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Localization of a Cerebral Pathology on Magnetic Resonance Images by the Level Set without Re-Initialization and Local Region Based Method
Corresponding Author:
Bendaoud Mohamed habib
Laboratory for Analysis and Application of Radiation, Department of Physics (LAAR),
University of Science and Technology of Oran Mohamed BOUDIAF, Algeria.
Tel: (213) 7 75 50 45 48, address: 1505 El Menaour Bir El Djir USTO Oran Algeria
Benabadji Nouredine
Belbachir Ahmed Hafid
Laboratory for Analysis and Application of Radiation, Department of Physics (LAAR),
University of Science and Technology of Oran Mohamed BOUDIAF, Algeria.
Abstract
Therapid development ofmedical imagingtechnologyisrevolutionizingmedicineevery day.Medical imagingallows scientistsand doctors todisclose potentiallyvitalinformationby scanningthe human bodynon-invasively. Theobjectiveof thisstudy is tolocateor detectacerebral pathologyby the methodof the active contour.
The present work is a study on the possibility to define the outline of brain pathology using two methods: Level Set without re-initialization and local based region method. The processed images are given by a magnetic resonance scanner (MRI) 1.5 tesla; of three patients included in the medical imaging center A BOUKHATEM Oran in Algeria. Knowing that the images are T2, T1 weighted. To give credibility to this study, a comparative study is implemented between the two methods studied. In the final analysis, we will reap the benefits of each method and the Downside.
Results have been able shown that the evolution of the level set algorithm without re-initialization is faster than the algorithm of based local Region, but is still less accurate in the localization of the pathology. For cons, the evolution of the algorithm based local area is very slow but much more accurate than the level set method without re-initialization. The only inconvenience is the requirement to initialize the curve C adjacent of pathology instead of taking the whole image.
It was foundthatthetime requiredforcalculatingthecontour of the imageby usingmagnetic resonanceinthe twomethods, is considerably reduced and the image quality obtained at the end of treatment is remarkable to be able make a good medical diagnosis.
Keywords: Medical imaging, Image segmentation, edge extraction, level set, local based region.
1.Introduction
Medical imagingis used to analyzethe tissues withextremely diversemedia, their farms andtheir interpretationscanfinerestablish the medical diagnosis. Theimaging techniquesare numerous,based on differenttypes of radiation(magnetic field, ultrasound, x-ray, gamma ray,...).
Animaging modalitiesmost frequently used, in which we were interestedinthis work, is Magnetic Resonance Imaging(MRI),which has become anindispensable tool for anyclinical examination. It has theadvantage of beingnon-invasive andallows the acquisition oftwo or three dimensionalimageon which thedifferent contrastsare possible. This modalityhas become anincreasinglyimportantmedicalresearchinbrain orcognitive neurosciencefields ofexplorationthat can be offeredby this techniqueare broad: MRIanatomy thatcan be observedwitha fine resolutioncerebral tissue, functional MRI, which offers the possibility to visualizecerebral activity anddiffusion MRIwhichto explorethe aspect ofconnectivitybrain areas.
In factthe study of thehuman brain isa difficult problem andremains ahighly topicalresearch, because an understanding ofits operationstill incomplete. To diagnose certaindiseases related tointernal cerebral damage, the doctor must analyzemedical images.To studythe evolution of atumor, it isnecessary to knowaccuratelythe changesin these images. Thevisual interpretation ofbrain MRIis notalways safe. Thisis whythe need foran automatic interpretationallowsassist the doctorsin theirdecision makingwas felt.
Thus, for areliableidentification and reliable diagnosisinthe medical field, precision is paramount.In terms ofimage analysis, it is necessarythat thesegmentationis accurate. Possibilities ofautomatic processingof these imagesprovedifficulthowever, because the capacity as insignificant the human eye as the recognition of an object presents real difficulties for computers.
The objective of thisstudyis to isolatepossible pathologiesthroughsegmentation;itis consideredthe heart ofmedical imaging. Several methods have beenproposed; includingthe method ofactive contoursthatoutlineresearchchainedevolvingfroman initial form. This form ispredeterminedas a resultofan optimization methodusing theimage dataat the locations ofcontrol pointsof the curvedeformable. Both methodsarestudiedrespectivelylevel set methodwithoutre-initialization andthelocalregionbasedmethodproposed by the authorsrespectivelyChunmingLiet al.[1] andShawnLankton [2].
