Automatic Ischemic Stroke Lesion Segmentation Using Single

MR Modality and Gravitational Histogram Optimization Based Brain Segmentation

Nooshin Nabizadeh1, Miroslav Kubat2, Nigel John3, Clinton Wright4

1,2,3 Electrical and Computer Engineering Department, University Of Miami, Coral Gables, FL 33146, USA 4Evelyn F. McKnight Brain Institute, University of Miami, 1120 NW 14th Street, Miami, FL, 33136

Abstract— In this paper the automatic and customized brain segmentation followed by a stroke lesion detection technique is presented applying single modality Magnetic Resonance Images (MRIs). A novel intensity-based segmentation technique called gravitational histogram optimization is developed for this purpose. By applying histogram gravitational optimization algorithm the brain can be segmented into discriminative area including stroke lesion. The mathematical descriptions as well as the convergence criteria of the developed algorithm are presented in detail. The application of the proposed algorithm in the segmentation of single Diffusion-Weighted Images (DWI) modality of healthy and lesion MR image slices for different number of segments is presented and the results are discussed. The segmented areas are then employed in automatic lesion slice detection and lesion extraction technique. The stroke lesion is extracted from the recognized lesion slice with acceptable accuracy. Index Terms—Brain segmentation, Stroke detection, Gravitational histogram optimization, MR imaging,

1. Introduction Stroke or cerebrovascular space accident is the one of

the most important causes of morbidity and mortality around the world [1]. Stroke is defined as a sudden development of a neurological deficit, and can be divided into two categories. The major category is ischemia, which comprises approximately 85%, in comparison to haemorrhage, which comprises 10% to 15% [2]. An accurate detection and diagnosis of ischemic lesion is extremely essential for clinical prognosis, treatment, and also stroke related research [3]. With limitations on access to stroke specialists and the need for timely diagnosis, an effective automatic stroke lesion detection algorithm is clinically useful and desirable.

In stroke diagnosis, Magnetic Resonsnce Imaging (MRI) (and specifically its Diffusion-Weighted Image modality (DWI)) is one of the strongest medical imaging techniques. MRI is a non-invasive procedure, which unlike other medical imaging techniques enables us to differentiate soft tissues.

Contact Author is Nooshin Nabizadeh, nzadeh@med.miami.edu

Another advantage of MRI is that it produces multiple images of the same tissue with different contrast mechanisms while applying different image acquisition protocols and parameters [4]. The pathophysiology of cerebral ischemia involves variation of brain water volume even in its earliest steps. Diffusion-Weighted Images (DWI)’s sensitivity to illustrate changes in tissue-free water content allows us to identify ischemic damage to the brain within one hour after onset [5]. Nevertheless, the random shape and location of infarct lesions make their segmentation a complex and difficult task. In confronting this challenge, manual segmentations have been widely employed but this is very time consuming, tedious, and subject to manual variation and subjective judgments. Another disadvantage of these interventions is their reliance upon subjective judgments, which raises the possibility that other observers will reach different conclusions about the presence or absence of lesions, or even that the same observer will reach different conclusions on separate occasions [2]. Thus there exits a clinical reason for the development of an automatic stroke lesion segmentation system.

Since collection of anatomical multi-spectral MR images is time and cost consuming, acquisition of just one anatomical MR modality is more practical in clinical conditions. In many situations such as ischemic stroke, due to patient condition severity and time importance, procurement of more than one MR modality is not feasible. Because of this, detecting and segmenting the stroke lesion based on single anatomical MR modality is necessary and important [6].

The majority of lesion segmentation methods employ multispectral MR images. That is because lesions usually have similar intensities to the normal tissues, and using multispectral MR images help to elucidate this problem. Applying multispectral MR images offers two difficulties [2]. First, acquiring such data is not always feasible. Second, available data suffer from not being consistent and aligned, thus registration is essential.

