research article segmentation of scarred myocardium in cardiac magnetic resonance … · 2017. 12....

Hindawi Publishing CorporationISRN Biomedical ImagingVolume 2013 Article ID 504594 12 pageshttpdxdoiorg1011552013504594

Research ArticleSegmentation of Scarred Myocardium inCardiac Magnetic Resonance Images

Lasya Priya Kotu1 Kjersti Engan1 Karl Skretting1 Stein Oslashrn2

Leik Woie2 and Trygve Eftestoslashl1

1 Department of Electrical Engineering and Computer Science University of Stavanger 4036 Stavanger Norway2 Cardiology Department Stavanger University Hospital 4011 Stavanger Norway

Correspondence should be addressed to Lasya Priya Kotu lasyakotugmailcom and Kjersti Engan kjerstienganuisno

Received 10 October 2013 Accepted 12 November 2013

Academic Editors B Tomanek and G Waiter

Copyright copy 2013 Lasya Priya Kotu et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

The segmentation of scarred and nonscarred myocardium in Cardiac Magnetic Resonance (CMR) is obtained using differentfeatures and feature combinations in a Bayes classifier The used features are found as a local average of intensity values and theunderlying texture information in scarred and nonscarred myocardium The segmentation classifier was trained and tested withdifferent experimental setups and parameter combinations and was cross validated due to limited data The experimental resultsshow that the intensity variations are indeed an important feature for good segmentation and the average area under the ReceiverOperating Characteristic (ROC) curve that is the AUC is 9158 plusmn 32 The segmentation using texture features also gives goodsegmentation with average AUC values at 8589 plusmn 58 that is lower than the direct current (DC) feature However the texturefeature gives robust performance compared to a local mean (DC) feature in a test set simulated from the original CMR data Thesegmentation of scarred myocardium is comparable to manual segmentation in all the cross validation cases

1 Introduction

After amyocardial infarction (MI) themyocardium does notfunction properly due to scarring of the tissue Late Gadolin-ium Enhanced Cardiac Magnetic Resonance (LGE-CMR)imaging is used for assessing morphology of myocardiumafter an MI

Segmenting the scarred areas from the healthy myocar-dium is an important prerequisite for various diagnostic anal-yses For example the scar size is largely responsible in leftventricular remodeling [1] The scar size and texture as wellas the left ventricle ejection fraction are also important toidentify patients with high risk of getting life threateningarrhythmias and decide who will benefit from implantationof implantable cardioverter-defibrillator (ICD) [2] The scarsize is also related to the heart rate of ventricular tachycardia[3]

Earlier work focuses mostly on manual or semiautomaticmethods for segmenting the scarred area [2 4] At StavangerUniversity Hospital (SUS) as in many other hospitals today

the cardiologists will provide their input in a semiautomaticsystem to segment the heart muscle from the surroundingareas as well as to segment scarred from healthy areas Thisis a time consuming job and will be vulnerable to inter-observer variability In recent years there has been somepublications on fully automatic methods for segmenting themyocardial muscle [5 6] and also methods to segment thescarred areas from the healthy parts of the heart muscle inLGE-CMR images [5 7ndash9] Algohary et al [10] are proposingan automatic method for segmenting the scar using a com-bination of two imaging techniques late enhancement andStrain Encoding (SENC) by using a combination of Otsursquosmethod morphological operations and clustering

Corsi et al [8] are doing a simple thresholding as theydefine scarred area as all myocardial tissue with inten-sity value ge80 of the maximum intensity value of themyocardium at each slice [8] This method can only be usedon slices where the presence of a scar is known In a slice (orpatient) without scar this method will induce a scar area andthe paper fails to mention this problem The method does

2 ISRN Biomedical Imaging

not take into account that the degree of damage can varyfrom patient to patient and therefore the threshold of 80 isnot suitable for all the patients A simple threshold is almostguaranteed to produce some small false detection areas insome slices

Dikici et al [5] use a Support Vector Machine (SVM)classifier to distinguish between the scarred and healthymyocardium tissue They argue to use a supervised classifierrather than a method based on thresholding because thedegree of damage can vary from patient to patient and alsobecause of the partial voluming effects The three featuresthey use in the classifier are (i) the intensity of a pixel relativeto the averagemyocardial intensity (ii) the standard deviationof the relative pixel intensities with respect to its nextneighbors and (iii) myocardial contrast defined as the ratioof the mean myocardial intensity over the mean intensity ofthe entire image Features (i) and (ii) are calculated for everypixel whereas feature (iii) is calculated for every slice Allthe calculations and scaling are performed on a slice by slicelevel In training and testing they use only three slices foreach patient from the middle of the ventricle The reportedsegmentation accuracy on these middle slices is 8839 witha sensitivity of 8134 and specificity of 9228 Feature (i)seems to be very dependent on the scar size at that particularslice and would possibly benefit from being calculated overthe entire 3D volume instead Since they only test the middleslices they will not experience the slices near the top orbottom of the heart where the scar can cover most of themyocardial muscle Feature (ii) applies local characteristicsand can be considered a textural measure

The approach by Tao et al [7] is a three step method(i) initialization (ii) false acceptance removal and (iii)false rejection removal The initialization is based on Otsursquosmethod for thresholding that is the probability densityfunction (PDF) of the intensity levels is estimated and athreshold is found as a function of the estimated PDF Thetechnique expects a bimodal PDF for a two class problemand uses an optimization criterion to maximize the ratioof between-class variance and within-class variance Startingwith a segmented heart muscle this does not work very wellbecause the scar is much smaller than the healthy area andthe bimodality of the PDF is not very evident Tao et alsuggest to improve this by including the blood pool Thusthey are actually finding a good threshold to separate theblood pool from the heart muscle The scar will be closerto the blood pool than to the healthy myocardium in termsof intensity levels and this way they separate the scarredarea from the healthy myocardial area The thresholding isperformed jointly on the entire 3D volume (all slices) It isfollowed by false acceptance removal by connectivity filteringusing a two pass algorithm [11] The false acceptance removalis performed on a slice to slice level and will remove smalland thin areas labeled as scar after the thresholding Regiongrowing is done as a last step Voxels that are connected to thescarred region and having intensity values larger than 2 times SDof the healthy region are included in the scarred region Theregion growing is done on a slice by slice level so that the SDis calculated for each slice Tao et al report experiments of20 postinfarction patients compared tomanually traced scars

from two individual observers using the Dice index metricsThe method is dependent on the blood pool intensity levelwhich might be questionable Local textures are not takeninto account

Recent studies showed that the scar tissue is hetero-geneous in nature and that the mortality of patients withreduced LVEF depends on the heterogeneity of scar tissue [1213] Texture features from gray-level co-occurrence matricesand Local Binary Patterns (LBPs) were used in our grouprsquosprevious work to classify patients with high and low risk ofgetting arrhythmia [14 15] Other results from our recentwork [16] strengthened our claim that there are texturaldifferences between the healthy myocardium and the scartissue thus we want to explore this furtherWe are concernedabout the fact that not all slices (or patients) have scar Wealso know that the degree of damage will vary from patientto patient and thus the intensity levels of the scar relative tothe healthy myocardiummight differ from patient to patientmaking relative features problematic On the other hand theintensity values of the healthy myocardium might vary frompatient to patient making absolute features problematicThus we do not want to base the method on thresholding butrather train a classifier with both textural and intensity basedfeatures conceptually related to Dikicirsquos method Howeverwe believe that we need to consider the whole 3D volumeof the myocardium as the basis in all our calculations Thiswill include slices without scar occasionally andor sliceswith scars covering the entire myocardium To avoid theproblemof the varying degree of damage (or even no damage)we classify the LGE-CMR images without scaling relativeto assumed healthy areas or maximum values (assumed tobe scar) The problem of the intensity values varying frompatient to patient also in the healthy areas is difficult toaddress since the degree of damage can vary at the sametime Thus we carefully exclude a couple of outliers fromour training set however they are included in the test set toexamine the robustness of the methodThe exclusion is doneautomatically in the training process

Section 2 discusses material and methods Section 3shows the experimental frameworkThe results are presentedand discussed in Section 4 Finally the paper is concludedand expected future work is suggested

2 Material and Methods

This section explains the material and methods used inthis work Section 21 discusses the CMR material used inthe experiments The proposed segmentation scheme usingBayes classifier and the feature extraction are illustrated inSection 22 and Section 23 respectively

21 Material The Department of Cardiology in StavangerUniversity Hospital provided the LGE-CMR images forour experiments and the experiments were conducted inMATLAB The LGE-CMR images is a group of 24 patientsall with high risk of getting arrhythmia and they were storedaccording to the Digital imaging and communications inmedicine (DICOM) format with 512 times 512 pixel resolutionThe number of image slices with visible scar in each patientvaries approximately from 5 to 12 depending on the size

ISRN Biomedical Imaging 3

of scar and heart Only short-axis CMR images were usedin our experiments The LGE-CMR images were acquiredfrom 15 Tesla Philips Intera machine Images were obtainedwith a pixel size of 082 times 082mm2 covering the wholeventricle with short-axis slices of 10m thickness withoutinterslice gap As shown in Figure 1 manual segmentation ofthe myocardium and infarction tissues were used to form thelabeled training sets for the both tissues The CMR imageswere not preprocessed before experimenting

