Identification, Segmentation, and Image Property Study of Acute Infarcts in Diffusion-Weighted...

Identification, Segmentation, and Image PropertyStudy of Acute Infarcts in Diffusion-Weighted

Images by Using a Probabilistic Neural Networkand Adaptive Gaussian Mixture Model1

Bhanu Prakash KN, Varsha Gupta, Michel Bilello, Norman J. Beauchamp, Wieslaw L. Nowinski

Rationale and Objectives. Accurate identification of infarcted regions of the brain is critical in management of strokepatients. An efficient and fast method for identification and segmentation of infarcts in the diffusion-weighted images(DWI) is proposed.

Materials and Methods. Thirteen stroke patients were studied. DWI scans were acquired with a slice thickness of 5 mm.We have used a probabilistic neural network for selecting infarct slices and an adaptive (two-level) Gaussian mixturemodel for segmentation of the infarcts. Statistical analysis, such as identification of distribution, first-order statistics calcu-lation, and receiver operating characteristic curve analysis, was performed.

Results. The average dice index is about 0.6, and average sensitivity and specificity are about 81% and 99%, respectively.The value of sensitivity and dice index are influenced by the number of false positives and false negatives. Because arti-facts and infarcts have similar imaging characteristics, it is difficult to completely eliminate the artifacts. The accuracy oflocalization is nearly 100% as there were only two false-positive and three false-negative slices of all 381 slices. The al-gorithm takes about 1 minute in the Matlab computing environment to process a volume.

Conclusion. A method to localize and segment the acute brain infarcts is proposed. The method aids the clinician in re-ducing the time needed to localize and segment the infarcts. The speed of localization and segmentation can be enhancedfurther by implementing the algorithm in VC�� and using fast algorithms for selection of Gaussian mixture model pa-rameters.

Key Words. Infarct; Diffusion; Segmentation; Gaussian mixture model; Artifact; Stroke.©
AUR, 2006
Cerebral stroke is one of the major causes of mortalityand morbidity in many countries. Prompt assessment andtreatment of stroke may help patients affected by this dis-

Acad Radiol 2006; 13:1474–1484

1 From the Biomedical Imaging Lab, Singapore Bioimaging Consortium,Agency for Science Technology and Research, 30 Biopolis Street, #07-01Matrix Singapore 138671 (B.P., V.G., W.L.N.), Department of Radiology,University of Pennsylvania, Philadelphia, PA (M.B.), and Department of Ra-diology, University of Washington Medical Center, Seattle, WA (N.J.B.). Re-ceived August 3, 2006; accepted September 11, 2006. Address corre-spondence to: B.P. e-mail: [email protected]

©
AUR, 2006doi:10.1016/j.acra.2006.09.045
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ease to recover some neurologic function that may havebeen lost during the acute phase. Besides classical mag-netic resonance imaging (MRI) sequences, two additionalmodalities have been used to evaluate acute stroke pa-tients. Diffusion-weighted imaging (DWI), in which theimages reflect microscopic random motion of water mole-cules, and perfusion imaging (PI), in which hemodynami-cally weighted MRI sequences are based on the passageof magnetic resonance contrast through brain tissue. Inthe study of acute strokes, DWI abnormalities are markersof critical ischemia that typically evolve into infarction.
There is limited literature about the automatic or semiau-

Academic Radiology, Vol 13, No 12, December 2006 STUDY OF ACUTE INFARCTS IN DIFFUSION-WEIGHTED IMAGES

tomatic tools for segmentation and evaluation of acutestroke regions. Martel et al (1) used a semiautomaticmethod to determine infarct volume by diffusion tensor-MRI. An adaptive threshold algorithm incorporating aspatial constraint was used to segment the images. Li etal (2) proposed an unsupervised segmentation methodusing multiscale statistical classification and partial vol-ume voxel reclassification in the case of diffusion tensorMRIs. Their main consideration was to correctly identifythe infarct regions and overcome the problem of intensityoverlapping caused by diffusion anisotropy, and to reclas-sify partial volume voxels. The method was robust tonoise and radiofrequency inhomogeneities. In the cur-rent clinical practice, the analysis of DWI-PI datasetsis based on manual image editing and segmentationtechniques provided by available commercial medicalsoftware. A complete study takes 15–20 minutes ofuser interaction (3).