Most stroke lesion segmentation methods suffer from dependency on multi-parameter MRI data, or multi-scale classification, or knowing the number of tissue classes [7-10]. Moreover, usually the dependency on local or global registration of brain image to an anatomical atlas is a drawback of majority of studies [9, 11]. Furthermore, the detection of the slices including the lesion usually has been neglected. The effort presented here is motivated by the need

to find a computationally light and fully automatic technique to detect the slice including lesion, and then segment ischemic stroke lesions using single-spectral MR Images. The DWI modality, which is the most useful modality for ischemic stroke diagnosis and prognosis, is employed here. The segmentation of the continuous spectrum of image intensity histogram into discrete segments is presented using a method called Histogram-based Gravitational Optimization Algorithm (HGOA). In this algorithm, convolving a rectangular window with brain histogram maximums, results in the generation of several clusters. Then applying three criteria and a gravitational optimization algorithm, the desired number of brain segments is achieved. Lower and upper cutoff boundaries of brain segments are then employed in the detection of the healthy and lesion slices. This also assists in the extraction of the location and area of the lesion strokes.

In Section III, the histogram-based gravitational optimization algorithm is explained. In Section IV, data acquisition and preprocessing are described. Results are discussed is Section V. Conclusion is addressed in Section VI.

2. Related Work

A number of studies have investigating lesion segmentation with respect to Multiple Sclerosis (MS), White Matter (WM) and tumor lesion segmentation but not stroke lesion segmentation. Parametric classifiers such as expectation maximization algorithm and non-parametric methods such as Parzen window and K-nearest neighbor are and the more frequently used methods in lesion classification [4, 12-14]. They can be categorized as statistical methods, which deals with the estimation of probability density functions. They are the most prevalent approaches in literature. In [15] a MS lesions segmentation method using a combined algorithm of parametric and non-parametric techniques is proposed.

Another group of lesion segmentation methods cover a wide range of Artificial Neural Networks (ANN), clustering methods, fuzzy sets, and their combinations [16-18]. The shortcomings of these methods are over-sensitivity to noise, the need for a suitable estimate of the number of layers and excessive training time [4].

There are some other studies employing multilevel thresholding and region growing techniques, which can be allocated into the data-driven methods category. These are the simplest approaches in that they only use the pixels intensities. This group accuracy is usually not very remarkable [19].

Some other methods concern volume estimation as deformable methods, which are the least prevalent group. Deformable techniques drawback is their need to match the MR images with an atlas, to locate the lesions [4].

The use of histograms for image segmentation has been adopted in many investigations. In [20], 2D histograms are employed to segment the brain images. In [21], brain MRI images are segmented using a fuzzy-clustering algorithm on the histogram. In [22], a fast automatic segmentation algorithm is proposed which is called random walk.

Very few studies work on ischemic stroke segmentation applying DWI sequence. In [11], ischemic lesion is segmented applying nonparametric density estimation based on mean shift algorithm and edge confidence map. In this study, applying a novel method called histogram-based gravitational optimization algorithm, the brain is segmented to four areas and stroke lesion is segmented using single modality (DWI) images.

3. Histogram Based Gravitational Optimization Algorithm

This algorithm can be separated into two parts as “histogram-based brain segmentation algorithm” and “gravitational optimization algorithm”.

Histogram-based brain segmentation algorithm starts by building the image histogram. It is assumed that the local maximums of the histogram are potentially representative of various segments in the brain. Therefore, the number and the value of the histogram local maximums can be related to the number and the center value of segments, respectively. Since every pixel in the image must be assigned only to single segment, therefore, the distance from one local maximum to another one should be equally or proportionally divided between the two local maximums to cover the whole intensity range. If it is divided proportionally, then the local maximum value affects the width of each segment. Doing so, the brain can be segmented to the same number of its histogram’s local maximums. However, if the desired number of brain segments is different from the total number of brain histogram’s local maximums, histogram-based gravitational optimization algorithm helps to dynamically segment the brain into the required number of segments. For this purpose, it is necessary to define an optimization process in which the objective function is created from the histogram analysis. An optimization process is defined to minimize the difference between the calculated number of segments and the desired number of segments. The optimization process works based upon an iterative calculation of an objective function, which is created from histogram-based brain segmentation algorithm. In this study, a gravitational optimization algorithm, which is a recently developed algorithm, is employed.

3.1 Histogram Based Brain Segmentation Algorithm

The histogram-based brain segmentation algorithm can be described as following.

Step1: the image histogram is calculated. Step2: for smoothing the histogram ![!], local

averaging technique is applied over the histogram using the equation (1).

![!!] =   ![!!]!!!

!