22 Segmentation Using Bayes DecisionTheory The segmen-tation of the scarred and nonscarredmyocardium is obtainedby using Bayes decision theory The class specific probabilitydensity function (PDF) modeling specific feature vectorvalues discriminating the scar or the healthymyocardial areasis estimated as 119901(k | scar) and 119901(k | myo) respectivelyIn addition prior probabilities expressing the proportions ofthe number of observed pixels being either scar or healthymyocardium are estimated as119875(scar) and119875(myo) Accordingto Bayes rule the posterior probability of a pixel being scarredand healthy myocardium can be calculated as

119875 (scar | k) =

(119875 (scar) 119901 (k | scar))119901 (k)

(1)

119875 (myo | k) =(119875 (myo) 119901 (k | myo))

119901 (k) (2)

where 119901(k) = 119875(scar)119901(k | scar)+119875(myo)119901(k | myo) and k isthe feature vector The class specific PDFs can be estimatedusing parametric or nonparametric methods In this workthe parameters in the class specific PDFs are calculatedusing Maximum Likelihood (ML) estimation The ML [17]technique is a popular method for parametric estimation ofan unknown PDF The ML estimates of the mean mML andthe covariance matrix SML of normally distributed data V =

k1 k2 k

119905 k

119871 are given below

mML =1

119871

119871

sum

119894=1

k119894

SML =1

119871

119871

sum

119894=1

(k119894minusmML) (k119894 minusmML)

119879

(3)

where 119871 is the number of training feature vectorsFor a specific image k can be computed for every pixel

in the segmented myocardium and the value of 119875(scar | k)and 119875(myo | k) can be computed for each of these pixelsaccording to (1) There could be different ways of finding thefeatures of the myocardium The feature value k can be ofany dimension and in this work they are based on meanintensity and texture of each pixel in the myocardium Theextraction of feature vectors for themyocardium is illustratedin the following Section 23 Feature vector k of myocardiumin general can be represented as

k = [feature1 feature

2 feature

119897] (4)

where 119897 is the dimension of feature vector k Finally thesegmentation of scarred and nonscarred myocardium isobtained by assigning the pixel to the class that has greaterposterior probability

Figure 1 Cropped short-axis CMR image showingmanual segmen-tation of myocardium and scar tissues The green and blue dotsin the image are manually marked (by cardiologist) coordinatesto segment the myocardium and scar The magenta and yellowcontours generated by cubic spline interpolations of the abovecoordinates show the myocardium and scar tissues respectively

23 Extraction of Features As discussed in Section 1 featuresbased on intensity and texture information are used for thesegmentation of scarred and nonscarred myocardium Themean intensity value of sliding window image patches is usedto obtain the DC feature for each pixel dc(119894 119895) The texturefeatures are calculated using sparse representation by cap-turing the underlying texture information using dictionarylearning techniques The texture features are named 119877

119904(119894 119895)

119877119898(119894 119895) and 119877

119901(119894 119895) and will be discussed in detail 119877

119898(119894 119895)

is correlated with textural features of the healthy myocardialregion and 119877

119904(119894 119895) is correlated with textural features of the

scarred region 119877119901(119894 119895) is a scaled value of the above two

texture featuresThe four combination of features used in thiswork are represented as follows

k = [dc (119894 119895)] k = [dc (119894 119895) 119877119904(119894 119895) 119877

119898(119894 119895)]1015840

k = [dc (119894 119895) 119877119901(119894 119895)]

1015840

k = [119877119901(119894 119895)]

(5)

The detailed process of extracting the DC and texturefeatures is discussed in the following Sections 231 and 232

231 DC Feature Historically in electronics field the meanis commonly referred to as DC (direct current) value [18]We define the feature dc(119894 119895) = mean(119868radic119873timesradic119873(119894 119895)) (where119868radic119873timesradic119873

is the neighborhood around the pixel 119868(119894 119895)) suchthat a new image 119868dc with dc(119894 119895) as values at pixel posi-tion (119894 119895) is made as a sliding window averaging over themyocardium DC-value dc(119894 119895) has been used to segmentscarred myocardium because of the intensity differencespresent in the healthy and scarred myocardium tissuesenhanced with the contrast agentsThe intensity variations ofthe scarred and healthy myocardium in LG enhanced CMRimage are visible in Figure 1 This is probably the featurethat would match the cardiologists segmentation best since


it reflects the type of information (intensity variations) theyuse to manually segment the scarred tissue from the healthymyocardium in the CMR images

232 Dictionary-Based Textural Features Sparse represen-tations and learned dictionaries have been shown to workwell for texture classification by Skretting and Husoy in [19]and by Mairal et al [20] Sparse representation of learneddictionary atoms reflects the typical texture present in thetraining set For each pixel in the myocardium two texturalfeatures are calculated using dictionary learning and sparserepresentation One is correlated with textural features ofhealthy myocardial region 119877

119898(119894 119895) and the other one is

correlated with textural features of scarred region 119877119904(119894 119895)

In this paper Recursive Least Squares Dictionary LearningAlgorithm (RLS-DLA) presented in [21] is used for dictionarylearning and ORMP vector selection algorithm presented in[22] is used for sparse representation

233 Recursive Least Squares Dictionary Learning AlgorithmA dictionary 119863 is an ensemble of finite number of atomsand can be used to represent signals A linear combinationof some of the atoms in the dictionary gives exact or approx-imate representation of the original signal Let a columnvector 119909 of finite length 119873 represent the original signal Thedictionary atoms are arranged as columns in a119873 times119870matrix119863 The representation or the approximation of the signal 119909and the representation error 119903 can be expressed as

119909 =

119870

sum

119896=1

119908 (119896) 119889(119896)

= 119863119908 119903 = 119909 minus 119909 = 119909 minus 119863119908 (6)

where 119908 is sparse coefficient vectorDictionary learning is the task of learning or training a

dictionary on a available training set such that it adapts wellto represent that specific class of signals The training vectorsand the sparse coefficients are arranged as columns in thematrices 119883 and 119882 respectively The objective in dictionarylearning is to give a sparse representation of the training set119883 in order tominimize the sum of the squared errorThe costfunction is formulated as

argmin119863119882

119865 (119863119882) = argmin119863119882

sum

119894

1003817100381710038171003817119903119894

1003817100381710038171003817

2

2st 1199080 le 119904 (7)

where 119904 is sparsity The pseudonorm sdot 0is the number of

nonzero elements This is a very hard optimization problemThe problem can be solved in two steps algorithm Step (1)find 119882 using vector selection algorithms keeping 119863 fixedEach column in119882 is given as

119908119894= argmin119908

1003817100381710038171003817119909119894minus 119863119908

119894

10038171003817100381710038172st 1199080 le 119904 (8)

Step (2) keeping119882 fixed find 119863 The dictionary update stepdepends on the dictionary learningmethodwe choose to use

The RLS-DLA algorithm presented in [21] is an on-line dictionary learning algorithm that address the aboveproblems It updates the dictionary with the arrival of each

new training vector In deriving updating rules for RLS-DLA we define 119883

119905= [1199091 1199092 119909

119905] of size 119873 times 119905 119882

119905=

[1199081 1199082 119908

119905] of size 119870 times 119905 and 119862

119905= (119882

119905119882119879

119905)minus1 for the

ldquotime steprdquo 119905 At each times step the dictionary 119863119905minus1

andthe 119862 matrix are updated so that they obey the least squaressolution 119863

119905= (119883

119905119882119879

119905)(119882119905119882119879

119905)minus1 The matrix inversion

lemma (Woodbury matrix identity) is applied on 119862119905to get

the following update rules

119862119905= 119862119905minus1

minus 120572119906119906119879

119863119905= 119863119905minus1

+ 120572119903119905119906119879

(9)

where 119906 = 119862119905minus1119908119905and 120572 = 1(1 + 119908119879

119905119906) and 119903

119905= 119909119905minus 119863119905minus1119908119905

is the approximation errorWith the inclusion of an adaptive forgetting factor 120582

119905in

RLS-DLA the update equation (9) is changed to

119862119905= (120582minus1

119905119862119905minus1) minus 120572119906119906

119879 (10)

where 119906 = (120582minus1119905119862119905minus1)119908119905 The remaining equations remain the

same Due to introduction of the forgetting factor RLS-DLAhas good converging properties and is less dependent on theinitial dictionary RLS-DLA requires less training time due toupdating the dictionaries on-line

234 Texture Feature Extraction Using Sparse RepresentationIn Frame Texture Classification Method (FTCM) presentedby Skretting and Husoy [19] texture in a small image patchis modeled as sparse linear combination of dictionary atomsFTCM is developed by modeling a texture as a tiled floorwhere all the tiles are identical The color or the gray levelat a given position in the floor is given by an underlyingcontinuous periodic two-dimensional function It is shownbased on this model that a vector from spatial neighborhoodis indeed a sparse combination of finite dictionary atoms