Fast and accurate segmentation of acute infarct is cru-cial for evaluation and treatment of stroke patients. Theobjective of this study was to develop a simple and effec-tive tool for fast segmentation of acute infarcts and esti-mation of infarcted region volumes on DWI datasets. Inaddition to possible use in the acute phase of stroke eval-uation and treatment, such an automated tool would alsobe useful in retrospective studies when large amounts ofimaging data need to be processed.

Segmentation is an important step in many medicalimage analyses. In many classification processes, segmen-tation forms the first step. The applications of segmenta-tion include diagnosis, quantitative evaluation, and treat-ment of disease. Because manual segmentation is tedious,time consuming, and subjective, attempts have been madeto automatically classify and quantify healthy and dis-eased tissues and organs from images obtained by variousmedical imaging modalities.

Segmentation of medical images is a challenging taskbecause of the complexity of the images and the absenceof models of anatomy that fully capture the possible de-formations in each structure. Also, because of the rela-tively low signal-to-noise ratios and inherent artifacts gen-erally present in medical images, their segmentation isparticularly difficult. Because of these problems, eventhough many algorithms have been reported, most ofthem have inconsistent results or limited applications.Thus only few computer-aided diagnosis algorithms arebeing used in clinical practice.

Medical images, including computed tomography,
MRI, positron emission tomography, and single photon
emission computed tomography data, add new complica-tions to the problem of segmentation. Each modality hasparticular characteristics that detract from a straightfor-ward solution. These difficulties range from the partialvolume effects common to all modalities to radiofre-quency inhomogeneities experienced by MRI, beam hard-ening effects of computed tomography, scatter and attenu-ation problems common to positron emission spectometry,and single photon emission computed tomography. Themain obstacles to segmentation of MRIs are the presenceof noise, errors in the scanners, and the structural varia-tions of the imaging objects, which can be categorizedinto four different types: thermal/electronic noise, mag-netic field inhomogeneities, biologic tissue variations, andpartial volume effects. In particular, DWI images areprone to susceptibility artifacts, especially near air-boneinterfaces. These artifacts have intensity profiles similar tothose of acute infarcts, and thus may be difficult to differ-entiate from acute stroke lesions.

There are two fundamental approaches to clustering,namely, parametric and nonparametric. If the purpose ofunsupervised learning is data description, then we assumea predefined distribution function for the dataset, and cal-culate the sufficient statistics that will describe the dataset. For example, if we assume that a dataset comes froma normal distribution, the sufficient statistics are the sam-ple mean and the sample covariance, which are sufficientto describe the distribution completely. Another approachuses a mixture of distributions to describe the data (4–6).We can approximate virtually any density function in thisway, but estimating the parameters of a mixture is nottrivial.

The mixture model is a semiparametric method of esti-mating the underlying density function (7–9). In the non-parametric, kernel-based approach to density estimation,the density function is represented as a linear superposi-tion of kernel functions, with one kernel centered on eachdata point. In our work, we have used the Gaussian mix-ture model (GMM), which is a measurement model forsegmentation. The model relates the image data to thesegmentation and takes the form of a finite Gaussian mix-ture (10). We have considered two levels for segmenta-tion based on image contrast. The model parameters areestimated completely from the input image data using theexpectation-maximization (EM) algorithm (5). Voxel in-tensities were used as input feature to the segmentationalgorithm.

This article is organized as follows. We describe
briefly the dataset used and the algorithm employed for
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PRAKASH ET AL Academic Radiology, Vol 13, No 12, December 2006

segmentation of acute infarcts, the statistical analysis per-formed, and the ground truth generation. Subsequent sec-tions describe the results and present the discussion.

MATERIALS AND METHOD

The data consisted of 13 DWI cases. The DWI scanshad in-plane resolutions of 1 mm � 1 mm or 1.5 mm �1.5 mm, and 5-mm slice thickness. The number of slicesin DWI scans was from 27 to 33. The matrix size ofDWI scans was 256 � 256.