!                                                            (1)

where ![!!] is histogram distribution value of !!! bin, ! is the length of the averaging window and ![!!] is local average value of the histogram. It is obvious the greater the !, the smother the averaged histogram will be. Also it shifts the histogram toward the higher intensities.

Step3: The local maximums of smoothed histogram are simply calculated by:

!!"#!!"#$%[!] = ![!!]| ![!!] > ![! !!! ]

∩ ![!!] > ![! !!! ]                                                          (2) Step4: a rectangular window is convolved with the

histogram local maxima calculated from step 3. It is assumed that the number and location of the local maxima of the histogram can be an indication of different segments in the brain image. Therefore, the key idea for brain image segmentation is to automatically grow a local maximum of the smoothed histogram toward its neighbor local maximum with respect to its amplitude, location, and anticipated number of brain segments. To do this, the convolution of !!"#!!"#$%[!] and a rectangular window is employed to connect the local maximums that are in neighborhood. Let “!” be the length of a rectangular window,  !"#, and “!” be the length of !!"#!!"#$%[!]. Then ![!] is the vector of length ! +! − 1 whose !!! element is calculated by: ! ! = !"# ! ∗ !!"# ! = !"#[!]!!"# ! − !            

!

(3)

!!"#!!"#$% ! is written as !!"# ! for simplicity. The

function ![!] potentially has several discriminative segments, which here are called clusters. The narrower window obviously produces higher number of clusters.

Step5: the lower and upper cutoff bondaries for all clusters are calculated using a threshold value. In order to have continuous and discriminative clusters, convolution of !!"#!!"#$% ! and a rectangular window !"# is applied. The result is called ![!]. Using a threshold value as !ℎ!, controls the cutoff boundary and removes the values smaller than the threshold value in the distribution. Also it helps to increase the flexibility of optimization method. The cutoff boundaries of ![!] are calculated as: !!"#[!!] = !|![! !!! ] > !ℎ! ∩ ![! !!! ] < !ℎ!              (4) !!!"![!!] = !|![! !!! ] > !ℎ! ∩ ![! !!! ] < !ℎ!              (5)

The number of the clusters which are visible in

histogram data is the same as the total number of lower or upper cutoff boundaries of the function ![!]. The value of selected threshold has a great influence on the final number of clusters. For example the !ℎ!! may only lead to one cluster and the choice of !ℎ!!may lead to four clusters.

Step 6: the upper cutoff border of n!" cluster is connected to the lower cutoff border of (n + 1)!" cluster proportionally to the clusters’ amplitudes. The reason is to cover all intensity bins and fill up the gaps between !!!"![!!] and !!"#[!(!!!)]. Also every pixel needs to be assigned to a single segment. In this step, upper cutoff border of one cluster proportionally reaches to the lower cutoff border of next one according to the following rule.

!!"_!"#[!!] = !!"#_!"#[!(!!!)] = !!" !! + !!"# !!!! − !!" !!

×!"(!!)

!" !! + !"(!!!!)

(6)

where the !! is the index of the nth cluster, !"(!!) is the local maximum amplitude of the cluster !! , and !"(!!!!) is the local maximum amplitude of the cluster !!!!.

Step 7: After filling the gaps between the clusters, one specific intensity value is specified for each generated cluster. All intensity values fall between lower and upper cutoff borders of one cluster would be represented by one intensity value named !!"#$"% !! .  The intensity of the !!!" cluster is defined as:

!!"#$"% !! =!!"#_!"# !! + !!"_!"# !!

2 (7)

Brain is segmented according to the number, intensity of

the center, and the cutoff borders of generated clusters. In order to automate this process, an optimization process is applied to minimize difference between the calculated number of brain segments and the desired number of brain segments. The objective function is described as squared difference between the desired number of brain segments and the calculated number of brain segments. There are three variables that influence the objective function. These are the length of averaging window described in step two, the length of convolution window described in step four, and the threshold value described in step five.

In next part, the Gravitational optimization algorithm is explained. Figure 1 shows the diagram of histogram-based brain segmentation algorithm.

Fig. 1: Flowchart of the seven steps histogram-based brain segmentation

3.2 Gravitational Optimization Algorithm

The second part of the proposed algorithm is a gravitational optimization algorithm (GOA). In order to achieve the required number of the brain segments GOA is

applied on the histogram-based brain segmentation algorithm, which plays the role of objective function. The objective function is defined as the squared difference between the desired number of segments and the calculated number of segments.