Texture feature extraction requires testing and trainingphases and the whole CMR data set is divided into trainingand testing images In training phase texture feature 119877

119901 is

computed by sparse representation of training images withthe help of dictionaries learned on the training images Thealgorithm for sparse representation in our work proceedsas follows Consider the myocardium in a CMR image119868 that contains two texture classes healthy and scarredmyocardium The training vector 119910

119897for each pixel in the

training image is made from that specific pixel and itsneighborhood radic119873 times radic119873 In the training set each pixelis categorized into a specified texture class Then the dic-tionaries119863

119904and 119863

119898are trained for the predefined texture

classes (scar and myocardium) using RLS-DLA Using thetwo trained dictionaries each training vector 119910

119897is then

represented sparsely using ORMP vector selection algorithm[22] For training set the residual images 119877

119904and 119877

119898which

are of same size as the original image are calculated for thetwo texture classes For each pixel in the myocardium of atraining image the residuals (or representation errors) for thedictionaries119863

119904and119863

119898are calculated as

119877119904(119894 119895) =

1003817100381710038171003817119910119897minus 119863119904119908119904

119897

1003817100381710038171003817 119877

119898(119894 119895) =

1003817100381710038171003817119910119897minus 119863119898119908119898

119897

1003817100381710038171003817 (11)

where 119908119904119897and 119908119898

119897are sparse coefficient vectors


A pixel should give less error or residual to the dictionaryit belongs Finally the residuals 119877

119904and 119877

119898are combined to

form the texture feature 119877119901 The texture feature is calculated

as the ratio of the residual using119863119898to the sumof the residuals

using119863119904and119863

119898 It is shown as follows

119877119901(119894 119895) =

119877119898(119894 119895)

(119877119904(119894 119895) + 119877

119898(119894 119895))

(12)

Pixel by pixel 119877119901value can be interpreted as the scaling of

residuals 119877119904and 119877

119898 Smaller values of 119877

119901means that the

pixel is not likely to be scar (ie healthy myocardium) andlarger values means that it is likely to be scar The texturefeatures calculated from the training set are used to estimatethe prior probabilities and PDFs The test feature vectorsare collected from the test image set in the same way astraining feature vectors The residual images 119877

119904and 119877

119898for

test images are calculated for 119863119904and 119863

119898as training images

Texture is defined as spatial distribution of gray levels Textureis not pixel-by-pixel local except in the edge between twotexturesTherefore some sort of smoothing is used on the testresidual images before the final segmentation of the scarredmyocardium [19] Before calculating 119877

119901 the test residual

images 119877119904and 119877

119898are smoothed using a 119886 times 119886 pixel separable

Gaussian low pass filter with variance 1205902

3 Experimental Setup

The main aim of our experiments was to compute differentfeatures and compare their ability in segmenting the scarfrom the healthy myocardium using Bayes classifier Theobjectives that were explored in our experiments are thediscriminative power of the features the robustness of the fea-tures and examples of the segmented images for illustrationThe subsequent subsections discuss about the experimentalsetup

31 Experimental Details Our experiments consist of threecases or setups Each experimental case used different param-eters for finding the DC and texture features Table 1 showsdetails of the used parameters The three cases were chosenin order to investigate the following (1) No of trainingpatients required for training the classifier (2) neighborhoodsize needed to find the features of scarred myocardiumand (3) to find sparsity required to represent the originalimage patch in scarred myocardium The three cases wereseparately cross validated four times to test the robustnessof our segmentation technique The 24 patients were dividedinto four groups (G1 G2 G3 and G4) each containing 6patients In case (i) and case (ii) we used one group fortraining and the remaining three groups for testing withfourfold cross validation In case (iii) two groups were usedfor training and the remaining two groups were used fortesting purposes While selecting two groups for trainingthere were six possible ways of combining the four groupsof patients All the six possible combinations were used totrain the dictionaries and the classifier in case (iii) In G3 theintensity values of one specific patient are four times higherthan the average intensity values of the entire CMR data It

Table 1 The three experimental cases used for segmentation ofscarred and nonscarred myocardium

Experimentalparameters

CasesCase (i) Case (ii) Case (iii)

Window size 3 times 3 3 times 3 5 times 5

Sparsity 2 4 2No of training groups(no of patients) 3 (18) 3 (18) 2 (12)

No of testing groups(no of patients) 1 (6) 1 (6) 2 (12)

was considered as an outlier while training the Bayes classifierand hence the patient was removed while training the Bayesclassifier for all feature combinations in three cases Howeverthe patient was allowed to be used as a test patient

32 Training and Testing Phase In all CMR Images we takeinto account only myocardium segmented by cardiologistsThe training phase involves extraction of the DC and texturefeatures in all the three cases The process was illustrated inSections 321 and 322

321 Extraction of DC Feature 119889119888(119894119895) Two sets of trainingvectors were generated from scar and healthy myocardiumThe neighborhood size 3 times 3 and 5 times 5 were used to formtraining vectors as explained in Section 231The sameneigh-borhood size must be used while training and finding the DCimages 119868dcTheDC images obtained from the training imageswere used to form the training feature set The parameters ofthe class specific PDFs the mean and the standard deviationwere found using ML estimation according to (1) using thetraining feature set DC values were scaled to have zeromean and unit variance before finding the ML estimates Thescaling coefficients from the training were stored to scale thetest vectors

322 Extraction of Texture Features 119877119904(119894119895) 119877

119898(119894119895) and

119877119901(119894119895) The texture features were calculated using the same

training and test set employed in finding the DC featuresTwo sets of training vectors were generated from the scarredand nonscarred myocardium segmented by cardiologistsThe training vector and test vectors were generated in thesame way as in the DC feature experiment using the sameneighborhood sizes Consider the pixels on the border zonestheir neighborhood extends into other regions that arenot under consideration If we use training vectors fromborder regions then the dictionaries might learn the textureproperties of other regions along with the texture propertiesthey were intended to learn So the training vectors forthe pixels whose neighborhood span other regions were notconsidered in our experiments This is depicted in Figure 2The dictionaries were learned by RLS-DLA as explainedin Section 233 after generating the training vectors fromboth areas The dictionary sizes of 9 times 90 and 25 times 150were used in the experiments with window sizes 3 times 3 and5 times 5 respectively The initial dictionaries were formed by


Myocardium

Scar

Other image parts

Other image parts

P1P2

P3P4

P5

Figure 2 The training vector of a pixel is extracted as long as itsneighborhood iswithin one texture areaTheneighborhood of pixels11987531198754 and119875

5includesmore than one texture and the corresponding

feature vectors are excluded from the training set 1198751and 119875

2have

the entire neighborhood within one texture region and hence thecorresponding feature vector is included in that texturersquos training set

randomly selecting 90(150) vectors of length 9(25) from thetraining sets The forgetting factor was initialized to 0995and slowly increased towards 1 according to the exponentialmethod described in [21] The sparsities 119904 used in our workare 2 and 4 For each pixel in the myocardium of trainingimages the scaled residual 119877

119901(119894 119895) was found from residual

images as explained in Section 234 The training feature setwas generated from119877

119904(119894 119895)119877

119898(119894 119895) and119877

119901(119894 119895)The training

feature set generated from texture features was used to trainthe Bayes classifier as described in Section 22

In the testing phase the DC and texture featureswere generated as in the training phase As described inSection 234 the only difference in the testing phase is thatthe test residual images 119877

119904(119894 119895) 119877

119898(119894 119895) and 119877

119901(119894 119895) were

smoothed using low pass Gaussian filter with 120590 = 5 and 9 times 9window size Finally the segmentation results of the scarredmyocardium were generated employing Bayes classifier asexplained in Section 22

33 ROC Analysis The DC and texture features 119877119904 119877119898

119877119901could be combined in different ways In all the three

experimental cases four combinations of feature vectors weretested They are (1) dc (2) dc 119877

119904 119877119898 (3) dc 119877

119901 and

(4)119877119901 The segmentation results obtained in all the three

cases with the four combinations of features were comparedto the manual segmentation to obtain Receiver OperatingCharacteristic (ROC) curves [23] Area under curve (AUC)was used to quantify the performance of the classifier In allthe three cases each feature combination was subjected tofourfold cross validation In order to find the discriminativepower of the four feature combinations the true positivesand true negatives of all the test patients in the fourfold crossvalidation were averaged to find the AUC values in the threecases

The standard deviation of AUC values was computed toexamine the robustness of the DC and texture features Thestandard deviation of AUC value was computed from the

Table 2 Comparison of the average AUC values from the ROCanalysis of the four different feature combinations in the threeexperimental cases

TestingAverage of AUC values

Cases (window size sparsity) dc 119877119904 119877119898 dc 119877

119901 dc 119877

119901

Case (i) (3 times 3 2) 092 092 092 085Case (ii) (3 times 3 4) 092 092 092 086Case (iii) (5 times 5 2) 091 090 091 086

mean true positives and true negative for all the 24 patientsThe sensitivity (true positives) and specificity (true negatives)of each patient in all the cross validations of case (i) case (ii)and case (iii) had to be averaged before finding the standarddeviation due to the multiple testing of each patient in allthe cases The confidence interval in Figure 4 was also foundin the same way The results are discussed in the followingsection