Selection of Infarct SliceThe probabilistic neural network (PNN) was developed

by Specht (11,12). This network provides a general solu-tion to pattern classification problems by following theapproach of Bayesian classifiers, which takes into accountthe relative likelihood of events and uses a priori informa-tion to improve prediction. The network paradigm alsouses Parzen Estimators, which were developed to con-struct the probability density functions required by Bayestheory. In the context of classification problems, the PNNoutputs are interpreted as estimates of probability of classmembership and the network learning as estimation of aprobability density functions (pdf) of the classes. Theprobabilistic neural network uses a supervised training setto develop distribution functions within a pattern layer.These functions, in the recall mode (classification mode),are used to estimate the likelihood of an input featurevector being part of a learned category, or class. Thelearned patterns can also be combined, or weighted, withthe a priori probability, also called the relative frequency,of each category to determine the most likely class for agiven input vector. If the relative frequency of the catego-ries is unknown, then all categories can be assumed to beequally likely and the determination of category is solelybased on the closeness of the input feature vector to thedistribution function of a class.

In kernel-based estimation, simple functions are lo-cated at each available case, and added together to esti-mate the overall pdf. Typically, the kernel functions areGaussians (bell-shapes). If sufficient training points areavailable, this will indeed yield an arbitrarily good ap-proximation to the true pdf. This kernel-based approachto pdf approximation is very similar to radial basis func-tion networks, and motivates the PNN and generalizedregression neural network. PNNs are designed for classifi-
cation tasks and generalized regression neural networks
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for regression. These two types of network are really ker-nel-based approximation methods cast in the form of neu-ral networks.

In the PNN, there are at least three layers: input, ra-dial, and output. The radial units are copied directly fromthe training data, one per case. Each radial unit models aGaussian function centered at the training case. There isone output unit per class. Each is connected to all theradial units belonging to its class, with zero connectionsfrom all other radial units. Hence the output units simplyadd up the responses of the units belonging to their ownclass. The outputs are all proportional to the kernel-basedestimates of the pdfs of the various classes; by normaliz-ing these to sum to 1.0, estimates of class probability areproduced.

The only control factor that needs to be selected forprobabilistic neural network training is the smoothing fac-tor (ie, the radial deviation of the Gaussian functions).The greatest advantages of PNNs include a probabilisticoutput (which makes interpretation of output easy) and afast training speed. Training a PNN actually consistsmostly of copying training cases into the network, andhence the training speed can be assumed to be real-time.The greatest disadvantage is network size: a PNN net-work actually contains the entire set of training cases, andis therefore space-consuming and may be slow to execute.

PNNs are particularly useful for prototyping experi-ments (eg, when deciding which input parameters to use),because the short training time allows a great number oftests to be conducted in a short period. PNN is good forimage processing and rapid analysis.

The selection of slices for segmentation was done us-ing a PNN that was trained with two features. The fea-tures were peak position in the histogram (excluding thebackground) and the texture measure derived from thespatial gray level difference matrix (SGLDM) of the im-age. First the spatial gray level difference matrix of theimage was calculated for a value of distance 2, fromwhich the contrast (texture measure) (13) is calculated. Adistance of 1 will give us the contrast between the neigh-boring pixels; to have the contrast over a region, we se-lected the value of distance as 2. Many features, such asfirst-order statistics and texture measures were tested tofind the difference between the infarct and artifact slices.The infarct slices were referred as true-positive slices(TPS) and the slices which did not contain infarcts wereconsidered as true-negative slices (TNS). The scatter plot(Fig 1) showed that a high degree of overlap among
them. The PNN was used to have the best possible sepa-


ration between TPS and TNS. If a slice has both artifactand infarct, it is considered as TPS because the presenceof infarct.

The implementation of PNN was done using the Neu-ral Network Toolbox of Matlab 7.1, release 14, and thevalue of sigma (smoothing parameter) was selected as0.006. The network was trained to have the least numberof false-negatives slices (FNS) from the training samples.

