MRI Brain Image Segmentation with Supervised

SOM and Probability-Based Clustering Method

Andres Ortiz1, Juan M. Gorriz2, Javier Ramirez2, and Diego Salas-Gonzalez2

1 Communications Engineering DepartmentUniversity of Malaga. 29004 Malaga, Spain

2 Department of Signal Theory, Communications and NetworkingUniversity of Granada. 18060 Granada, Spain

Abstract. Nowadays, the improvements in Magnetic Resonance Imag-ing systems (MRI) provide new and aditional ways to diagnose somebrain disorders such as schizophrenia or the Alzheimer’s disease. Oneway to figure out these disorders from a MRI is through image segmen-tation. Image segmentation consist in partitioning an image into differentregions. These regions determine diferent tissues present on the image.This results in a very interesting tool for neuroanatomical analyses. Thus,the diagnosis of some brain disorders can be figured out by analyzing thesegmented image. In this paper we present a segmentation method basedon a supervised version of the Self-Organizing Maps (SOM). Moreover, aprobability-based clustering method is presented in order to improve theresolution of the segmented image. On the other hand, the comparisonswith other methods carried out using the IBSR database, show that ourmethod ourperforms other algorithms.

1 Introduction

Nowadays, Magnetic Resonance Imaging systems (MRI) provide an excellentspatial resolution as well as a high tissue contrast. Nevertheless, since actualMRI systems can obtain 16-bit depth images corresponding to 65535 gray lev-els, the human eye is not able to distinguish more than several tens of graylevels. On the other hand, MRI systems provide images as slices which com-pose the 3D volume. Thus, computer aided tools are necessary to exploit allthe information contained in a MRI. These are becoming a very valuable toolfor diagnosing some brain disorders such as the Alzheimer’s disease [1]. More-over, modern computers which contain a large amount of memory and severalprocessing cores, have enough process capabilities for analyzing the MRI in rea-sonable time. Image segmentation consist in partitioning an image into differentregions. In MRI, segmentation consist of partitioning the image into differentneuroanatomical structures which corresponds to different tissues. Hence, an-alyzing the neuroanatomical structures and the distribution of the tissues onthe image, brain disorders or anomalies can be figured out. Hence, the impor-tance of having effective tools for grouping and recognizing different anatomicaltissues, structures and fluids is growing with the improvement of the medical

J.M. Ferrandez et al. (Eds.): IWINAC 2011, Part II, LNCS 6687, pp. 49–58, 2011.c© Springer-Verlag Berlin Heidelberg 2011

50 A. Ortiz et al.

imaging systems. These tools are usually trained to recognize the three basic tis-sue classes found on a on a healthy brain MR image: white matter (WM), graymatter (GM) and cerebrospinal fluid (CSF). All of the non-recognized tissues orfluids are classified as suspect to be pathological. The segmentation process itcan be performed in two ways. The first, consist of manual delimitation of thestructures present within an image by an expert. The second consist of usingan automatic segmentation technique. As commented before, computer imageprocessing techniques allow exploiting all the information contained in a MRI.There are several automatic segmentation techniques. Some of them use the in-formation contained in the image histogram [2, 3, 11]. This way, since differentcontrast areas should correspond with different tissues, the image histogram canbe used for partitioning the image. In the ideal case, three different image in-tensities should be found in the histogram corresponding to Gray Matter (GM),White Matter (WM) and CerebroSpinal Fluid (CSF). Moreover, the resolutionshould be high enough that each voxel is composed by a single tissue type. Nev-ertheless, variations on the contrast of the same tissue are found in an imagedue to RF noise or shading effects due to magnetic field variations. These effectswhich affects to the tissue homogeneity on the image are a source of errors forautomatic segmentation methods. Other methods use statistical classifiers basedon the expectation-maximization algorithms (EM) [1, 5, 6], maximum likelihood(ML) estimation [7] or Markov random fields [8, 9]. Nevertheless, artificial in-telligence based techniques, have been proved to be noise-tolerant [10–16] andprovide promising results. Some of these methods are based on the Kohonen’sSelf-Organizing Maps (SOM) [12–15]. In this paper, we present a segmentationmethod based on a supervised version of SOM, which is trained by using one ofthe volumes present on the IBSR [14] repository. Moreover, multiobjective opti-mization is used for feature selection and a probability-based clustering methodover the SOM aids to improve the segmentation process resolution. After thisintroduction, Section 2 describes the feature extraction and selection process,Section 3 introduces the supervised version of SOM, and Section 4 describesthe use of supervised SOM and the probability-based clustering method. FinallySection 5 presents the results obtained by using the IBSR database [14] andSection 6 concludes this paper.