4 Results and Discussion

Referring to the ROC analysis the discriminative power ofthe four feature combinations and the robustness of the DCand texture feature are discussed in the subsequent sections

41 Discriminative Power of Features The average ROCcurves of the three cases are shown in Figure 3 and thecorresponding AUC values are tabulated in Table 2 The DCfeature performed well as seen in Figure 3 and Table 2 FromTable 2 it can be found that the feature combinations (1)dc (2) dc 119877

119904 119877119898 and (3) dc 119877

119901give almost similar AUC

values in all the three cases The performance of DC featurealone aswell as other combinations using theDC feature givesalmost same performance with different number of trainingpatients and window size The texture features did not addany discriminative power to the DC based classifier Complexclassifiers and improved ways of combining DC and texturefeatures might be required to take advantage of the DC andtexture feature combinations

The average AUC values of texture feature 119877119901 are less

than the average AUC values of the other feature combina-tions This could be partly due to the smoothing of residualsimages during final segmentation The smoothing helped inincreasing the classification power between the two textureregions but it might had introduced false negatives at borderareas The sparsity 119904 was chosen as two and four as thediscriminative power of residuals of both texture classes willbe less when we use more dictionary atoms to representthe test vector The texture feature 119877

119901performed better in

case (iii) and it shows that the texture feature might needmore training patients or a window size of 5 times 5 for bettersegmentation There has been good agreement between theaverage AUC values of training and test patients in all casesand feature combinations

Figure 7 shows the segmentation of scarred myocardiumusing the DC and texture feature 119877

119901 at 80 sensitivity


1

09

08

07

06

05

04

03

02

01

00 02 04 06 08 1

DCRp

Rp DCRs Rm DC

DCRp

Rp DCRs Rm DC

Sens

itivi

ty

1 minus specificity

1

09

08

07

06

05

04

03

02

01

0

Sens

itivi

ty

1

09

08

07

06

05

04

03

02

01

0

Sens

itivi

ty

0 02 04 06 08 1

1 minus specificity0 02 04 06 08 1

1 minus specificity

DCRp

Rp DCRs Rm DC

Window = 3 times 3 sparsity = 2 Window = 3 times 3 sparsity = 4 Window = 5 times 5 sparsity = 2

Case (iii) window size 5 times 5 and S = 2Case (i) window size 3 times 3 and S = 2 Case (ii) window size 3 times 3 and S = 4

Figure 3 ROC curves for the three experimental cases and feature combinations (i) dc (ii) dc 119877119898 119877119904 (iii) dc 119877

119901 and (iv) 119877

119901 In all the

three cases the first three feature combinations have similar performance and the fourth feature performance is low when compared to otherfeature combinations

1

09

08

07

06

05

04

03

02

01

010908070605040302010

Sens

itivi

ty

1 minus specificity

DCUpper confidence limit of DCLower confidence limit of DCRp

Upper confidence limit of Rp

Lower confidence limit of Rp

Case (iii) window size 5 times 5 and S = 2

Window = 5 times 5 sparsity = 2

Ciofolo et al [6] (reported results)

Figure 4 ROC curves of the DC dc and texture feature 119877119901 with

confidence interval in case (iii)

level in the second trial of case (i) (the color description isexplained under the figure) The segmentation results fromDC and texture feature in Figure 7 shows that at the samesensitivity level the texture feature gives more false positivesin the first three CMR slices

Figure 8 shows the segmentation of scarred myocardiumat various sensitivity levels (95 90 85 80 and 75)on the ROC curves of DC and texture feature 119877

119901 The

specificity decreases faster for texture feature 119877119901 compared

to DC feature at the same sensitivity levelsThe false positivessegmented with the texture feature in Figure 8 at varyingsensitivity levels are connected together instead of beingrandom One can speculate that this can be gray-zone areaof the scarred myocardium Gray-zone area [12 13] is the

Table 3 Comparison of the standard deviation AUC values of 24patients from the fourfold cross validation of four different featurecombinations in the three experimental cases

Standard deviation of AUC values of 24 patientsCases (window size sparsity) dc 119877

119904 119877119898 dc 119877

119901 dc 119877

119901


area where the healthy and the scarred myocardium areinterwoven together

42 Robustness of Features Patient specific scaling of inten-sity values might be a problem as for the robustness ofthe analyzed features Hence we focused to analyze therobustness of DC and texture features individually Table 3shows the standard deviation of theAUCvaluesThe standarddeviation of AUC values of DC feature and its combinationsare less compared to the texture feature 119877

119901 The standard

deviation of AUC values of 119877119901in case (iii) is slightly less

compared to other cases of 119877119901 Though the number of test

patients are different in the cases the reduction in standarddeviation of 119877

119901of case (iii) shows that the texture feature

might require more training patients and a window sizeof 5 times 5 Figure 4 shows ROC curves of DC and texturefeature 119877

119901 with confidence limits of case (iii) In case (iii)

where the texture feature performswell the upper confidencelimit of the texture feature 119877

119901 almost coincidences with

average ROC curve of the DC feature This indicates that theperformance of DC and texture is not significantly different

In order to show that the texture feature performance isrobust on the outliers we simulated a test set by scaling theoriginal intensities of CMR slices The CMR images used inour work are from the same MRI device Even though theMRI machine automatically tries to produce MRI images tobe in the same scale of intensities the CMR images of all the


0 1 2 3 4 5 6 7 8 9 10

Intensity scale

0 1 2 3 4 5 6 7 8 9 10

Intensity scale0 1 2 3 4 5 6 7 8 9 10

Intensity scale

0 1 2 3 4 5 6 7 8 9 10

Intensity scale0 1 2 3 4 5 6 7 8 9 10

Intensity scale

0 1 2 3 4 5 6 7 8 9 10

Intensity scale0 1 2 3 4 5 6 7 8 9 10

Intensity scale

0 1 2 3 4 5 6 7 8 9 10

Intensity scale

AUC

valu

eAU

C va

lue

AUC

valu

e

DCRp

DCRp

1

095

09

085

08

075

1

098

096

094

092

1

095

09

085

08

1

095

09

085

092

09

088

086

084

082

1

095

09

085

1

095

09

085

08

095

09

085

08

075

AUC

valu

eAU

C va

lue

AUC

valu

eAU

C va

lue

AUC

valu

e

Figure 5 AUC values of 8 patients whose CMR slices are scaled at different factors

09

08

07

06

05

04

03

02

01

0

minus010 10 20 30 40 50 60 70 80 90 100

Sensitivity level

Dic

e met

ric

DCDC-upper limitDC-lower limitRp

Rp-upper limitRp-lower limitRp DC

Rp DC-upper limitRp DC-lower limitRs Rm DCRs Rm DC-upper limitRs Rm DC-lower limitTao Dice metric Da1Tao Dice metric Da2

Figure 6 Similarity measuremdashDice index [7] calculated on our CMR data at different sensitivity levels of the ROC analysis The Dice indexat various sensitivity levels is compared to the reported results by Tao et al in [7]


(a) (b) (c)

Figure 7The segmentation plots of the scarred myocardium in the CMR images of the patients implanted with ICD using the DC value andtexture feature 119877

119901 in the second trial of case (i) at 80 sensitivity level on the ROC curve Column (a) the cropped CMR images containing

left ventricle (b) The manually segmented myocardium along with the segmentation results using the DC feature (c) The segmentationresults of the scarred myocardium using the texture feature 119877

119901 Color Specification blue myocardium cyan scar and yellow other image

parts and black contour is the cardiologists segmentation of the scarred myocardium

patients used in our work vary from one patient to anotherWith our CMR data the DC feature performed better thanthe texture feature The AUC values for the simulated testwere calculated using the already trained classifier in case(iii) The AUC values of the simulated testing set of a patientare plotted against the scaling factor in Figure 5 Figure 5shows the plots of several AUC values versus intensity scalingfactor of eight patients The initial impression of Figure 5is that the texture features give the same performance fordifferent scaling factors whereas the DC feature performancevaries either by increasing or decreasing the scaling factorFigure 5 infers that theDC feature gives good performance onthe test patient whose intensities fall in the range of the train-ing patient set whereas texture feature119877

119901 performance is not

altered with intensity variations The robust performance ofthe texture feature on different scaling factors might implythat the dictionaries captured the physiological differencebetween the scarred and nonscarredmyocardiumThereforewe belief that the textural features might give details that are

not perceived by the cardiologist and not credited in the ROCanalysis

43 Comparison to Previous Works The segmentation ofthe scarred and nonscarred myocardium using the DC andtexture feature was compared to Dikici et al [5] The mainresults reported by Dikici et al [5] (sensitivity 8134 andspecificity 9228) were plotted as one isolated point inFigure 4 compared to the ROC plots of DC and texturefeatures in case (iii) This point lies above both these ROCcurves but not above the 95 confidence interval of the DCfeature The result is however not calculated on our studymaterial but is included for comparison Dikici et al [5] doesnot include all the CMRI slices of a patient for training andtesting where as in our work we include all the CMRI slicesthat is the scar volume