Segmentation AlgorithmThe segmentation of infarcts is done using a GMM

whose parameters are tuned by the EM algorithm. GMM-based segmentation is used extensively in morphologicMRI segmentation. We have not found any references onapplication of GMM to infarct segmentation in DWI vol-umes. The advantage of GMM-based segmentation is itsability to perform unsupervised classification. The formu-lation of the segmentation problem can be described asfollows:

Let I denote an intensity image matrix and y � (yb,b � I) where yb denotes image intensity at pixel b.

N � total number of classes, and � � �1,2,. . .,N� –class labels.

xb denote an instance of a random variable represent-ing the tissue class at pixel site b (ie, xb � k) indicatethat the class k is assigned to pixel at site b.

Figure 1. Scatter plot showing the degree of overlap betweentrue-positive slices (o) and true-negative slices (*) (with peak posi-tion and contrast features) in the feature space.

Segmentation is denoted by x � (xb, b � I).

Process of segmentation is to find x, which representsthe correct tissue class (ie, find x � x*), which representsoptimal segmentation.

x * � argmax[p(x�y)],

x � �

� � set of all possible segmentations. p(x | y) � poste-rior density of segmentation x given image y.

Assuming each tissue class is normally distributed,Let D � {y1, y2, y3, . . . . . . . ., yM} be the sample set

and N � number of clusters.

Sample mean of kth class �̂k �1

Mk�j�1

Mk

yj; where M is

the number of samples in the kth class.

sample variance of kth class � �̂k2 �

1

Mk�1�j�1

Mk

�yj �

�̂k�2

The Gaussian function is defined as

g(y��) �1

�2��exp��

(y � �^

)2

2�̂2 and

the Gaussian mixture model is considered as

G(Y�) � �k�1

N

wk gk(y��k),

where wk are the weights and �k�1

N

wk � 1, where �k �

vector containing parameters � and �, and � � vectorcontaining wk and �k.

The values of the Gaussian parameters � and � areestimated using maximum likelihood estimation method.

The likelihood function � L�� k�1

N

G�yk�� and its

corresponding log-likelihood function is defined as

loglikelihood function � L() � log(L())

� �k�1

N

log G(yk�)

To estimate the parameters of the Gaussian mixturemodel we have used EM algorithm (6-7).

Input: samples (feature), no. of clusters (N), variancelimit, and variance threshold.
[rows, cols] � size (feature);
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Initialize: means � random (cols, N);Find

dist � distance ( means, feature); [value, index]� min (dist);

formulate clusters of each index by assigningsamples which are close to index.Find

variance of each cluster and weight � wk �(# samples in kth cluster)/Total # samples.

BeginInitialize �0, threshold, n � 0 (where n is the itera-tion number)Do n ¢ n � 1;

E step: compute L (�n; �n–1)M step: evaluate and assign �n �1 ¢ argmax

[L (�n, �n–1 )]Until

L (�n, �n–1) – L (�n–1, �n–2) � thresholdEnd;

End;The reestimation in every step of EM iteration is done

as follows:

Mixture weights:wk �1

Mk�l�1

N

p�k�yl,�, means: �k �

�l�1

N

p�k�yl,�

�l�1

M

p�k�yl,�, and variances: �k �

�l�1

N

p�k�yl,� �yl��i�2

�l�1

N

p�k�yl,�In our study, the samples were the pixel intensity, and

the number of classes considered were 5 in level 1(coarse) and 3 in level 2 (fine). Higher number of Gauss-ian functions was used to get a good approximation to thepdf of the image and has higher resolution. Only onelevel was sufficient (Fig 2) if the contrast of the imagewas lower than the average contrast of the volume, andtwo levels of segmentation was carried when the contrastwas higher than average contrast of the volume. For thesecond level segmentation (Fig 3) only those pixelswhose intensity was in class 5 were considered for furthersegmentation. These slices had severe inhomogeneity andartifacts. The number of Gaussian functions is generallyselected based on the number of classes required. In thecurrent study, we do not consider classification into graymatter, white matter, and cerebrospinal fluid, but segmen-tation of the acute infarct region. The pixels belonging tothe higher level class were considered for construction ofthe segmented image. In cases in which severe inhomoge-
neity is present, it is difficult to resolve between infarcts
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and artifacts. The Gaussian approximation and the initialsegmented images are shown in the following section.