This article describe new methods that can be remedied this problem. The extraction by active contour was our choice. We chose for this, two methods; the Level Set without Re-initialization and the local based region implement. Both algorithmsare applied toradiological imagestaken bymagneticresonance in two weights:
-HighlycontrastingImagesin T2 weightedof threepatients who weardifferent pathologies.
-Thelow contrast imagesin T1weightedfor the fourth.
The results arethen comparedwithtwo studies: the energy evolution of thegeneral functionaccording to thenumber of iterationsandcompilation time.And an analysisofthe importanceof contrast product onlow contrastimagesT1-weighted.
In order todelimitthe boundaries of eachpathology;athird algorithmis used to extracteach pathology
of theresultingimagefollowingapplicationof both algorithmson a blackbackground.
2. The Level Set Method
The principle ofthe Level Set methodis to definea developments function in thecomputingfield with thezero levelcurvesdescribed by therelationshipbelow:
C(t) = {(x, y) | ϕ(t, x, y) = 0} (1)
Solving aconvection equationcalledLevel Setequation[3]can predictthe movements of thechangesinthe velocity field:
(2)
WithFisthe speed function.
Forimage segmentation, this depends on its data and function. The functionis theninitializedas asigneddistance functionbefore the evolutionand"remodel"as a function ofsigned distanceperiodically duringevolution [4, 5]. Resetis to solvethe following equation:
(3)
where0 is the function tobe re-initialization,andthe signed functionφ [4, 6, 7].
2.1Removalprocess of re-initialization by theenergypenalty
It is crucial tomaintain the evolution function of thelevel setas asigned distancefunction approximatecourse of evolution.It iswell known that asigned distancefunctionmust satisfy adesirable property |vϕ|=1 [8]. Naturally, this processbeginsby calculatinginternal energy:
(4)
The variational formulationis as follows:
(5)
Wheren > 0isa parameter controllingtheeffect of penalizingthe deviation offrom asigneddistance function, andm()is the energy that will drive themovement of thezerolevel curve.
We denote by∂/∂first variant[9]of the functionalandthe evolution equationas follows:
(6)
Duringthe evolution ofinfunction of the gradientflow(6)that minimizes the functional(5), the curve of the zero levelis moved by theexternal power m. Meanwhile,due tothe effect ofpenalizingtheinternal energy,theevolution functionis automaticallymaintainedas anapproximatesigneddistance functionduring the evolution. Therefore,the re-initialization procedureis completely eliminatedinthe proposed formulation.
2.2. Variation formulation oflevel setwithoutre-initialization of the active contour
In theimage segmentation,active contoursaredynamic curveswhich movetowards the object limit.To achieve this goal, we must explicitly definean external energythat can movethezerolevel curvestowardtheobject boundaries. Let I be animageandgtheedgeindicator functiondefined by:
(7)
WhereGσisthe Gaussian kernelwith standard deviationσ. Theexternal energy g,, thatcauses thezero leveltothe object boundaries, is defined for a function(x, y):
(8)
With >0, isoperative energy tocalculate the lengthof the curveof the zero levelof ϕin theconformal metric.
p ϵ [0,1] is differentiablecurvethat represents thesetofzero.
(9)
is theoperating energy that is introducedto acceleratethe evolution curve:
(10)
whereδis theDiracdimensional function, and H is the Heaviside function.
Thetotalenergyfunctional is:
(11)
Internal energyP()penalizesthe deviation offrom asigneddistance functionduringevolution.Bycalculating changes[9], the derivative of thefunctionalℇcan be written as:
(12)
WhereΔis theLaplacian operator.Functionthat minimizesthis functionalmeetsthe Euler-Lagrange
.
The process ofminimization of the functionalℇisgradient flowgivenby the following equationwhich representstheequation of motionof the Level Set function:
3. The Local Region Based method
TheLocalRegionBased methoddirectly manipulatesregions.Orshe leavesa firstpartitionof the image,which is thenmodifiedby splitting orgroupingofregions. Or she leaves some regions, which are grown by incorporation of pixels until the entire image is covered. This method is based on statistical modeling jointof the regularity of regions and grayscale of each region also exist.
The analysis oflocal regionsleads to the constructionof a local energyfamilyat each pointalong thecurve. To optimizetheselocal energies, each point is examinedseparately,and looksto minimize or maximizethe energy calculatedin itsownlocal region.To calculatethelocal energy,local neighborhoodsare divided intooutside and insidelocal by the curveevolution.Theenergy optimizationis thenperformed byfitting a modeltoeach local region.