The GOA is launched by initializing an N set of K-dimensional mass randomly seeded over the K-dimensional searching space. [23]. In other words, for the K-dimensional search space, the !!! mass, can be represented by an K-dimensional vector X! = x!", x!",… , x!" !, and the velocity V! = v!", v!",… , v!" !. Therefore the total size of population is a (N×K) matrix. In GOA, the gravitational force on the !!! object is calculated as:

F! =g.m!.m!. X! t − X! t

x!" − x!"!+⋯+ x!" − x!"

! !.!                     7!!!

Here, g is the gravity constant; m! is defined by the

value of the inverse objective function value, equation (8). In equation (8), ε is added to denominator to prevent dividing by zero.

m! =1

ObjectiveFunctionValue! + ε                                (8)

Following the calculation of the gravitational force on

the !!! mass, by assuming a unit time length, the new speed of the object is calculated as:

V! t + 1 = F! m! +  V! t                                                      (9)

Having the speed of the system at t + 1 and the previous location of the !!! mass at X! t , the position in the next iteration is adjusted by:

X! t + 1 = V! t + 1 + X! t                                              (10)

The GOA is initialized by random selection of the N set of K-dimensional mass and the iteration number. Here ! = 100, and ! = 3,  regarding to three variables, which affect on objective function. These three variables are “!” i.e. the length of the averaging window, “!” i.e. the length of a rectangular convolution window (!"#), and !ℎ! i.e. the threshold of cutoff borders as explained in section II. The equations (7) to (10) are iteratively calculated until the objective function or the iteration number is met or the V! t + 1 becomes lower than a threshold value. 3.2.1 Convergence of Gravitational Optimization Algorithm

The initial population and the number of iterations are two factors that affect the convergence rate in the evolutionary optimization algorithms. In gravitational optimization algorithm the gravity constant, g, controls the acceleration rate of optimization. The higher value of g, the higher the acceleration rate will be.

In spite of all of these considerations, one may not see the objective value satisfaction since the convergence rate is also dependent to the nature of the objective function. For

example, strictly speaking a second order function has only one local and global maximum. However, summing this function with a low value random function increases the number of local maximums or minimums. This idea is employed here to increase the chance of convergence. On the other word, the convergence of the optimization algorithm is not guaranteed but adding a low value random function !!, with a growing rate !!, to the preprocessed function !!, during the optimization process increases the convergence chance. The size of !! will be the same as function !! as !×!. The initial amplitude of the !! is about one percent of !! values. This leads to a random but slight movement of local maximums along the intensity vector. These movements increase the chance of optimization convergence. The whole process for image segmentation is summarized in figure 2. 4. Data Acquisition and Preprocessing 4.1 Image Acquisition

In all, 12 subjects (6 with stroke and 6 healthy, female = 5, mean age = 57.23, and standard deviation = 10.96, less than one months after stroke) were scanned in this study. All MR images were attained on a 3T Siemens Avanto scanner (Germany). High-resolution 3-D brain MRI images were acquired using a T1-weighted magnetization, with the following characteristics: repetition time (TR) = 6000 ms, echo time (TE) = 128 ms, inversion time = 2200 ms, one acquisition, flip angle = 90◦, field of view (FOV) = 71 mm, 46 slices, voxel size = 1 mm × 1 mm × 1 mm, and in-plane matrix = 256 × 256. Prior to scanning, all participants gave written informed consent according to the guidelines of the University of Miami Institutional Review Board. Participants were not paid for participation.

The ground truth is prepared by labeling the ischemic stroke lesion by an expert. In this study the DWI sequences with stroke lesion are called LD; the DWI sequences without stroke lesion are called HD.

Fig. 2: Flowchart of the lesion detection

4.2 Noise Reduction and Normalization Preprocessing includes background segmentation,

noise reduction using low pass filter as Gaussian filter, and normalization. Gaussian Filter is a low-pass spatial frequency filter where all elements in this filter are weighted according to a Gaussian (Normal) distribution. Depending on the mean and the variance value, !,! , in the Gaussian distribution, the convolution of this kernel with the image results in a smooth image [24]. Result of applying Gaussian filters with different variance value is represented in Fig. 3. By dividing the intensity values by the maximum intensity, normalized image is prepared.