Figure 6 shows the similarity measure Dice index [7]calculated on volume of the scar at different sensitivity levels


(a) (b) (c)

Figure 8The segmentation results of the scarred myocardium in the CMR image of a patient implanted with ICD using the DC and texturefeature 119877

119901 in the second trial of case (i) at 95 90 85 80 and 75 sensitivity levels on the ROC curve Column (a) the cropped CMR

images containing left ventricle (b)The manually segmented myocardium along with the segmentation results using the DC feature (c) Thesegmentation results of the scarred myocardium using the texture feature 119877

119901 Color Specification blue myocardium cyan scar and yellow

other image parts and black contour is the cardiologists segmentation of the scarred myocardium

on our CMR data Dice index gives the percentage of overlapbetween manual and automatic segmentation [7] The Diceindex increases till 80 sensitivity level and falls later dueto the increase in false positives The Dice index measuresreported by Tao et al in [7] were compared to Dice indexmeasures calculated at 80 sensitivity level and they wereplotted as two isolated points (compared to two manualsegmentations) in Figure 6 Figure 6 shows that one point isabove all the Dice index curves whereas the other point lieson the upper limit of the DC feature and its combinationsTheDice index of DC and otherDC combinations performed

better than the texture feature While Tao et al calculatedDice index at volumetric level in [7] CMR image slices withsmall scar size were removed totally as the slices with smallscar sizes give zero Dice index and it effects the averageDice index measures In our Dice index calculations weconsidered all image slices regardless of the size of the scarThis could be a reason for the low Dice index measures onour data compared to Tao et al [7] reported results Anotherreason for the low Dice index measures of our method couldbe due to the false acceptance and false rejection removalstages after thresholding in [7]


5 Conclusion

The DC feature segments the scarred myocardium compara-tively better than the texture feature on our CMR data andthe combination of the DC and texture features does notseem to improve the overall performance compared to theDC feature alone The DC feature also needs fewer trainingpatients than the texture feature method seems to needHowever the texture feature from the learned dictionariesand sparse representation is shown to be much more robustwhen it comes to scaling variations that is variations in theintensity value range The DC feature seems to reflect theway cardiologist perceive the scarred myocardium in CMRimages whereas our results indicate that the texture featurescan be explored to investigate the heterogeneous nature of thescarred myocardium Our belief that the texture feature canbe used to explore the properties of the scarred myocardiumgot strengthenedwith the cardiac segments experiment basedon the probability mapping of the scarred myocardium inour recent paper [24] Our method uses the entire scarvolume for training and testing the classifier and works wellin comparison to the previous works which did not use thethe entire scar volume either during training or testing [5 7]Other ways of combining DC and texture features and othertexture features will be explored in future work

Conflict of Interests

The authors declare that they have no conflict of Interests

References

[1] S Oslashrn CManhenke I S Anand et al ldquoEffect of left ventricularscar size location and transmurality on left ventricular remod-eling with healed myocardial infarctionrdquo American Journal ofCardiology vol 99 no 8 pp 1109ndash1114 2007

[2] A T Yan A J Shayne K A Brown et al ldquoCharacterization ofthe peri-infarct zone by contrast-enhanced cardiacmagnetic re-sonance imaging is a powerful predictor of post-myocardial inf-arction mortalityrdquo Circulation vol 114 no 1 pp 32ndash39 2006

[3] LWoie T Eftestoslashl K Engan J T Kvaloslashy DW T Nilsen and SOslashrn ldquoThe heart rate of ventricular tachycardia following an oldmyocardial infarction is inversely related to the size of scarringrdquoEuropace vol 13 no 6 pp 864ndash868 2011

[4] E Heiberg H Engblom J Engvall E Hedstrom M Uganderand H Arheden ldquoSemi-automatic quantification of myocardialinfarction from delayed contrast enhanced magnetic resonanceimagingrdquo Scandinavian Cardiovascular Journal vol 39 no 5pp 267ndash275 2005

[5] E Dikici T OrsquoDonnell R Setser and R DWhite ldquoQuantifica-tion of delayed enhancement MR imagesrdquo in Proceedings of the7th International Conference on Medical Image Computing andComputer-Assisted Intervention (MICCAI rsquo04) vol 3216 pp250ndash257 September 2004

[6] C Ciofolo M Fradkin B Mory G Hautvast andM BreeuwerldquoAutomatic myocardium segmentation in late-enhancementMRIrdquo in Proceedings of the 5th IEEE International Symposiumon Biomedical Imaging from Nano to Macro (ISBI rsquo08) pp 225ndash228 May 2008

[7] Q Tao J Milles K Zeppenfeld et al ldquoAutomated segmentationof myocardial scar in late enhancement MRI using combinedintensity and spatial informationrdquo Magnetic Resonance inMedicine vol 64 no 2 pp 586ndash594 2010

[8] C Corsi G Tarroni A Tarroni et al ldquoAutomatic quantificationof cardiac scar extent from late gadolinium enhancement mrirdquoin Proceedings of the Computing in Cardiology HangzhouChina 2011 httpwwwcincorg2011preprints205pdf

[9] A Kolipaka et al ldquoSegmentation of non-viable myocardium indelayed enhancement magnetic resonance imagesrdquo Scandina-vian Cardiovascular Journal vol 39 no 5 pp 267ndash275 2005

[10] A O Algohary AM El-Bialy et al ldquoDetection of cardiac infar-ction in MRI C-SENC imagesrdquo Universal Journal of ComputerScience Engineering Technology pp 36ndash40 2010

[11] L Shapiro and G Stockman Computer Vision Prentice HallUpper Saddle River NJ USA 2001

[12] S D Roes C J W Borleffs R J Van Der Geest et al ldquoInfarcttissue heterogeneity assessed with contrast-enhancedmri pred-icts spontaneous ventricular arrhythmia in patients with ische-mic cardiomyopathy and implantable cardioverter-defibrilla-torrdquo Circulation vol 2 no 3 pp 183ndash190 2009

[13] A Schmidt C F Azevedo A Cheng et al ldquoInfarct tissue hete-rogeneity by magnetic resonance imaging identifies enhancedcardiac arrhythmia susceptibility in patients with left ventric-ular dysfunctionrdquo Circulation vol 115 no 15 pp 2006ndash20142007

[14] K Engan T Eftestoslashl S Oslashrn J T Kvaloslashy and LWoie ldquoExplorat-ory data analysis of image texture and statistical features onmy-ocardium and infarction areas in cardiac magnetic resonanceimagesrdquo in Proceedings of the 32nd Annual International Con-ference of the IEEE Engineering in Medicine and Biology Society(EMBC rsquo10) pp 5728ndash5731 September 2010

[15] L P Kotu K Engan T Eftestoslashl S Oslashrn and L Woie ldquoTextureclassification of scarred and non-scarred myocardium in car-diac MRI using learned dictionariesrdquo in Proceedings of the 18thIEEE International Conference on Image Processing (ICIP rsquo11) pp65ndash68 September 2011

[16] L P Kotu K Engan T Eftestoslashl et al ldquoLocal binary patternsused on cardiacmri to classify high and low risk patient groupsrdquoin Proceedings of the 20th European Signal Processing Conference(EUSIPCO rsquo12) pp 2586ndash2590 2012

[17] S Theodoridis and K Koutroumbas Pattern Recognition Aca-demic Press 4th edition 2008

[18] K Sayood Data Compression Academic Press London UK2nd edition 2000

[19] K Skretting and J HHusoy ldquoTexture classification using sparseframe-based representationsrdquo Eurasip Journal on Applied SignalProcessing vol 2006 pp 1ndash11 2006

[20] J Mairal F Bach J Ponce G Sapiro and A Zisserman ldquoDis-criminative learned dictionaries for local image analysisrdquo inProceedings of the 26th IEEEConference onComputer Vision andPattern Recognition (CVPR rsquo08) pp 1ndash8 June 2008

[21] K Skretting and K Engan ldquoRecursive least squares dictionarylearning algorithmrdquo IEEE Transactions on Signal Processing vol58 no 4 pp 2121ndash2130 2010

[22] M Gharavi-Alkhansari and T S Huang ldquoFast orthogonal mat-ching pursuit algorithmrdquo in Proceedings of the IEEE Interna-tional Conference on Acoustics Speech and Signal Processing(ICASSP rsquo98) pp 1389ndash1392 May 1998


[23] T Eftestoslashl ldquoControlling true positive rate in ROC analysisrdquo inProceedings of the 36th Annual Conference of Computers inCardiology CinC 2009 pp 353ndash356 September 2009

[24] L P Kotu et al ldquoProbability mapping of scarred myocardiumusing texture and intensity features inCMR imagesrdquoBioMedicalEngineering Online vol 12 article 91 2013

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

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Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



not take into account that the degree of damage can varyfrom patient to patient and therefore the threshold of 80 isnot suitable for all the patients A simple threshold is almostguaranteed to produce some small false detection areas insome slices