The binarized image is labeled into individual regionsusing 8-pixel neighborhoods. The intensity range of eachregion is calculated, and the maximum intensity for eachregion is obtained from the histogram. It has been ob-served in the study that some of the artifact regions havea lesser range of intensity values than the infarct regions.A new threshold is calculated using the range of intensitydistributions of each region. A list (Vmax) consisting ofmaximum intensities for each region is formed and sortedin ascending order of intensities. The difference betweentwo consecutive values is then calculated. If it falls belowa (user-defined) percentage of the maximum range of in-tensities, new segmented regions are computed. The in-tensity at which the difference is higher than the specifiedthreshold is taken as the threshold for refining the over-segmented regions and eliminating some artifact regions.In our study, the value is fixed at 1% of the maximumrange of intensity of the segmented regions. Figures 4a-e

Figure 2. (a) Plots of Gaussian mixture model: cumulative distri-bution (top), distribution of each class (represented by differentline styles) and centers for segmentation (middle), and weightedGMMs (bottom), (b) original image, segmented image, and finalregion of segmentation.

show the original image, segmented image, segmented

s, an


regions, labeled regions, and final segmented regions for aslice.

The results of refined segmentation and removal ofsome of the artifact regions are shown in Fig 4e. Theremay be some artifact regions left because they have simi-

Figure 3. (a) Plots of Gaussian mixture model (GMM): cumulativestyles) and centers for segmentation, and weighted GMMs (two levfinal region of segmentation.

Figure 4. Images showing the segmented regions based on initiamented regions selected for analysis, (d) labeled segmented region

lar first-order statistics as the infarct regions (indeed, the

upper region in Fig 4e is likely an artifact). After the re-fined segmentation, one more round of check is carriedout to find possible artifacts in the images. Assuming thatthe infarcts do not occur symmetrically, we processed therefined segmented regions and removed the regions that

ribution, distribution of each class (represented by different lineleft, coarse; right, fine), (b) original image, segmented image, and

shold (Tint). (a) Original image, (b) segmented regions, (c) seg-d (e) final segmented image.

distels:

l thre

were approximately equidistant from the midsagittal plane

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and had similar first-order statistics. The midsagittal planeis calculated using our algorithm (14). One drawbackwith this elimination procedure is, in some cases, infarctregions and artifacts (susceptibility) are located symmetri-cally with respect to the midline and both will be elimi-nated. This leads to false negatives in the results. In somecases, artifacts show characteristics of infarct and are re-tained, resulting in false positives. Infarcts in the anteriorcerebral artery territory are rare. In our cases, only arti-facts were present in the frontal regions that correspondto anterior cerebral artery territories. Hence a manuallyselectable Volume of Interest (VOI) was defined in thefrontal region and the segmented regions within the de-fined VOI were considered as the artifacts and were elim-inated from the segmented image.

Generation of Ground TruthThe ground truth (GT) was generated by a neuroradi-

ologist (MB). The GT volumes were marked on the hardcopies. The software developed in our laboratory wasused to translate the markings of the infarct regions fromhard copies to soft copies. The infarct region is markedwith the help of points, and a contour-generation programconnects all the points using cardinal spline interpolationmethod. The area within the contours is set to 255 andthe rest of the region is set to 0, thus producing a binaryimage for each slice. These binary images are stored asGT volumes, which are used for evaluation.

Statistical AnalysisThe first-order gray level statistics of artifact and in-

farct regions was analyzed. This analysis included mean,variance, skewness, and kurtosis. The artifact and infarctregions were identified from the segmented volumes usingthe GT volumes. We checked for the distribution of in-tensities in the infarct and artifact regions. Both had simi-lar distributions. As identification of stroke slice in thevolume is equally important as the segmented area itself,we analyzed the results in two ways.