2 Supervised Self-Organizing Maps (SOM)

SOM [17] is one of the most used artificial neural network models for unsuper-vised learning. The main purpose of SOM is to group the similar data instancesclose in into a two or three dimensional lattice (output map). On the otherhand, different data instances will be apart in the output map. SOM consist ofa number or neurons also called units which are arranged following a previouslydetermined lattice. During the training phase, the distance between an inputvector and the weights associated to the units on the output map are calculated.Usually, the Euclidean distance is used as shown in Equation 1. Then, the unitcloser to the input vector is referred as winning unit and the associated weight is

MRI Brain Image Segmentation with Supervised SOM 51

updated. Moreover, the weights of the units in the neighbor of the winning unitare also updated as in Equation 2. The neighbor function defines the shape of theneighborhood and usually, a Gaussian function which shrinks in each iterationis used as shown in Equation 3. This deals with a competitive process in whichthe winning neuron each iteration is called Best Matching Unit (BMU).

Uω(t) = argmini‖x(t) − ωi(t)‖ (1)

ωi(t + 1) = ωi(t) + αi(t)hUi(t)(x(t) − ωi(t)

)(2)

hUi(t) = e−‖rU −ri‖

2σ(t)2 (3)

In Equation 3, ri represents the position on the output space (2D or 3D) and‖rU − ri‖ is the distance between the winning unit and the i-neuron on theoutput space. On the other hand, σ(t) controls the reduction of the Gaussianneighborhood on each iteration. σ(t) Usually takes the form of exponential decayfunction as in Equation 4.

σ(t) = σ0e

(−tτ1

)(4)

In the same way, the learning factor α(t) in Equation 2, also diminishes in time.However, α may decay in a linear or exponential fashion. Unsupervised SOM arefrequently used for classification. Nevertheless, it does not use class informationin the training process. As a result, the performance with high-dimensional inputdata highly depends on the specific features and the calculation of the clustersborders may be not optimally defined. Therefore, we used a supervised version ofthe SOM, by adding an output layer composed by four neurons (one per class).This architecture is shown in Fig. 2. In this structure, each weight vector ωij onthe SOM is connected to each neuron on the output layer yk.

After all the input vectors have been presented to the SOM layer, some of theunits remain unlabeled. At his point, a probability-based relabeling method is

SOM Layer

Output Layer

Input Layer

Fig. 1. Architecture of the supervised SOM

52 A. Ortiz et al.

Fig. 2. SOM layer relabeling method

applied by using a 2D Gaussian kernel centered in each BMU. Thus, a mayority-voting scheme with the units inside the Gaussian kernel is used to relabel theunlabeled units.

In Equation 5, the Gaussian kernel used to estimate the label for unlabeledunits is shown. In this equation, σ determines the width of the Gaussian kernel.In other words, it is the neighborhood taken into account for the relabelingprocess. On the other hand, (x, y) is the position of the BMU in the SOM grid.

L(x, y, σ) =1

2πσ2e− (x2+y2)

2σ2 (5)

Regarding the calculation of the quality of the output map, there exist twomeasures. The first is the quantization error, which is a measure of the resolutionof the map. This can be calculated by computing the average distance between allthe BMUs and the input data vectors. There is another measure of the goodnessof the SOM. This measure is the topographic error, which measures how theSOM preserves the topology. This error can be computed with the Equation 6,where N is the total number of input vectors and u(xi) is 1 if first and secondBMU for the input vector x(i) are adjacent units (0 otherwise) [5].

te =1N

N∑i=1

u(xi) (6)

Then, the lower qe and qt, the better the SOM is adapted to the input patterns.

3 Feature Extraction and Selection for MRI Segmentation

The segmentation method we have implemented consist of four stages as shownin Fig. 3.