Dikici et al [5] use a Support Vector Machine (SVM)classifier to distinguish between the scarred and healthymyocardium tissue They argue to use a supervised classifierrather than a method based on thresholding because thedegree of damage can vary from patient to patient and alsobecause of the partial voluming effects The three featuresthey use in the classifier are (i) the intensity of a pixel relativeto the averagemyocardial intensity (ii) the standard deviationof the relative pixel intensities with respect to its nextneighbors and (iii) myocardial contrast defined as the ratioof the mean myocardial intensity over the mean intensity ofthe entire image Features (i) and (ii) are calculated for everypixel whereas feature (iii) is calculated for every slice Allthe calculations and scaling are performed on a slice by slicelevel In training and testing they use only three slices foreach patient from the middle of the ventricle The reportedsegmentation accuracy on these middle slices is 8839 witha sensitivity of 8134 and specificity of 9228 Feature (i)seems to be very dependent on the scar size at that particularslice and would possibly benefit from being calculated overthe entire 3D volume instead Since they only test the middleslices they will not experience the slices near the top orbottom of the heart where the scar can cover most of themyocardial muscle Feature (ii) applies local characteristicsand can be considered a textural measure

The approach by Tao et al [7] is a three step method(i) initialization (ii) false acceptance removal and (iii)false rejection removal The initialization is based on Otsursquosmethod for thresholding that is the probability densityfunction (PDF) of the intensity levels is estimated and athreshold is found as a function of the estimated PDF Thetechnique expects a bimodal PDF for a two class problemand uses an optimization criterion to maximize the ratioof between-class variance and within-class variance Startingwith a segmented heart muscle this does not work very wellbecause the scar is much smaller than the healthy area andthe bimodality of the PDF is not very evident Tao et alsuggest to improve this by including the blood pool Thusthey are actually finding a good threshold to separate theblood pool from the heart muscle The scar will be closerto the blood pool than to the healthy myocardium in termsof intensity levels and this way they separate the scarredarea from the healthy myocardial area The thresholding isperformed jointly on the entire 3D volume (all slices) It isfollowed by false acceptance removal by connectivity filteringusing a two pass algorithm [11] The false acceptance removalis performed on a slice to slice level and will remove smalland thin areas labeled as scar after the thresholding Regiongrowing is done as a last step Voxels that are connected to thescarred region and having intensity values larger than 2 times SDof the healthy region are included in the scarred region Theregion growing is done on a slice by slice level so that the SDis calculated for each slice Tao et al report experiments of20 postinfarction patients compared tomanually traced scars

from two individual observers using the Dice index metricsThe method is dependent on the blood pool intensity levelwhich might be questionable Local textures are not takeninto account

Recent studies showed that the scar tissue is hetero-geneous in nature and that the mortality of patients withreduced LVEF depends on the heterogeneity of scar tissue [1213] Texture features from gray-level co-occurrence matricesand Local Binary Patterns (LBPs) were used in our grouprsquosprevious work to classify patients with high and low risk ofgetting arrhythmia [14 15] Other results from our recentwork [16] strengthened our claim that there are texturaldifferences between the healthy myocardium and the scartissue thus we want to explore this furtherWe are concernedabout the fact that not all slices (or patients) have scar Wealso know that the degree of damage will vary from patientto patient and thus the intensity levels of the scar relative tothe healthy myocardiummight differ from patient to patientmaking relative features problematic On the other hand theintensity values of the healthy myocardium might vary frompatient to patient making absolute features problematicThus we do not want to base the method on thresholding butrather train a classifier with both textural and intensity basedfeatures conceptually related to Dikicirsquos method Howeverwe believe that we need to consider the whole 3D volumeof the myocardium as the basis in all our calculations Thiswill include slices without scar occasionally andor sliceswith scars covering the entire myocardium To avoid theproblemof the varying degree of damage (or even no damage)we classify the LGE-CMR images without scaling relativeto assumed healthy areas or maximum values (assumed tobe scar) The problem of the intensity values varying frompatient to patient also in the healthy areas is difficult toaddress since the degree of damage can vary at the sametime Thus we carefully exclude a couple of outliers fromour training set however they are included in the test set toexamine the robustness of the methodThe exclusion is doneautomatically in the training process

Section 2 discusses material and methods Section 3shows the experimental frameworkThe results are presentedand discussed in Section 4 Finally the paper is concludedand expected future work is suggested

2 Material and Methods

This section explains the material and methods used inthis work Section 21 discusses the CMR material used inthe experiments The proposed segmentation scheme usingBayes classifier and the feature extraction are illustrated inSection 22 and Section 23 respectively

21 Material The Department of Cardiology in StavangerUniversity Hospital provided the LGE-CMR images forour experiments and the experiments were conducted inMATLAB The LGE-CMR images is a group of 24 patientsall with high risk of getting arrhythmia and they were storedaccording to the Digital imaging and communications inmedicine (DICOM) format with 512 times 512 pixel resolutionThe number of image slices with visible scar in each patientvaries approximately from 5 to 12 depending on the size




119875 (scar | k) =

(119875 (scar) 119901 (k | scar))119901 (k)

(1)

119875 (myo | k) =(119875 (myo) 119901 (k | myo))

119901 (k) (2)


k1 k2 k

119905 k


mML =1

119871

119871

sum

119894=1

k119894

SML =1

119871

119871

sum

119894=1


119879

(3)




2 feature

119897] (4)




119904(119894 119895)

119877119898(119894 119895) and 119877


119898(119894 119895)





k = [dc (119894 119895)] k = [dc (119894 119895) 119877119904(119894 119895) 119877

119898(119894 119895)]1015840

k = [dc (119894 119895) 119877119901(119894 119895)]

1015840

k = [119877119901(119894 119895)]

(5)











119909 =

119870

sum

119896=1

119908 (119896) 119889(119896)

= 119863119908 119903 = 119909 minus 119909 = 119909 minus 119863119908 (6)



argmin119863119882

119865 (119863119882) = argmin119863119882

sum

119894

1003817100381710038171003817119903119894

1003817100381710038171003817

2

2st 1199080 le 119904 (7)



119908119894= argmin119908

1003817100381710038171003817119909119894minus 119863119908

119894

10038171003817100381710038172st 1199080 le 119904 (8)




119905= [1199091 1199092 119909

119905] of size 119873 times 119905 119882

119905=

[1199081 1199082 119908

119905] of size 119870 times 119905 and 119862

119905= (119882

119905119882119879




119905= (119883

119905119882119879

119905)(119882119905119882119879




119862119905= 119862119905minus1

minus 120572119906119906119879

119863119905= 119863119905minus1

+ 120572119903119905119906119879

(9)

where 119906 = 119862119905minus1119908119905and 120572 = 1(1 + 119908119879

119905119906) and 119903

119905= 119909119905minus 119863119905minus1119908119905


119905in


119862119905= (120582minus1

119905119862119905minus1) minus 120572119906119906

119879 (10)





119901 is




119904and 119863



119897is then


119904and 119877

119898which


119904and119863


119877119904(119894 119895) =

1003817100381710038171003817119910119897minus 119863119904119908119904

119897

1003817100381710038171003817 119877

119898(119894 119895) =

1003817100381710038171003817119910119897minus 119863119898119908119898

119897

1003817100381710038171003817 (11)

where 119908119904119897and 119908119898




119904and 119877




using119863119904and119863


119877119901(119894 119895) =

119877119898(119894 119895)

(119877119904(119894 119895) + 119877

119898(119894 119895))

(12)


residuals 119877119904and 119877




119904and 119877

119898for





images 119877119904and 119877
















119898(119894119895) and




Myocardium

Scar

Other image parts

Other image parts

P1P2

P3P4

P5




2have





119904(119894 119895)119877

119898(119894 119895) and119877

119901(119894 119895)The training



119904(119894 119895) 119877

119898(119894 119895) and 119877

119901(119894 119895) were





119904 119877119898 (3) dc 119877

119901 and







119901 dc 119877

119901






119904 119877119898 and (3) dc 119877










1

09

08

07

06

05

04

03

02

01

00 02 04 06 08 1

DCRp

Rp DCRs Rm DC

DCRp

Rp DCRs Rm DC

Sens

itivi

ty

1 minus specificity

1

09

08

07

06

05

04

03

02

01

0

Sens

itivi

ty

1

09

08

07

06

05

04

03

02

01

0

Sens

itivi

ty

0 02 04 06 08 1


1 minus specificity

DCRp

Rp DCRs Rm DC




119901 and (iv) 119877

119901 In all the


1

09

08

07

06

05

04

03

02

01

010908070605040302010

Sens

itivi

ty

1 minus specificity











119901 The





119904 119877119898 dc 119877

119901 dc 119877

119901




119901 The standard












0 1 2 3 4 5 6 7 8 9 10

Intensity scale

0 1 2 3 4 5 6 7 8 9 10

Intensity scale0 1 2 3 4 5 6 7 8 9 10

Intensity scale

0 1 2 3 4 5 6 7 8 9 10

Intensity scale0 1 2 3 4 5 6 7 8 9 10

Intensity scale

0 1 2 3 4 5 6 7 8 9 10

Intensity scale0 1 2 3 4 5 6 7 8 9 10

Intensity scale

0 1 2 3 4 5 6 7 8 9 10

Intensity scale

AUC

valu

eAU

C va

lue

AUC

valu

e

DCRp

DCRp

1

095

09

085

08

075

1

098

096

094

092

1

095

09

085

08

1

095

09

085

092

09

088

086

084

082

1

095

09

085

1

095

09

085

08

095

09

085

08

075

AUC

valu

eAU

C va

lue

AUC

valu

eAU

C va

lue

AUC

valu

e


09

08

07

06

05

04

03

02

01

0

minus010 10 20 30 40 50 60 70 80 90 100

Sensitivity level

Dic

e met

ric






(a) (b) (c)