4.3 Background Segmentation

Due to the prior knowledge of the background intensity values, it is necessary to exclude the back ground from the calculations wherever the histogram of the image is evaluated. The reason for doing this is that the background normally has much larger pixel number than brain ones.

5. Results 5.1 MRI Brain Segmentation

Original LD1 is represented in Fig. 3. The segmentation of LD1 into two, three and four levels is depicted in Fig. 4. Correspondingly, Fig. 5 displays the segmentation of LD1 into five, eight and twelve levels. It can be seen that after two levels of segmentation the stroke lesion appears in the segmented image. It can also be seen that in high levels of segmentation, some of the segments are visually indiscriminative; however, there is still a clear appearance of the stroke in the segmented image.

Figure 6 shows the original image of HD1 and its segmentation into three and four levels.

Figure 8(a) to 8(d), 9(a) to 9(d), respectively show the segmentation of LD1 for three and four level segmentation. Figures 8(a) and 9(a) correspond to image histogram after step 2. Figures 8(b) and 9(b) shows the local maximums of the histogram in step 3. Figures 8(c) and 9(c) show results of step 4. Figures 8(d) and 9(d) show the results of step 5 and 6. In all, red dots are initial lower and upper cutoff borders, which are result of step 5, and black dots are final lower and upper cutoff borders, which are result of step 6.

Figures 10 and 11 show the corresponding result as was explained for figures 8 and 9 respectively for HD1 slice.

5.2 Lesion Slice Detection

With comparison of position of cutoff borders, it is clear when brain is segmented into three or four segments, the last segment’s width differs for healthy and lesion slices. After segmentation of the brain into L segment, !!! segment’s width for lesion slices is much less than healthy ones. The following criterion is defined as first condition for lesion slice detection as: !!"!!"(!) − !!"#!"#(!) > !                                                (11)

The equation of (11) is interpreted as if !!!segment’s width is less than !, the slice is considered as lesion slice and vise verse as healthy one. Here, the ! is selected as 1.8.

By comparison of figure 10(d) with 8(d), and 11(d) with 9(d), one can see the obvious differences in (! −1)!!  segment’s initial and final lower and upper cutoff border movement in healthy and lesion slices. After segmentation of the brain into ! segment, the following criterion is defined as second condition for lesion slice detection as:

!!!!"# ! − 1 − !!"#!"# ! − 1 > 1 + ! . !!"!"# ! − 1 − !!"#!"# ! − 1                          (12)

The equation of (12) is interpreted as if the width of new

cut off border is larger than 1 + ! times of the old cutoff borders. Here, the ! is selected as 0.2; The implementation results show that for higher number of segmentation the movement of cut-off borders at segment ! − 1 is more discriminative than that of the lower number of segmentation. Therefore, for detection of the lesion slice the high number of segmentation is preferred. Foe example, brain is segmented to eight or twelve area. However, for lesion extraction from a detected lesion slice, the lower number of segmentation is more preferable since it covers wider areas around the stroke with a distributed intensity. For lesion extraction purpose, ! = 3 and ! = 4 is selected. All in all, for a complete stroke slide detection and lesion extraction two separate segmentation is needed. Initially the slice is segmented into a high number of segments (here 8) and the stroke slice is detected as to be a healthy or a lesion slice. If the slice was detected as a lesion slice, it is again segmented into three and four slices and the last segment is chosen as the stroke lesion. Here with considering logical OR between condition one and condition two, healthy and lesion slices are detected with 94.7 ± 1.2% accuracy.

5.3 Stroke Lesion Detection

After detection of healthy and the lesion slices, three and four area segmentation is implemented on the lesion slice. Because of high the intensity of stroke lesion, the stroke normally is positioned in the last segment and therefore with extracting the last segment, the stroke lesion can be extracted. Result of this step is depicted in Fig. 7. It is shown that the lesion extracted after segmenting the brain into four segments has smaller area than the labeled lesion, but include less false positives. Lesions extracted after brain segmentation into three segments have closer area to the labeled lesion but include more false positive. In the next step it is necessary to exclude false positive areas. With using the lesion results after segmenting the brain into three areas, the average overlap error is 16.39 ± 2.3%, that is mainly because of false positive. With segmenting the brain into four areas, average overlap error is 21.6 ± 1.9%, that is mostly because of smaller area of extracted lesion than labeled one. The total number of detected pixels, which do not have overlap with grand truth label divided by total number of grand truth pixels, is considered as error. 6. Conclusion

