SPIE_PAPER

1
Segmentation of Multiple Sclerosis Lesions Using Support Vector
Machines
Ricardo J. Ferrari*a,c
, Xingchang Weia,b,c
, Yunyan Zhanga,b,c
, James N. Scottb
, J.Ross Mitchella,b,c
a
Electrical and Computer Engineering, University of Calgary, University of Calgary.
b
Radiology and Clinical Neurosciences.
c
Seaman Family MR Research Centre, Foothills Medical Centre
1403 29th Street NW, Calgary, AB, CANADA - T2N 2T9.
ABSTRACT
In this paper we present preliminary results to automatically segment multiple sclerosis (MS) lesions in multispectral
magnetic resonance datasets using support vector machines (SVM). A total of eighteen studies (each composed of T1-,
T2-weighted and FLAIR images) acquired from a 3T GE Signa scanner was analyzed. A neuroradiologist used a
computer-assisted technique to identify all MS lesions in each study. These results were used later in the training and
testing stages of the SVM classifier. A preprocessing stage including anisotropic diffusion filtering, non-uniformity
intensity correction, and intensity tissue normalization was applied to the images. The SVM kernel used in this study
was the radial basis function (RBF). The kernel parameter (γ) and the penalty value for the errors (C) were determined
by using a very loose stopping criterion for the SVM decomposition. Overall, a 5-fold cross-validation accuracy rate of
80% was achieved in the automatic classification of MS lesion voxels using the proposed SVM-RBF classifier.
Keywords: : Segmentation of multiple sclerosis, support vector machines, multiple sclerosis, MRI.
1. INTRODUCTION
Multiple sclerosis (MS) is an inflammatory and demyelinating disease of the central nervous system (CNS) with a
lifetime risk of one in 400, and is the most common cause of neurological disability in young adults. MS affects twice as
many women as it does men [1]. It is regarded to be an autoimmune disorder, wherein the immune system mistakenly
recognizes CNS myelin as "foreign" and attacks it, resulting in inflammation and damage. Although the factors
triggering the pathological change in MS remain poorly understood, in the past few years, therapies have emerged that
impact the course of the illness. Due to the excellent properties such as high resolution, good soft tissue differentiation,
and different contrast information, multispectral magnetic resonance imaging (MRI) has been used routinely to diagnose
and monitor MS. In fact MRI-derived measurements now serve as the primary outcomes in phase I and phase II trials
and as secondary outcome in phase III trials [2].
The conventional method to measure volumes of MS lesions is to delineate the lesions manually by experts with
some extent of computer assistance. However manual outlining of lesion boundaries is arduous, time consuming, costly,
and prone to a large inter- and intra-observer variability. Consequently, there is considerable ongoing research into
automated techniques to determine lesion burden [3-7]. Many of these techniques use various form of the Expectation-
Maximization algorithm (EM). Although the EM algorithm is very suitable for classification problems using a small
number of features, its performance degrades rapidly as the number of features increases (the “curse of dimensionality”
phenomenon, [8]).
Support Vector Machines (SVM) [9], were developed fairly recently for regression and classification problems.
They have been used with great success in text categorization, face recognition, and bioinformatics [10]. SVMs have
good generalization and the ability to work with large datasets, regardless of their dimensionality, making them suitable
for applications in MRI analysis. However, they have not yet been used in MRI segmentation. In this paper we present
initial results using SVM to automatically segment MS lesions in multispectral magnetic resonance datasets.
*
ferrari@ucalgary.ca ; phone: (403) 944-8786; fax: (403) 270-7907
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2. METHODOLOGY
2.1 Patients and Image Acquisition
Eighteen patients with clinically definite relapsing-remitting MS were imaged on a 3 T GE Signa (GE Medical
Systems, Waukesha, WI). Each study consists of the following sequences obtained in a single session for all the
patients: a) FLAIR [TR/TE/TI =12002/135/2500 ms]; b) T1-weighted [TR/TE = 500/9 ms]; c) fast spin-echo T2-
weighted [TR/TE=5000/98 ms, echo train length (ETL) = 10]. To cover the entire brain, 19 axial 5-mm-thick slices with
2-mm gaps were obtained for all the sequences, with 220 mm field-of-view (FOV) and 512×512 image reconstruction
matrix, thus an in-plane resolution of 0.4348×0.4348 mm was obtained. A standard patient setup and exam slice
orientation procedure were used to minimize patient motion during the scans [11].
2.2 Training data
All MS lesions in each study were delineated by a neuroradiologist using a computer-assisted technique [11].
Marks for the lesion regions and normal tissue regions were saved for posterior use in the training and testing stages of
the projected SVM classifier.
2.3 Pre-processing
Before performing the segmentation by using the SVM, all images were preprocessed according to the stages
presented in the block diagram in Figure 1. Each stage is described in details below.
Figure 1: Flow diagram showing the stages of the proposed method for the segmentation of MS-lesions.
Original image
Preprocessingstage
Segmented image
Anisotropic diffusion
filter
Bias field
correction
Co-registration of
T1-w, T2-w, FLAIR
Image intensity
normalization
Image segmentation
using SVM