(a) (b) (c)









5 Conclusion




References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












119875 (scar | k) =

(119875 (scar) 119901 (k | scar))119901 (k)

(1)

119875 (myo | k) =(119875 (myo) 119901 (k | myo))

119901 (k) (2)


k1 k2 k

119905 k


mML =1

119871

119871

sum

119894=1

k119894

SML =1

119871

119871

sum

119894=1


119879

(3)




2 feature

119897] (4)




119904(119894 119895)

119877119898(119894 119895) and 119877


119898(119894 119895)





k = [dc (119894 119895)] k = [dc (119894 119895) 119877119904(119894 119895) 119877

119898(119894 119895)]1015840

k = [dc (119894 119895) 119877119901(119894 119895)]

1015840

k = [119877119901(119894 119895)]

(5)











119909 =

119870

sum

119896=1

119908 (119896) 119889(119896)

= 119863119908 119903 = 119909 minus 119909 = 119909 minus 119863119908 (6)



argmin119863119882

119865 (119863119882) = argmin119863119882

sum

119894

1003817100381710038171003817119903119894

1003817100381710038171003817

2

2st 1199080 le 119904 (7)



119908119894= argmin119908

1003817100381710038171003817119909119894minus 119863119908

119894

10038171003817100381710038172st 1199080 le 119904 (8)




119905= [1199091 1199092 119909

119905] of size 119873 times 119905 119882

119905=

[1199081 1199082 119908

119905] of size 119870 times 119905 and 119862

119905= (119882

119905119882119879




119905= (119883

119905119882119879

119905)(119882119905119882119879




119862119905= 119862119905minus1

minus 120572119906119906119879

119863119905= 119863119905minus1

+ 120572119903119905119906119879

(9)

where 119906 = 119862119905minus1119908119905and 120572 = 1(1 + 119908119879

119905119906) and 119903

119905= 119909119905minus 119863119905minus1119908119905


119905in


119862119905= (120582minus1

119905119862119905minus1) minus 120572119906119906

119879 (10)





119901 is




119904and 119863



119897is then


119904and 119877

119898which


119904and119863


119877119904(119894 119895) =

1003817100381710038171003817119910119897minus 119863119904119908119904

119897

1003817100381710038171003817 119877

119898(119894 119895) =

1003817100381710038171003817119910119897minus 119863119898119908119898

119897

1003817100381710038171003817 (11)

where 119908119904119897and 119908119898




119904and 119877




using119863119904and119863


119877119901(119894 119895) =

119877119898(119894 119895)

(119877119904(119894 119895) + 119877

119898(119894 119895))

(12)


residuals 119877119904and 119877




119904and 119877

119898for





images 119877119904and 119877
















119898(119894119895) and




Myocardium

Scar

Other image parts

Other image parts

P1P2

P3P4

P5




2have





119904(119894 119895)119877

119898(119894 119895) and119877

119901(119894 119895)The training



119904(119894 119895) 119877

119898(119894 119895) and 119877

119901(119894 119895) were





119904 119877119898 (3) dc 119877

119901 and







119901 dc 119877

119901






119904 119877119898 and (3) dc 119877










1

09

08

07

06

05

04

03

02

01

00 02 04 06 08 1

DCRp

Rp DCRs Rm DC

DCRp

Rp DCRs Rm DC

Sens

itivi

ty

1 minus specificity

1

09

08

07

06

05

04

03

02

01

0

Sens

itivi

ty

1

09

08

07

06

05

04

03

02

01

0

Sens

itivi

ty

0 02 04 06 08 1


1 minus specificity

DCRp

Rp DCRs Rm DC




119901 and (iv) 119877

119901 In all the


1

09

08

07

06

05

04

03

02

01

010908070605040302010

Sens

itivi

ty

1 minus specificity











119901 The





119904 119877119898 dc 119877

119901 dc 119877

119901




119901 The standard












0 1 2 3 4 5 6 7 8 9 10

Intensity scale

0 1 2 3 4 5 6 7 8 9 10

Intensity scale0 1 2 3 4 5 6 7 8 9 10

Intensity scale

0 1 2 3 4 5 6 7 8 9 10

Intensity scale0 1 2 3 4 5 6 7 8 9 10

Intensity scale

0 1 2 3 4 5 6 7 8 9 10

Intensity scale0 1 2 3 4 5 6 7 8 9 10

Intensity scale

0 1 2 3 4 5 6 7 8 9 10

Intensity scale

AUC

valu

eAU

C va

lue

AUC

valu

e

DCRp

DCRp

1

095

09

085

08

075

1

098

096

094

092

1

095

09

085

08

1

095

09

085

092

09

088

086

084

082

1

095

09

085

1

095

09

085

08

095

09

085

08

075

AUC

valu

eAU

C va

lue

AUC

valu

eAU

C va

lue

AUC

valu

e


09

08

07

06

05

04

03

02

01

0

minus010 10 20 30 40 50 60 70 80 90 100

Sensitivity level

Dic

e met

ric






(a) (b) (c)













(a) (b) (c)









5 Conclusion




References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
















119909 =

119870

sum

119896=1

119908 (119896) 119889(119896)

= 119863119908 119903 = 119909 minus 119909 = 119909 minus 119863119908 (6)



argmin119863119882

119865 (119863119882) = argmin119863119882

sum

119894

1003817100381710038171003817119903119894

1003817100381710038171003817

2

2st 1199080 le 119904 (7)



119908119894= argmin119908

1003817100381710038171003817119909119894minus 119863119908

119894

10038171003817100381710038172st 1199080 le 119904 (8)




119905= [1199091 1199092 119909

119905] of size 119873 times 119905 119882

119905=

[1199081 1199082 119908

119905] of size 119870 times 119905 and 119862

119905= (119882

119905119882119879




119905= (119883

119905119882119879

119905)(119882119905119882119879




119862119905= 119862119905minus1

minus 120572119906119906119879

119863119905= 119863119905minus1

+ 120572119903119905119906119879

(9)

where 119906 = 119862119905minus1119908119905and 120572 = 1(1 + 119908119879

119905119906) and 119903

119905= 119909119905minus 119863119905minus1119908119905


119905in


119862119905= (120582minus1

119905119862119905minus1) minus 120572119906119906

119879 (10)





119901 is




119904and 119863



119897is then


119904and 119877

119898which


119904and119863


119877119904(119894 119895) =

1003817100381710038171003817119910119897minus 119863119904119908119904

119897

1003817100381710038171003817 119877

119898(119894 119895) =

1003817100381710038171003817119910119897minus 119863119898119908119898

119897

1003817100381710038171003817 (11)

where 119908119904119897and 119908119898




119904and 119877




using119863119904and119863


119877119901(119894 119895) =

119877119898(119894 119895)

(119877119904(119894 119895) + 119877

119898(119894 119895))

(12)


residuals 119877119904and 119877




119904and 119877

119898for





images 119877119904and 119877
















119898(119894119895) and




Myocardium

Scar

Other image parts

Other image parts

P1P2

P3P4

P5




2have





119904(119894 119895)119877

119898(119894 119895) and119877

119901(119894 119895)The training



119904(119894 119895) 119877

119898(119894 119895) and 119877

119901(119894 119895) were





119904 119877119898 (3) dc 119877

119901 and







119901 dc 119877

119901






119904 119877119898 and (3) dc 119877










1

09

08

07

06

05

04

03

02

01

00 02 04 06 08 1

DCRp

Rp DCRs Rm DC

DCRp

Rp DCRs Rm DC

Sens

itivi

ty

1 minus specificity

1

09

08

07

06

05

04

03

02

01

0

Sens

itivi

ty

1

09

08

07

06

05

04

03

02

01

0

Sens

itivi

ty

0 02 04 06 08 1


1 minus specificity

DCRp

Rp DCRs Rm DC




119901 and (iv) 119877

119901 In all the


1

09

08

07

06

05

04

03

02

01

010908070605040302010

Sens

itivi

ty

1 minus specificity











119901 The





119904 119877119898 dc 119877

119901 dc 119877

119901




119901 The standard












0 1 2 3 4 5 6 7 8 9 10

Intensity scale

0 1 2 3 4 5 6 7 8 9 10

Intensity scale0 1 2 3 4 5 6 7 8 9 10

Intensity scale

0 1 2 3 4 5 6 7 8 9 10

Intensity scale0 1 2 3 4 5 6 7 8 9 10

Intensity scale

0 1 2 3 4 5 6 7 8 9 10

Intensity scale0 1 2 3 4 5 6 7 8 9 10

Intensity scale

0 1 2 3 4 5 6 7 8 9 10

Intensity scale

AUC

valu

eAU

C va

lue

AUC

valu

e

DCRp

DCRp

1

095

09

085

08

075

1

098

096

094

092

1

095

09

085

08

1

095

09

085

092

09

088

086

084

082

1

095

09

085

1

095

09

085

08

095

09

085

08

075

AUC

valu

eAU

C va

lue

AUC

valu

eAU

C va

lue

AUC

valu

e


09

08

07

06

05

04

03

02

01

0

minus010 10 20 30 40 50 60 70 80 90 100

Sensitivity level

Dic

e met

ric






(a) (b) (c)













