of the image is regularized with an an-isotropic diffusion term which can not only reduce noise butalso preserve edge information In [31] the method namedselective binary and Gaussian filtering regularized level set(SBGFRLS) is proposed which selectively penalizes the level setfunction to be binary and then uses a Gaussian smoothingkernel to regularize it Zhi and Shen [32] proposed a saliencydriven region-edge-based top-down level set (SDREL) by usingboth saliencymap and color intensity as region external energyto motivate an initial evolution of level set function (LSF) -issaliency map term improves the performance of extractingobjects from a complicated background and also enhances theasynchronous evolution of single LSF results

-e magnetostatic active contour (MAC) model [33] isproposed by Xie and it utilizes the edge information to realizethe segmentation of objects Different from the ACMs basedon traditional vector fields the problem of equilibrium pointsdoes not exist in MAC and it can effectively extract objectswith a concave region By combining the level set method thechange of topology structure is permitted to extract multipleobjects But there are two main problems with MAC (1)robustness to noise should be improved (2) the detected edgeis sometimes deviant from the real target edge which leads tothe inaccuracy of the segmented result In order to solve thesetwo problems an improved MAC model with a classificationmethod of sparse representation is proposed

2 Background

21 MACModel -e edge information of the image is usedin the MAC model It takes the force of the magnetic field tothe current as the original force to move the contour to theedge of the target

In theMACmodel the direction of current for the objectboundary can be computed using boundary orientationestimation And the boundary orientation O(x) can beobtained by

O(x) (minus 1)λ

minus Iy(x) Ix(x)1113872 1113873 (1)

-at is a 90∘ rotation of the normalized gradient vector(Ix(x) Iy(x))Ix(x) and Iy(x) are the partial derivatives inx and y of image I

λ 1 anticlockwise rotation

2 clockwise rotation1113896 (2)

Next the magnetic flux density B(x) at each pixel po-sition x due to the electric current applied to the objectboundary is computed Given a current If(s) B(x) is definedas

B(x) μ04π

1113944sisinS

If(s)Γ(s) times1113954Rxs

R2xs

(3)

μ0 and π are constants S is a set of some pixels and s

denotes a boundary pixel Γ(s) is an electric current vector ats and proportional to the edge strength andΓ(s) f(s)O(s) f is the gradient magnitude of image IF(c) ICΥ(c) times B(c) is the unit vector from x to s and Rxs

is the distance between them -en given the current IC

applied to the active contour C its magnetic field F(c) iscomputed as

F(c) ICΥ(c) times B(c) (4)

Υ(c) represents the current vector at each point F(c) isreplaced by F(x) and the evolution equation of the MACmodel is defined as follows

Ct αg(x)κ 1113954N +(1 minus α)(F(x) middot 1113954N) 1113954N (5)

α is a real constant κ denotes the curvature and 1113954N is theunit normal of the evolving contour g(x) is a stoppingfunction which is defined as

g(x) 1

1 +|nablaI|p(p 1 2) (6)

-en the evolution equation of the MAC model withrespect to level set function Φ is as follows

Φt αg(x)nabla middotnablaΦ

|nablaΦ|1113888 1113889|nablaΦ| minus (1 minus α)F(x) middot nablaΦ (7)

22 Classification Method of Sparse Representation -e twomain tasks of signal sparse representation are the gener-ation of dictionaries and the sparse decomposition ofsignals



Y DL 1113944N

i1DiLi

D D1 DN1113858 1113859


(8)


Y 1113957Y + Y (9)


1113957Y 1113944M

i1DiLi MleN (10)


Y 1113944N

i1Di (11)



3 Proposed Method






E e1 e2 eN1113858 1113859(12)



e 1113957e + e (13)





1113957e e1 + e2 (14)


(a) (b)


(a) (b) (c)

(d) (e) (f )














JS(A B) |AcapB|

|AcupB| (15)