3
Noise reduction using Anisotropic Diffusion: For MR images the primary source of noise is thermal noise, which can
be characterized by a Rician distribution in MR magnitude images [12]. Although this type of noise can be reduced by
time averaging techniques, that approach is time consuming and often not feasible in clinical MR imaging. In the
present work, we have used a 3D robust anisotropic diffusion filter [13] to reduce image noise (i.e., improve the signal-
to-noise ratio) without blurring or moving object boundaries. In this filter, the blurring applied to the image is guided by
local gradient strengths in different directions. The filter requires three parameters: 1) the scale parameter, noiseσ ,
computed for each image as the standard deviation of the gray level intensity for different cerebral spinal fluid (CSF)
regions in FLAIR images; 2) the diffusion rate parameter, λ , fixed to 0.25 for all images; 3) the number of iteration, set
to 50. The Turkey smoothing function was used, which provides sharper edges. Although the number of iterations was
empirically set to 50 in the present work, the robust anisotropic diffusion filter has a stop-edge mechanism based on
robust statistics, that avoids an over smoothing of the image.
Nonuniformity correction: Image intensity inhomogeneity or bias field is an adverse phenomenon may be caused by a
number of factors including poor nonuniform radio frequency (RF) energy distribution, inhomogeneity in the static
magnetic field, and variations in RF coil sensitivity. While such variation may have little effect on the visual
interpretation of brain images, it can affect substantially the automatic processing of MR images [14]. In this work, the
N3
algorithm [15] was used to correct any intensity nonuniformities in the images. The technique was applied to the
images by using the default parameter values proposed by the authors. Briefly, the N3
algorithm is an iterative approach
that corrects the intensity nonuniformities by finding a smooth, slowly varying multiplicative field that maximizes the
frequency content of the image intensity distribution.
Intensity Normalization: In case of automatic segmentation of multispectral MR images using supervised techniques
(such as SVM, Artificial Neural Network, Bayesian approach, etc.), image normalization to correct the dynamic range
of the signal intensity may have a significant impact in the classification results [16, 17]. In the present work, the image
intensities were calibrated by applying a linear scaling factor defined as
ri =
µi
CSF
µT
, i =1,...,18, (1)
where µi
CSF
is the mean vector CSF intensity of the th
i study and T
µ is the mean vector CSF intensity computed using
all eighteen studies [18]. CSF was selected as the normalization tissue since its MR signal is unlikely to be affected by
the disease process.
Image Registration: The registration of multispectral MR images allows the establishment of the one-to-one mapping
between the points in images with different contrasts. In this work the images within each study (T1-, T2-weighted, and
FLAIR images) were co-registered by using a 2D rigid body registration algorithm [18].
2.4 Support Vector Machines
Support Vector Machines are supervised machine learning techniques, recently developed in the framework of
statistical learning theory [9, 19]. They have been used with a great success in a variety of applications such as text
categorization, face recognition, and bioinformatics. In many of these areas SVM have outperformed well-established
methods such as artificial neural networks, radial basis functions, and non-parametric cluster classification [10]. The
great advantage of the SVM technique over conventional techniques, besides the well-established theoretical definition,
is its capacity of working with high dimensional feature vectors without losing the generalization performance [9]. This
property makes SVMs very suitable for segmentation of multispectral MR images.
For binary classification problems, the main idea of the SVM is to find a decision boundary between classes in the
original feature space by mapping the feature vectors to a high dimensional space, where the features are more likely to
be linearly separable.
The optimal separating hyperplane (OSH) is choose in the high-dimensional space as the one that maximizes the
margin of separability between the two sets of data points. This choice counteracts the increasing generalization error
when constructing a decision boundary in higher-dimensional space. This approach also satisfies the Empirical Risk

4
Minimization principle, which seeks to minimize the upper bound on the generalization error [9]. The OSH, in case of a
linearly separable problem, is computed as a decision function of the form:










∑
=
+⋅=
svl
i
bsv
iii
yf
1
)(sign)( xxx α , (2)
where x is the vector to be classified, yi is the class label (-1=normal and +1=lesion in this work),
sv
l
i
sv
i
x 1
}{ =
is a subset of
the data training, called “support vectors” (SVs) and the coefficients bi
andα are computed by maximizing
the Lagrange dual formulation:
∑∑ ==
⋅−=
l
ji
jijiji
l
i
iD yyL
1,1
)(
2
1
)( xxαααα , (3)
subject to the following constraints:
∑=
=≤≤=
l
i
iii liCy
1
.,...,1for0,0 αα (4)
The parameter C can be regarded as a regularization parameter that penalizes training errors (training data points
incorrectly classified).
In order to extend the above formulation for nonlinear separable problems, the dot products between the training
data points in Equation (2) are implicitly mapped via kernel functions [20] into another high dimensional dot product
space F (called the feature space) where the new problem has high probability to be linearly separable. The mapping
Fn
→ℜΦ : is linear in F, but the new decision function, computed as