Isan I picture,defined to the domainΩ, andlet C be aclosed contourrepresenteddefinedas the zero(zeroLevel Set) of a function signed distance, ie, C = {x | (x) = 0} [9, 10]. The specification of theinsidecontour Cinthe approximation of thesmoothedHeaviside function:
(14)
The exteriorcontourC is defined by
To specifythe area justaround the curve, use the derivative of,a smoothed versionof theDirac delta:
We now introduce asecond variablespacey,usingx and yas independent variablesspace, each representing a single point in thedomainΩ.
We then introduce afunction B (x, y)is used to ignorelocal regions. The interaction ofB (x, y)with theinner and outerregionsis illustrated inFigure 1.
This circle isdividedinto regionsby the contourinterior and exteriorlocal. In bothimages,each point is representedby a yellow dot. NeighborhoodB (x, y)is represented by thelarge red circle. Figure 1(a) iswithinthe localisthe shadedcircle. The shadedcircle indicatestheoutsideroom isillustrated inFigure 1(b).
3.1 Formulation of the functional energy
Theoperating energyE is definedaccording to thegeneric forceF, which is defined bythefollowing relationship:
(16)
WithF isa generic measureof internal energyused to represent thelocal membershipat each pointalong the contour, is expressed by [11, 12]:
(17)
Withuxand vxwhich respectively representthe intensity of themediuminsideand outsidethe contourlocatedin B(x, y) at a point x:
And
λ is parameter for maintain thesmooth curve and regularization termpenalizingthearc length ofthe curve.Taking the firstvariationofthis energy with respectto, we obtain the followingevolution equation:
4. Results and discussion
To test thetwo methodsstudied in thisarticle, the choiceis based onmedical imagessnuffwith amagnetic resonance scanner1.5 tesla.
Figure 2.a present tumoral process of the temporal fossa of the left cavernous cranial, figure 2.b show a lesion process solido-cystic right fronto-parietal and figure 2.c illustrate a little expansive formation oedematogene moderately compressive in the left cerebellar hemisphere withcystic and tissular component.
Bothalgorithmswerecompiled withadual-core processorat 3.4Ghz. The Level Setmethodwithoutre-initializationmethodandLocalRegionBasedwill begin withan initialization of thecurveCin the form ofa rectangle, Figure 3.
Figure 4 gives the results obtained by the method of level-set without re-initialization for an iterations number of 1500 and the computation timefor the three cases respectively138s, 145sand150s.
We can easily notice that the contour of the initial curve is perfectly fit the contour of the pathology. The computation timeforthe final detectionof the pathologyincreases with thecomplexityof the disease.
Figure 5 and 6 gives the results obtained by the method of local based region. This time too, the outline of the initial curve takes shape of the contour of the pathology more accurately than the previous method.
In the Figure 5, the number of iterationsis 3000which is highercompared tothe first method andincreases thecalculation time whichis 740seconds. Theinitial curveCcannotsurround thepathologydespite the increasediterations number, is due to the complexity of the information contained in the image. That time can be reduced if the algorithm is applied directly near the pathology.However, in Figure 6, curve C is initialized adjacent of the disease, this solution gives very good results because it manages to perfectly surround the disease.With an iteration number of 500, this is 6 times less reduced.
4.1 Pathology extractionof the image
The pathology extractionof the all image isperformed followingthe threetransformations:
- Extractthe outlineproduced by the twomethods,
- Change theoutlineof awhite spot,
- Rebuildingthe diseasefromthe white spot.
First, for extractingthe contour, all pixels in the image willbe set to zero, that is to say,black colorexcept for thecontour pixelswill retain theiroriginal color, green for the outlineproduced by theLocalRegionBasedmethod, and red forthelevel set methodwithoutre-initialization. This produces ablack imagewith singleinformation that represents theoutline(Figure 7).
Secondly, the contour obtainedfromthe first stagewill be transformed intoa white spot ona black background.Itwill initializefour imagesm1, m2, m3andm4;Figure8. The algorithm changes the color of all contour pixels, within the contour well as respectively the pixels of the right, left, low, high contourin white.Forthe white spot, the algorithmdoesthe product offour matrices(image).