A new brain segmentation algorithm called histogram based gravitational optimization algorithm was proposed. The automatic brain segmentation into discrete segments

was presented. The stroke slice detection and stroke extraction using single modality diffusion-weighted MR images with comparable and promising accuracy was implemented. Simplicity, low computational complexity, independency on multi-spectral MR images, multi-scale classification, and anatomical atlas registration are prominent advantages of this work. Furthermore, lesion slice detection is included before the lesion segmentation step. The algorithm is capable of detection and segmentation of small lesions (< 1.5  !"!).

The disadvantage of presented approach is the rate of false positives. It was demonstrated adding spatial information amends the capability of lesion segmentation methods and reduces false positive rates. For future work, applying anatomical atlas will be considered. Furthermore, more work will focus on evaluation of algorithm on other MRI modalities. Finally, additional focus on amending the current method to attain clinically worthwhile system in more general applications will be done. The potential outcome is remarkable for medical field and justifies further studies

Fig. 3: Original DWI image with stroke lesion (first), the filtered DWI image (LD1) using Gaussian filter with ! = 0.1, (second), and with ! = 4 (third)

Fig. 4: Segmentation of the lesion DWI image (LD1) into two (first), three (second), and four (third) segments

Fig. 5: Segmentation of the lesion DWI image (LD1) into five (first), eight (second), and twelve (third) segments after min-max filter

Fig. 6: Original healthy DWI image (first), its segmentation of the healthy three (second), and four (third) segments

Fig. 7: Original DWI image with stroke lesion (first), stroke lesion extraction on LD1 after three levels of segmentation (second), after four levels of segmentation (third)

Fig. 8: The image histogram of LD1 after step 2 for 3 segmented areas (a), the local maximums of the histogram in step 3 (b), results of step 4 for three segments (c), and the results of step 5 and 6 (d)

Fig. 9: The image histogram of LD1 after step 2 for 4 segmented areas (a), the local maximums of the histogram in step 3 (b), results of step 4 for four segments (c), and the results of step 5 and 6 (d)

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Fig. 10: The image histogram of HD1 after step 2 for 3 segmented areas (a), the local maximums of the histogram in step 3 (b), results of step 4 for three segments (c), and the results of step 5 and 6 (d)

Fig. 11: The image histogram of HD1 after step 2 for 4 segmented areas (a), the local maximums of the histogram in step 3 (b), results of step 4 for four segments (c), and the results of step 5 and 6 (d) 7. References

[1] C L M. Sudlow et al. “Comparable studies of the incidence of stroke and its pathological types. Results from an international collaboration”. Stroke 1997;28(3):491–9.

[2] Y.Kabir, M.Dojat, B.Scherrer, F.Forbes, C.Garbay, “Multimodal MRI segmentation of ischemic stroke lesions,” Proceedings of the 29th Annual International Conference of the IEEE EMBS, August 2007.

[3] S. Shen, W. Sandham, M. Granat, and A. Sterr,“MRI Fuzzy Segmentation Of Brain Tissue Using Neighborhood Attraction With Neural-Network Optimization,” IEEE Trans. Inf. Technol. Biomed., vol. 9, no. 3, pp. 459–467, Sep. 2005.

[4] Daryoush Mortazavi & Abbas Z. Kouzani & Hamid Soltanian-Zadeh, “Segmentation of multiple sclerosis lesions in MR images: a review,” Springer 2011, Neuroradiology, DOI 10.1007/s00234-011-0886-7

[5] D. David et al., Magnetic Resonance Imaging, C.V. Mosby; 3rd edition (January 15, 1999)

[6] Shen S, Szameitat AJ, Sterr A, “Detection of infarct lesions from single MRI modality using inconsistency between voxel intensity and spatial location a 3-D automatic approach,” IEEE Trans 2008

[7] M. A. Jacobs, S. Patel, P. Mitsias, H. Soltanian-Zadeh, D. J. Peck, and A. Ghanei, “Unsupervised segmentation of clinical stroke with multiparameter MRI,” Proc. Intl. Soc. Mag. Reson. Med., vol. 8, p. 669, 2000.