∑
=
+=
svl
i
bsv
i
K
ii
yf
1
),(sign)( xxx α , (5)
is nonlinear in the original input variables. The function )()(),( xxxx Φ⋅Φ= sv
i
sv
i
K in Equation (5) is called a kernel
function and according to the Mercer’s theorem [20] can be any symmetric positive definite function. However, the
three most common types of kernel functions used are: polynomial for polynomial classifiers, gaussian for radial-basis
function (RBF) classifiers, and tangent hyperbolic for two-layer perceptron classifiers.
2.4.1 Selection of the kernel function and the model parameters
The SVM formulation proposed initially by Vapnik [9] does not include any criteria to select the regularization
parameter C or a kernel function that gives good generalisation (or results in a classifier with low expected error
bound). In practical problems, where the dataset does not present a large number of vectors, the VC-dimension and the
training errors can be used to select the best kernel function. However, in problems involving several thousands of
examples, such as segmentation of MS-lesions from magnetic resonance images, this process becomes a very time-
consuming task.
In this work a Gaussian kernel,
2
),(
yx
eyxK
−
=
γ
, was selected. This kernel implements an RBF classifier. The
choice of the kernel was based on the evaluation of the most three common kernel functions used in the literature
(polynomial, Gaussian, and tangent hyperbolic) over a small fraction of the data (40% of the feature dataset) randomly
sampled. The performance of the SVM-classifiers is presented in Table 1.
Kernel function Polynomial (degree 3) Gaussian Tangent hyperbolic
Overall accuracy 74% 80% 73%
Table 1: Overall accuracy obtained from different SVM-classifiers. The classification was performed by
using a small fraction of the original dataset, and the default values of the kernels parameter values of
the libSVM [21].

5
Unlike the kernel selection procedure where only a fraction of the training dataset was used, the Gaussian kernel
parameter ( γ = 8) and the regularization parameter (C=4096, penalty value for the errors) were determined from the
whole dataset using a cross-validation criterion (fold=5) with a very loose stopping tolerance (ε = 0.1) for the SVM
decomposition method [21]. The ratio between the number of positive (MS-lesion) and the negative (normal) examples
was 0.99.
2.5 Assessment of the segmentation results
Since it is not possible to obtain the ground truth of the volume of lesions being measured, the general approach is
to compare the results with respect to segmentation of experts. In this work, the SVM segmentation results were
assessed with respect to the lesions outlined by a neuroradiologist.
The SVM classifier was applied only to the normal and MS-lesion regions identified by the neuroradiologist,
corresponding in this case to 0.3% (272,632 input vectors) of the entire MR dataset. The normal tissue regions were
collected randomly among the eighteen studies, and the neuroradiologist was advised to mark all types of normal
intracranial tissue. Based on this limited application, the true positive (TP), true negative (TN), false positive (FP), and
false negative (FN) voxel rates derived from the confusion matrix (Table 2), gives the information about classification
accuracy performed by the SVM-classifier. The truth is considered to be the marks delineated by a neuroradiologist.
SVM segmentation
Normal MS-lesion
Normal a B
Radiologist segmentation
MS-lesion c D
Table 2: Confusion matrix used to derive the true positive, true negative, false positive, false negative,
and the overall accuracy rates, computed respectively as
dc
d
TPrate
+
= , FPrate =
b
a + b
, TNrate =
a
a + b
,
FNrate =
c
c + d
, accuracy =
a + d
a +b+ c + d
.
3. RESULTS AND DISCUSSIONS
A cross-validation (5-fold) accuracy rate of 80% was achieved from the automatic identification and classification
of MS lesion voxels using the SVM-RBF classifier. The number of FP and FN voxels was relatively high at 37.5%,
32.4% respectively.
The high false positive misclassification rate maybe explained by partial volume effects that smear the normal and
MS-lesion clusters distribution in the input feature space. This problem is particularly amplified in this work due to the
limited spatial resolution of the images – 5mm slice-stickiness. Figure 3 shows false positives voxels resulting from the
image segmentation.
The high false negative misclassification rate indicated above maybe explained by wrong marks delineated by the
radiologist in the boundary of the lesions along with partial volume effect (PVE) [12]. The MS-lesions should appear
brighter in both T2-w and FLAIR contrasts. However, when delineating the lesions, the radiologist may overestimate
their sizes by including small white and gray matter regions as part of the lesions. The PVE also can contribute to
reduce the brightness of the lesion regions. Therefore, a false cluster is created as indicated by the arrows in Figures
3(c)-(d). Figures 4 and 5 illustrate two cases presenting false negative voxels after the segmentation.
Most false-negative lesion voxels occurred around the perimeter of MS lesions. In essence, the lesion boundary
identified by the neuroradiologist was one or two voxels larger in diameter than that identified by the SVM classifier.
The radiologist is likely better at identifying voxels near the lesion edge that have subtly higher contrast than the
surrounding normal appearing tissues. However, this is not always a benefit. In a previous work we showed that human
raters consistently overestimate lesion volumes from phantom studies [18]. Partial volume effects also can reduce the
brightness of the lesion regions.