(a) (b) (c) (d)







(a) (b) (c) (d) (e) (f )




P TP

(TP + FP)

R TP

(TP + FN)

F 2lowastPR

(P + R)

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(16)



(a) (b) (c) (d) (e) (f )













ID 1 2 3 4 5 6 7 8 9 10JS 08495 08096 09370 08592 08397 09751 09329 09696 09394 09929



5 Conclusion


Data Availability




Acknowledgments


References






ModelA B C D


(a)

(b)








































Y DL 1113944N

i1DiLi

D D1 DN1113858 1113859


(8)


Y 1113957Y + Y (9)


1113957Y 1113944M

i1DiLi MleN (10)


Y 1113944N

i1Di (11)



3 Proposed Method






E e1 e2 eN1113858 1113859(12)



e 1113957e + e (13)





1113957e e1 + e2 (14)


(a) (b)


(a) (b) (c)

(d) (e) (f )














JS(A B) |AcapB|

|AcupB| (15)


(a) (b) (c) (d)







(a) (b) (c) (d) (e) (f )




P TP

(TP + FP)

R TP

(TP + FN)

F 2lowastPR

(P + R)

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(16)



(a) (b) (c) (d) (e) (f )













ID 1 2 3 4 5 6 7 8 9 10JS 08495 08096 09370 08592 08397 09751 09329 09696 09394 09929



5 Conclusion


Data Availability




Acknowledgments


References






ModelA B C D


(a)

(b)









































1113957e e1 + e2 (14)


(a) (b)


(a) (b) (c)

(d) (e) (f )














JS(A B) |AcapB|

|AcupB| (15)


(a) (b) (c) (d)







(a) (b) (c) (d) (e) (f )




P TP

(TP + FP)

R TP

(TP + FN)

F 2lowastPR

(P + R)

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(16)



(a) (b) (c) (d) (e) (f )













ID 1 2 3 4 5 6 7 8 9 10JS 08495 08096 09370 08592 08397 09751 09329 09696 09394 09929



5 Conclusion


Data Availability




Acknowledgments


References






ModelA B C D


(a)

(b)


















































JS(A B) |AcapB|

|AcupB| (15)


(a) (b) (c) (d)







(a) (b) (c) (d) (e) (f )




P TP

(TP + FP)

R TP

(TP + FN)

F 2lowastPR

(P + R)

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(16)



(a) (b) (c) (d) (e) (f )













ID 1 2 3 4 5 6 7 8 9 10JS 08495 08096 09370 08592 08397 09751 09329 09696 09394 09929



5 Conclusion


Data Availability




Acknowledgments


References






ModelA B C D


(a)

(b)











































(a) (b) (c) (d) (e) (f )




P TP

(TP + FP)

R TP

(TP + FN)

F 2lowastPR

(P + R)

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(16)



(a) (b) (c) (d) (e) (f )













ID 1 2 3 4 5 6 7 8 9 10JS 08495 08096 09370 08592 08397 09751 09329 09696 09394 09929



5 Conclusion


Data Availability




Acknowledgments


References






ModelA B C D


(a)

(b)








































P TP

(TP + FP)

R TP

(TP + FN)

F 2lowastPR

(P + R)

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(16)



(a) (b) (c) (d) (e) (f )













ID 1 2 3 4 5 6 7 8 9 10JS 08495 08096 09370 08592 08397 09751 09329 09696 09394 09929



5 Conclusion


Data Availability




Acknowledgments


References






ModelA B C D


(a)

(b)













































ID 1 2 3 4 5 6 7 8 9 10JS 08495 08096 09370 08592 08397 09751 09329 09696 09394 09929



5 Conclusion


Data Availability




Acknowledgments


References






ModelA B C D


(a)

(b)








































5 Conclusion


Data Availability




Acknowledgments


References






ModelA B C D


(a)

(b)







































Magnetostatic Active Contour Model with Classification...

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