[8] H. Soltanian-Zadeh, P. D. Mitsias, M. M. Khalighi, M. Lu, H. B. Ebadian, and J. R. Ewing, “Relationships among ISODATA, DWI, MTT, and T2 lesions in stroke,” Proc. Intl. Soc. Mag. Reson. Med., vol. 11, p. 2245, 2003.

[9] Y. Han, E. Li, J. Tian, J. Chen, H. Wang, and J. Dai, “The application of diffusion – and perfusion – weighted magnetic resonance imaging in the diagnosis and therapy of acute cerebral infarction,” Int. Jour. of Biomedical Imaging, vol. 2006, pp. 1–11, 2006.

[10] W. Li, J. Tian, E. Li, and J. Dai, “Robust unsupervised segmentation of infarct lesion from diffusion tensor MR images using multiscale statisti- cal classification and partial volume voxel reclassification,” Neuroimage, vol. 23, pp. 1507–1518, 2004.

[11] Nidiyare Hevia-Montiel, “Robust Nonparametric Segmentation of Infarct Lesion from Diffusion-Weighted MR Images,” IEEE Conference, 2007

[12] P. Anbeek, K. L. Vincken, M. J. P. van Osch, R. H. C. Bisschops, and J. Van Der Grond, “Automatic segmentation of different-sized white mat- ter lesions by voxel probability estimation,” Med. Image Anal. vol. 8, pp. 205–215, 2004.

[13] S. Datta, B. R. Sajja, R. He, J. S. Wolinsky, R. K. Gupta, and P. A. Narayana, “Segmentation and quantification of black holes in mul- tiple sclerosis,” NeuroImage, vol. 29, pp. 467–474, 2006.

[14] K. Van Leemput, F. Maes, D. Vandermeulen, A. Colchester, and P. Suetens, “Automated segmentation of multiple sclerosis lesions by model outlier detection,” IEEE Trans. Med. Imag., vol. 20, no. 8, pp. 677–688, Aug. 2001.

[15] Sajja BR, Datta S, He R, Mehta M, Gupta RK et al (2006) Unified approach for multiple sclerosis lesion segmentation on brain MRI. Ann Biomed Eng 34(1): 142–151

[16] Zijdenbos AP, Forghani R, Evans AC (2002) Automatic "pipeline" analysis of 3-D MRI data for clinical trials: application to multiple sclerosis. IEEE Trans Med Imag 21(10):1280–1291

[17] D. L. Pham and J. L. Prince, “Adaptive fuzzy segmentation of magnetic resonance images,” IEEE Trans. Med. Imag., vol. 18, no. 9, pp. 737–752, Sep. 1999.

[18] S. Shen, W. Sandham, M. Granat, and A. Sterr,“MRI fuzzy segmentation of brain tissue using neighborhood attraction with neural-network optimization,” IEEE Trans. Inf. Technol. Biomed., vol. 9, no. 3, pp. 459–467, Sep. 2005.

[19] Goldberg-Zimring D, Achiron A, Miron S, Faibel M, Azhari H (1998) Automated detection and characterization of multiple sclerosis lesions in brain MR images. J Magn Reson Imaging 16 (3): 311–318

[20] Nakib, A., Roman, S., Oulhadj, H., and Siarry, P., “Fast brain MRI segmentation based on two-dimensional survival exponential entropy and particle swarm optimization.,” Proc. of IEEE Engineering in Medicine and Biology Society 1(2), 5563–5566 (2007).

[21] Dou, W., Ren, Y., Chen, Y., Ruan, S., Bloyet, D., and Constans, J.-M., “Histogram-based generation method of membership function for extracting features of brain tissues on MRI images,” 2005.

[22] Jean-Philippe Morin, Christian Desrosiers, Luc Duong, “Image segmentation using random-walks on the histogram” Medical Imaging 2012: Image Processing, Proc. of SPIE Vol. 8314, 83140U

[23] Ying-Tung Hsiao, C. Chuang, J. Jiang, C. Chien, “A Novel Optimization Algorithm: Space Gravitational Optimization," IEEE International Conference On Systems, Man And Cybernetics, 2005

[24] Shapiro, L. G. & Stockman, G. C: "Computer Vision", page 137, 150. Prentence Hall, 2001

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