(a) (b) (c)









5 Conclusion




References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119904and 119877




using119863119904and119863


119877119901(119894 119895) =

119877119898(119894 119895)

(119877119904(119894 119895) + 119877

119898(119894 119895))

(12)


residuals 119877119904and 119877




119904and 119877

119898for





images 119877119904and 119877
















119898(119894119895) and




Myocardium

Scar

Other image parts

Other image parts

P1P2

P3P4

P5




2have





119904(119894 119895)119877

119898(119894 119895) and119877

119901(119894 119895)The training



119904(119894 119895) 119877

119898(119894 119895) and 119877

119901(119894 119895) were





119904 119877119898 (3) dc 119877

119901 and







119901 dc 119877

119901






119904 119877119898 and (3) dc 119877










1

09

08

07

06

05

04

03

02

01

00 02 04 06 08 1

DCRp

Rp DCRs Rm DC

DCRp

Rp DCRs Rm DC

Sens

itivi

ty

1 minus specificity

1

09

08

07

06

05

04

03

02

01

0

Sens

itivi

ty

1

09

08

07

06

05

04

03

02

01

0

Sens

itivi

ty

0 02 04 06 08 1


1 minus specificity

DCRp

Rp DCRs Rm DC




119901 and (iv) 119877

119901 In all the


1

09

08

07

06

05

04

03

02

01

010908070605040302010

Sens

itivi

ty

1 minus specificity











119901 The





119904 119877119898 dc 119877

119901 dc 119877

119901




119901 The standard












0 1 2 3 4 5 6 7 8 9 10

Intensity scale

0 1 2 3 4 5 6 7 8 9 10

Intensity scale0 1 2 3 4 5 6 7 8 9 10

Intensity scale

0 1 2 3 4 5 6 7 8 9 10

Intensity scale0 1 2 3 4 5 6 7 8 9 10

Intensity scale

0 1 2 3 4 5 6 7 8 9 10

Intensity scale0 1 2 3 4 5 6 7 8 9 10

Intensity scale

0 1 2 3 4 5 6 7 8 9 10

Intensity scale

AUC

valu

eAU

C va

lue

AUC

valu

e

DCRp

DCRp

1

095

09

085

08

075

1

098

096

094

092

1

095

09

085

08

1

095

09

085

092

09

088

086

084

082

1

095

09

085

1

095

09

085

08

095

09

085

08

075

AUC

valu

eAU

C va

lue

AUC

valu

eAU

C va

lue

AUC

valu

e


09

08

07

06

05

04

03

02

01

0

minus010 10 20 30 40 50 60 70 80 90 100

Sensitivity level

Dic

e met

ric






(a) (b) (c)













(a) (b) (c)









5 Conclusion




References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Myocardium

Scar

Other image parts

Other image parts

P1P2

P3P4

P5




2have





119904(119894 119895)119877

119898(119894 119895) and119877

119901(119894 119895)The training



119904(119894 119895) 119877

119898(119894 119895) and 119877

119901(119894 119895) were





119904 119877119898 (3) dc 119877

119901 and







119901 dc 119877

119901






119904 119877119898 and (3) dc 119877










1

09

08

07

06

05

04

03

02

01

00 02 04 06 08 1

DCRp

Rp DCRs Rm DC

DCRp

Rp DCRs Rm DC

Sens

itivi

ty

1 minus specificity

1

09

08

07

06

05

04

03

02

01

0

Sens

itivi

ty

1

09

08

07

06

05

04

03

02

01

0

Sens

itivi

ty

0 02 04 06 08 1


1 minus specificity

DCRp

Rp DCRs Rm DC




119901 and (iv) 119877

119901 In all the


1

09

08

07

06

05

04

03

02

01

010908070605040302010

Sens

itivi

ty

1 minus specificity











119901 The





119904 119877119898 dc 119877

119901 dc 119877

119901




119901 The standard












0 1 2 3 4 5 6 7 8 9 10

Intensity scale

0 1 2 3 4 5 6 7 8 9 10

Intensity scale0 1 2 3 4 5 6 7 8 9 10

Intensity scale

0 1 2 3 4 5 6 7 8 9 10

Intensity scale0 1 2 3 4 5 6 7 8 9 10

Intensity scale

0 1 2 3 4 5 6 7 8 9 10

Intensity scale0 1 2 3 4 5 6 7 8 9 10

Intensity scale

0 1 2 3 4 5 6 7 8 9 10

Intensity scale

AUC

valu

eAU

C va

lue

AUC

valu

e

DCRp

DCRp

1

095

09

085

08

075

1

098

096

094

092

1

095

09

085

08

1

095

09

085

092

09

088

086

084

082

1

095

09

085

1

095

09

085

08

095

09

085

08

075

AUC

valu

eAU

C va

lue

AUC

valu

eAU

C va

lue

AUC

valu

e


09

08

07

06

05

04

03

02

01

0

minus010 10 20 30 40 50 60 70 80 90 100

Sensitivity level

Dic

e met

ric






(a) (b) (c)













(a) (b) (c)









5 Conclusion




References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










1

09

08

07

06

05

04

03

02

01

00 02 04 06 08 1

DCRp

Rp DCRs Rm DC

DCRp

Rp DCRs Rm DC

Sens

itivi

ty

1 minus specificity

1

09

08

07

06

05

04

03

02

01

0

Sens

itivi

ty

1

09

08

07

06

05

04

03

02

01

0

Sens

itivi

ty

0 02 04 06 08 1


1 minus specificity

DCRp

Rp DCRs Rm DC




119901 and (iv) 119877

119901 In all the


1

09

08

07

06

05

04

03

02

01

010908070605040302010

Sens

itivi

ty

1 minus specificity











119901 The





119904 119877119898 dc 119877

119901 dc 119877

119901




119901 The standard












0 1 2 3 4 5 6 7 8 9 10

Intensity scale

0 1 2 3 4 5 6 7 8 9 10

Intensity scale0 1 2 3 4 5 6 7 8 9 10

Intensity scale

0 1 2 3 4 5 6 7 8 9 10

Intensity scale0 1 2 3 4 5 6 7 8 9 10

Intensity scale

0 1 2 3 4 5 6 7 8 9 10

Intensity scale0 1 2 3 4 5 6 7 8 9 10

Intensity scale

0 1 2 3 4 5 6 7 8 9 10

Intensity scale

AUC

valu

eAU

C va

lue

AUC

valu

e

DCRp

DCRp

1

095

09

085

08

075

1

098

096

094

092

1

095

09

085

08

1

095

09

085

092

09

088

086

084

082

1

095

09

085

1

095

09

085

08

095

09

085

08

075

AUC

valu

eAU

C va

lue

AUC

valu

eAU

C va

lue

AUC

valu

e


09

08

07

06

05

04

03

02

01

0

minus010 10 20 30 40 50 60 70 80 90 100

Sensitivity level

Dic

e met

ric






(a) (b) (c)













(a) (b) (c)









5 Conclusion




References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 1 2 3 4 5 6 7 8 9 10

Intensity scale

0 1 2 3 4 5 6 7 8 9 10

Intensity scale0 1 2 3 4 5 6 7 8 9 10

Intensity scale

0 1 2 3 4 5 6 7 8 9 10

Intensity scale0 1 2 3 4 5 6 7 8 9 10

Intensity scale

0 1 2 3 4 5 6 7 8 9 10

Intensity scale0 1 2 3 4 5 6 7 8 9 10

Intensity scale

0 1 2 3 4 5 6 7 8 9 10

Intensity scale

AUC

valu

eAU

C va

lue

AUC

valu

e

DCRp

DCRp

1

095

09

085

08

075

1

098

096

094

092

1

095

09

085

08

1

095

09

085

092

09

088

086

084

082

1

095

09

085

1

095

09

085

08

095

09

085

08

075

AUC

valu

eAU

C va

lue

AUC

valu

eAU

C va

lue

AUC

valu

e


09

08

07

06

05

04

03

02

01

0

minus010 10 20 30 40 50 60 70 80 90 100

Sensitivity level

Dic

e met

ric






(a) (b) (c)













(a) (b) (c)









5 Conclusion




References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a) (b) (c)













(a) (b) (c)









5 Conclusion




References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a) (b) (c)









5 Conclusion




References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










5 Conclusion




References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article segmentation of scarred myocardium in cardiac magnetic resonance … · 2017. 12....

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