1. Slice-wise evaluation: infarct present or absent.2. Area-wise evaluation: area of infarct in the slice.

The determination whether a slice had infarct or notwas done using PNN with two features. Additionally, theemphasis was set on identifying the location of infarctrather than its complete segmentation. Hence there is aninherent undersegmentation in the process. By identifying
the correct region of stroke we obtain an exact match
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with the GTs. This evaluation eliminates the variability(inter- and intra-) because there will be more reliableagreement in recognizing the stroke regions.

RESULTS

The results of the algorithm were evaluated against theGT marked by the expert. The segmented slices and GTslices of a given volume were overlaid in order to esti-mate the following quantities:

1) TPS: slice containing infarct and also identified asinfarct slice by the algorithm.

2) False-positive slice (FPS): slice not having an in-farct but identified as infarct slice by the algorithm.

3) TNS: slice without infarct and also identified asnon infarct slice by algorithm.

4) FNS: slice containing an infarct but not identifiedby the algorithm as infarct slice.

5) True-positive area: area of intersection between theinfarct area marked by GT and the identified areabecause of segmentation in a slice.

6) False-positive area (FPA): area not marked by GTbut that the segmentation procedure recognizes it asan infarct region. FPA could also include the partialregion connected to true-positive area or could betotally isolated from true-positive area region.

7) False-negative area (FNA): area identified as aninfarct by GT, but not by the segmentation proce-dure. As mentioned previously, this could be apartly unrecognized area of infarct or a completelyisolated unidentified infarct region.

8) True-negative area: area without infarct and alsoidentified by the algorithm as non infarct region.

The first four entities are based on the location of in-farct in the volume data, whereas the last four quantifythe area of infarct in the slices. We studied the statisticsof correct recognition of infarct location as well as thearea of infarct identified by the segmentation procedure.By removing the artifacts from the segmented images, wewere able to focus on how well the infarct region is pin-pointed by our algorithm. Also, by performing this sepa-ration, we were able to investigate some of the properties(mean, variance, skewness, kurtosis, and fractal dimen-sion) of infarct and artifact separately. The overall statis-tics was also estimated by retaining the artifacts in the
segmented images.


Statistics of Slice IdentificationInitially, we attempted to identify the slice with in-

farcts on the basis of the position of maximum intensitypeak in the histogram. This had a very high FPS rate andhence we considered another feature (ie, contrast) to iden-tify the infarct slices. However, there was high overlapbetween the features of TPS and TNS. Hence we usedPNN to obtain the separation at a higher dimension space.The PNN was trained with 60% of the samples. Therewere two slices incorrectly identified as TPS and threeslices as TNS of 381 slices. These are the FPS and FNS,respectively. In total, there were 102 TPS and 279 TNS.The results of identification are given in Table 1.

Statistics of Region SegmentationThe Dice Index of individual images was estimated to

quantify the overlap of area (15), and sensitivity andspecificity were used to evaluate the algorithm.

1) Dice Index �2�A�B�

A�B, where A is segmented re-

gion and B is the ground truth region,

2) Sensitivity �TPA

�TPA�FNA�*100,

3) Specificity �TNA

�TNA�FPA�*100,

The comparison of mean dice index for each data setis given in Fig 5. The bars in light gray indicate the resultof segmentation, bars in dark gray indicate the sensitivity,and bars in white indicate the results of specificity of thealgorithm.

Investigation of Infarct and Artifact PropertiesTo look for any distinguishing characteristics, intensity

distribution of the infarct region (identified using the GTimages) and the artifacts were subjected to evaluation of

Table 1Results of Identification of Infarct and Non-Infarct Slices byPNN

TPS TNS FPS FNS Total

Ground truth 102 279 — — 381PNN 99 277 2 3 381

PNN, probabilistic neural network; TPS, true-positive slices;TNS, true-positive slices; FPS, false-positive slices; FNS, false-positive slices.

the first-order statistics such as mean, variance, skewness,

kurtosis, and fractal dimensions (using Matlab). The arti-facts and infarct regions showed a similar distribution ofthese quantities (Table 2).