Figure 9 illustrate the results for three pathologies, with the method mentioned in this section.We note that, using this process, the local area based method allowed us to accurately detect the disease in contrast to the level setwithoutre-initialization method.
4.2. Performance of theLevelsetandlocal region based methodoncontour extractionof pathologyforlow contrast images
So farthe twoalgorithmswe weretested onhigh-contrast images, wherethe pathology isvisible.Theapplicationspresented in this sectionare applied tolow-contrast images, images are taken byT1-weightedmagnetic resonancebeforeand meadowshaveinjectedcontrast material.Figure 10 and Figure 11 show the cerebral images of a patient who is suffering from a tumor of the right ventricular junction process can evoke a meningioma.
Figure10shows the resultsobtained byboth algorithmsbefore injectionof contrast product. The algorithmof theLevel Set methodfailstodetect the edgesof the pathology.The evolution curve converges towards the inner portion of the image until it disappears completely.
Byagainst, the algorithmthe LocalRegionsbasedmethodcan hardlysurroundedpathology,this is due tothe initialization ofthe evolution curveat the edgeof the pathology.
Figure11 indicates thatthe pathologyis easily detectedby the two methodsusedin this studyafterinjectionof contrast product, knowing that this product (gadolinium) is a radiological contrast agentwith opacifying properties prescribed for an MRI exam
In this sectionwe can saythat theLevel Setwithoutre-initializationmethod andbasedLocalRegionsmethodareperforming andprovide a goodlocalizationof the pathologywithinjectionof contrast materialtothe case of imageswith lowcontrast.
The tablebelowpresents a quantitativemeasurementresultsobtained by the twomethodsfortenpatients.
According to this analysis, tenpatientswereable to deduce that67.5% of testsdonewe weresatisfied.
4.3. Comparative study oftwo methods
To givecredibility tothis study,a comparative studyis implementedbetween the two methodsstudiedin this article.Firsttimeweevenvariation of the energyas a function ofnumber of iterations, after which the time variationversus the numberof iteration.
4.3.1 Variation of energyaccording to theiterations number
The evolution of theenergy as a functionof the iterationsnumberforlevel setmethodswithoutre-initialization for threedifferent patientsis shown inFigure 12a.This figure clearly showsthat thevariation of the energywith the number ofiterationis different from onecase to another. This difference is dueto the type ofinformationcontained ineach image.The energy varies continuously for the three cases studied, this means that if the choice of the number of iterations is not good for stopping the algorithm, the energy will continue to vary. This will probably push the evolution curve to ignore the edges of the pathology.
Figure 12b showsthe variation of theenergy accordingof theiteration numberfor the methodLocal Region based. There is a differencein the evolution ofenergyfrom one case tothe otheris dueto informationthatcontainseach image. Alltimes itsallureremains the same forall three cases.The energy increased in a manner proportional with the iteration number, until it reachesa stabilization point.
It was noted that it is this point that the curve of evolution will happen to detect the pathology. This leads us to say that for the local region based method once the object is detected, the energy ceases to vary in contrast to that obtained by the level set method without re-initialization, which continues to vary even after the detection of the object, which makes the level set method without re-initialization less accurate.
4.3.2Time variationinthe iterationnumber
In this section, we study the time variationversus the numberof iteration.Figure 13shows the evolutionwithtimeofthe iteration number.
Time variationis almost identicaltothe 3 casestested;we also notethatthe computation time of the level set method without re-initialization is much reduced that the method Local Region Based.
Proceeding now to a comparison between the results of two methods studied,we can deduce thatthe following points:
-The evolution of thelevel setalgorithmwithout re-initializingis fasterthan thealgorithm of based localRegion, but is stillless accuratein the localization ofthe pathology.
-For cons, the evolution of the algorithm based local area is very slow but much more accurate than the level set method without re-initialization. The only inconvenience is the requirement to initialize the curve C adjacent of pathology instead of taking the whole image.
5. Conclusion
The present work is an implementation of two new methods to ensure that the contour extraction to the medical image acquired by magnetic resonance. The models described are respectively Level Set without Re-Initialization and the Local Based Region method. The main advantage of these two approaches is in the computation time, which is considerably reduced.The results achievedare quite remarkable, except that, despite all best efforts to accelerate the algorithm, it remains relatively long.
We can deduce the following points:
- The level set method without re-initialization is faster than the method local region based.
- The change in time is not dependent on the information includes the image but the number of iterations.
6. Reference
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