6
The small number of input features (T1-, T2-weighted, and FLAIR image contrasts), combined with large partial
volume effects and consequent high overlap between tissue clusters (see Figure 2), and the high value used for the
regularization parameter (C=4096) resulted in a very difficult learning problem. The training stage of our SVM-model
took 23 hours running on a 2 GHz Linux-Athlon system with 1GB of memory. The classification stage also was
computational expensive (approximately 40min classifying just the lesion regions). This fact is due to the number of
SVs (#SVs = 38,322 in this work from the total of 272,632 input data vectors) necessary to define the optimal boundary
between the normal and lesion classes.
(a) (b)
(c) (d)
Figure 2: Scatter plotting showing the image intensity distribution of the MR contrasts T1-, T2-weighted, and FLAIR
used in this work. The two arrows in the plots (c) and (d) indicate a cluster of false-positive lesion voxels likely due to
overestimation of MS-lesions boundaries in the truth dataset.
Figures 3, 4, and 5 show three results of MS-lesion segmentation obtained from the SVM-RBF method. By
mapping back the intensity values of the false-positive and false-negative voxels we could notice that they are closely
located in the regions indicated by arrows in Figure 2(c)-(d) where the class overlapping is high. These voxels
correspond to portions of gray and white matter in the image and the difficulty in differentiate them from lesion tissue
maybe caused by PVE.

7
(a) (b)
(c) (d)
Figure 3: Example of segmentation using SVM. Only T2-weighted and FLAIR images are presented here. (a) T2-
weighted. (b) FLAIR with lesion regions identified by the neuroradiologist. (c) FLAIR with classified regions – white
marks indicate the voxels correctly classified, brighter gray marks indicate the false-positive voxels and the dark gray
marks (only a few in this case) indicate false negative voxels. (d) Difference between the radiologist marks (marks of
normal and MS-lesion - truth - tissues delineated by a neuroradiologist using a semi-automatic tool) and the classified
voxels showing only the false positive and false negative voxels.

8
(a) (b)
(c) (d)
Figure 4: Example of segmentation using SVM. Only the FLAIR contrast is presented here to show the results. (a)
FLAIR. (b) Marks for MS-lesion delineated by a neuroradiologist (truth) using a semi-automatic tool overlaid on the top
of FLAIR image. (c) Segmentation result obtained for the proposed method inserted over the top of FLAIR image. (d)
Difference between radiologist lesion marks in (b) and the automatic segmentation in (c) showing false-negative voxels.

9
(a) (b)
(c) (d)
Figure 5: Example of segmentation using SVM. Only the FLAIR contrast is presented here to show the results. (a)
FLAIR. (b) Marks for MS-lesion delineated by a neuroradiologist (truth) using a semi-automatic tool overlaid on the top
of FLAIR image. (c) Segmentation result obtained for the proposed method inserted over the top of FLAIR image. (d)
Difference between radiologist lesion marks in (b) and the automatic segmentation in (c) showing false-negative voxels.

10
4. CONCLUSIONS
An MRI-derived MS lesion segmentation program was developed and preliminary results on a small dataset are
promising results.
Image intensity non-uniformity is a significant problem for supervised classification techniques such as SVM.
Although in this work we have used a procedure for the normalization of the images, we believe better algorithms may
improve our results further by reducing the misclassified voxels [17].
Nevertheless, these preliminary results, derived from a small number of input images, are promising. Further
optimization and investigation of the proposed method are underway to exploit its full potential, particularly the use of
additional input features and use of a brain atlas to help remove false positive voxels.
Due to the large number of support vectors determined from the SVM-learning stage, the resulting classification of
the images was computationally expensive. For further work, we intend to investigate the use of techniques [22, 23] that
reduce the computational complexity of the algorithm.
ACKNOWLEDGEMENTS
JRM is supported by salary awards from the Multiple Sclerosis Society of Canada and the Alberta Heritage Foundation
for Medical Research. This work was supported by grants from the Canadian Institutes of Health Research
Interdisciplinary Health Research Team studying MMP’s in MS, and by the MS Society of Canada.
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