The Receiver Operating Characteristic (ROC) curveanalysis (16) was performed (Fig 6) on the estimatedquantities to look for any marked classification featuresusing the Medcalc software package. The area under theReceiver Operating Characteristic curve is close to 0.5 ineach of the cases (Table 3), which indicates that there isno marked difference in the characteristics of artifacts andinfarct regions.

DISCUSSION

Speed and accuracy are critical in clinical acute strokemanagement. In this study, we propose an automaticmethod for segmentation of acute infarcts, which mayspeed up the assessment of stroke region for stroke man-agement applications. The method uses techniques suchas Gaussian mixture-based modeling, PNN-based selec-tion of slices and use of common features for classifica-tion of artifact and infarct, and allows the user to finetune parameters according to the requirements (eg, selec-tion of threshold for fine tuning, fixing the minimum sizeof infarct region).

Selection of Sigma for PNNSigma needs to be selected to cause a reasonable

amount of overlap—too-small deviations cause a veryspiky approximation which cannot generalize and too-large deviations smooth out detail. An appropriate figureis easily chosen by experiment, by selecting a numberthat produces a low selection error; fortunately, PNNs arenot very sensitive to the precise choice of the smoothingfactor. In our study, the value of sigma was chosen as0.006, based on experimentation.

Accuracy of LocalizationAccurate localization of infarct region automatically

within a volume is very important because it may savetime for the clinicians. Because the intensity and first-order statistical features are almost identical for bothinfarct and artifact regions, it is difficult to determinewhich slice has infarct and which does not. In thisstudy, we have used peak position (intensity) and con-trast (extracted from SGLDM) features and identifiedthe infarct slices using PNN. Although there is a high
overlap between the TPS and TNS in the feature space,
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it was resolved in a higher dimension space by map-ping the feature space to the parametric space usingGaussian basis functions. The accuracy of localizationdepends on the number of training samples for PNN;the more the training samples, the higher the classifica-tion accuracy. The accuracy of localization also de-pends on the sigma or the smoothing function of theGaussian kernel. The training time for PNN is veryshort, because it assigns one node for each trainingsample and during the testing phase it classifies the testsample to the class of the nearest node. Althoughhighly accurate, this method requires training, and this

Figure 5. Bar graph is indicating the value of dspecificity (white).

Table 2Stroke and Artifact Characteristics

Parameters Minimum Maximum Mean Median

MeanInfarct 38.1 209.7 128.7 129.1Artifact 46.2 228.0 129.6 124.7

VarianceInfarct 913.1 13665 5124 5050Artifact 6.9 12649 4920 4785

SkewnessInfarct �4.26 0.67 �1.15 �1.12Artifact �4.07 1.04 �1.01 �0.93

KurtosisInfarct 1.07 19.46 3.5 2.7Artifact 1.04 18.5 3.5 2.44

Fractal dimensionInfarct �3.20 �0.63 �2.46 �2.35Artifact �2.9 �0.49 �2.04 �2.20

is one of its limitations.

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Accuracy of SegmentationThe accuracy of segmentation entirely depends on how

accurately the GMM approximates the given pdf of theimage, on the number of Gaussian functions used, numberof iterations selected, and on the type of solution ob-tained. Because there is more than one solution for the

ndex for (light gray), sensitivity (dark gray), and

Figure 6. ROC curves for Mean, Variance, Skewness, Kurtosisand Fractal Dimension.

Table 3Results of ROC Curve Analysis

ParameterArea Under the ROC Curve

Prob (Area � 0.5)95% Confidence

Interval

Mean 0.59 � 0.04 (0.033) 0.52–0.66Variance 0.51 � 0.04 (0.80) 0.44–0.59Skewness 0.62 � 0.04 (0.004) 0.54–0.69Kurtosis 0.62 � 0.04 (0.004) 0.54–0.69Fractal dimension 0.69 � 0.04 (�0.0001) 0.62–0.76

ROC, receiver operating characteristic.

ice i

approximation of pdf by the GMM model, sometimes the


EM algorithm converges to a local minimum rather thanto the global minimum. This leads to either oversegmen-tation or undersegmentation of the infarct regions. Iffewer Gaussian functions are selected in the GMM, over-segmentation occurs, and selecting more functions leadsto undersegmentation. Hence correct choice of the num-ber of Gaussian functions is critical for this method. Be-cause our emphasis was set on accurate localization of theinfarct regions, we opted for a higher number of Gaussianfunctions in the GMM model. The results of our algo-rithm may not extract completely the infarct area but, inalmost all cases, it identified the infarct regions correctly.Hence undersegmentation can be expected in some casesbecause it is inherent in the model used.

Value of Dice IndexThe dice index is influenced by TPS, FPS, and FNS,

and it is unaffected by TNS. For some datasets, the valueof dice index is low (Fig 5). These datasets had infarctregions that were very small (about 300 pixels). Thesedatasets also had severe inhomogeneity, which contrib-uted for higher FPS. Though there is significant overlapof the segmented region with GT, the value of dice indexis low because of high FPS.

Value of SpecificityThe value of specificity is close to 100% for all the

datasets because the number of TNS in a given volume isvery high compared with the number of FPS. Hence theeffect of FPS is insignificant in the calculation of speci-ficity.

Identification of Artifacts and InfarctsTables 2 and 3 show the similarities of the features of

artifacts and infarcts. In some cases, it is difficult to dis-criminate artifacts and infarcts, even on the basis of vi-sual inspection. In this study, we have attempted to elimi-nate as many artifacts as possible based on some assump-tions. The assumptions made in the study are 1) infarctsdo not appear symmetrically with respect to the Midsagit-tal Plane (MSP), 2) infarcts are more than 50 pixels inarea (this threshold value can be changed), and 3) infarctsdo not occur in the frontal regions of the brain that corre-spond to the anterior cerebral artery territory. After theinitial segmentation by GMM, the segmented regionswere evaluated for location and size. Based on these as-sumptions, they were further classified as artifacts or in-farcts. In some cases, artifacts were symmetrically located
from infarcts. Because the two regions have similar first-
order statistics, they were eliminated by the algorithm,thus increasing the FNA in the segmentation. In somecases, artifacts were retained because they had similarcharacteristics to those of infarcts. Such cases increasedthe FPA. For these reasons, it is difficult to achieve avery high percentage of accurate segmentation.

Influence of IntensityAlong with the issues mentioned previously, there was

a very high degree of intensity variation in slices withinthe same volume. In many cases, the stroke region wasvery small and was hidden within the intensity inhomoge-neity. In such cases, the GMM model approximated thepredominantly higher inhomogeneity and was unable tosegment the infarct regions, resulting in increased FPAand FNA. Intensity normalization may be one way ofsolving the issue. However, this may in turn change thenature of intensity distributions in the infarct regions. Wedid not attempt to do intensity normalization/standardiza-tion across the slices of the volume because it changesthe initial characteristics of the regions. The intensity arti-facts could also be due to the pulse sequence and instru-ment effects.

CONCLUSION

In this study, we have proposed a technique thatmay assist radiologists and clinicians in speeding upthe process of stroke management. The algorithm canbe considered as a semiautomatic method as it requirestraining of PNN and setting some thresholds. The re-sults of localization were high, with only two FPS andthree FNS. The average dice index was about 0.6 andaverage sensitivity and specificity were 81% and 99%,respectively. In the current method, we had fewer FNAvoxels, but a higher number of FPA contributed tolowering the dice index. We believe this is not a veryserious limitation, because not many infarct regions aremissed, which is more important. The algorithm takesabout 1 minute to perform segmentation of a volume inthe Matlab computing environment. The speed can beincreased further by implementing the algorithm inVC��.

ACKNOWLEDGMENTS

The authors would like to thank the Biomedical Re-
search Council, Agency for Science, Technology and Re-
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search, Singapore. We would also like to thank our col-league Mrs. Aminah Beevi for her assistance in preparingthe manuscript.

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