Fig. 3. Feature extraction and selection for training the SOM classifier

MRI Brain Image Segmentation with Supervised SOM 53

Since we deal with a supervised version of SOM classifier, we use one of thevolumes on the IBSR repository [14]. The segmented volume on the IBSR repos-itory is considered as ground truth and therefore, a reference for SOM training.The first for training the SOM which will be used for segmenting further imagesconsist of splitting the image by using overlapping windows. There are workswhich deals with the influence of the window size with image processing [21].However, after several trials, we chose square windows of 7x7 pixels. As we onlyuse square windows, the size is referred to the dimension of one side or w = 7.As a result of this preprocessing stage, we obtain a matrix where the numberof rows is the number of the center pixels on each window and another matrixwhich stores the coordinates of the central pixel of each window. This way, firstand second order features as well as moment invariants are computed from thewindow data. First order features are the intensity of the central pixel, and meanand variance of the intensity on each window. On the other hand, second orderfeatures are computed by using the Gray Level Co-Occurrence Matrix (GCLM)method for calculating the 14 textural features proposed by Haralick et al. in[18]. Having into account the 17 computed features, we compose the input vec-tors for the SOM classifier. As a result we have a feature vector which dimensionis equal to the number of extracted features. These features will be the input tothe classifier which will work with the feature space (IR17). Hence they have todescribe the image and if possible, not to content redundant information. Thus,the feature vector has to be enough different from one segment to another forthe classifier. Thus, the features have to be properly selected in order to keeponly the more discriminant. However, selecting a set of features is not a trivialtask since it varies from one image to another and the feature extraction pro-cess plays a decisive role in the segmentation performance. In order to selectthe more discriminant features we use multiobjective optimization. This way, wekeep only the features which maximize the SOM performance. As commented inSection 1, the quality of the SOM can be evaluated by two measurements. Thefirst is the quantization error, qe, and the second is the topographical error te.Hence, the lower the quantization and topographical errors, the better the qual-ity of the SOM. Thus, the features can be selected in order to provide the lowerqe and te quantities. This can be accomplished by using evolutive computingmultiobjective optimization. In order to minimizing both, qe and te, the multi-objective optimization problem can be reduced to a single objective problem byminimizing the function shown in Equation 7.

Fqt =(qt

2+

qe

2

)(7)

As a result of the selection process, we obtain a feature set which depends onthe plane the segmentation is carried out.

4 Segmentation Process

Once the SOM has been trained with one of the volumes on the IBSR databaseand using the features selected by the algorithm described in Section 2, we

54 A. Ortiz et al.

Fig. 4. Feature Selection and SOM training

proceed to segment new images. These new images are also taken from the IBSRdatabase in order to be able to compare with the ground truth segmentation.For segmenting a new image, the first step is to extract windows of size w ascommented in Section 2. Then, the optimal set of features calculated in thefeature selection stage are extracted from each pixel, depending on the imageplane (coronal, sagital or axial). After presenting the computed feature vectorsto the architecture in Fig. 2, each pixel is determined to belong to a tissue class(White Matter, Gray Matter, Cerebrospinal Fluid or Background).

5 Experimental Results

In this Section, we present the segmentation results obtained with several im-ages from the IBSR database. Moreover, the Jaccard/Tanimoto [14] coefficienthas been calculated in order to compare the overlap average metric with othersegmentation protocols.

These results are available from the IBSR web. Thus, in Fig. 5 segmenta-tion results for the axial plane and the ground truth segmentation for visualcomparison. Moreover, in Fig. 6, results for the coronal plane are shown.

In Fig. 5 and Fig. 6, the segmentation results can be compared with the groundtruth. Nevertheless, the use of an index which measure the similarity betweeneach segment and its ground truth is convenient. This way we use the AverageOverlap Metric, which is calculated from the Jaccard distance. Jaccard distanceis a commonly used overlap measurement between two sets. This can be definedas shown in Equation 8. In this equation, TP,AB represents the number of pixelswhich are positive for a specific tissue in the set A (image A) and negative for theother (image B), TP,BA represents the number of pixels which are positive forthe same tissue in the set B (image B) and positive for the other (image B). TP isthe number of pixels which are positive for the tissue for both, A and B images.However, the more commonly used similarity index is the Jaccard/Tanimotocoefficient. This is defined as 1 − Jd(A, B).

Fig. 5. Pixel Classification Process

MRI Brain Image Segmentation with Supervised SOM 55

(a) WM (b) GM (c) CSFGround Truth

(d) WM (e) GM (f) CSFSegmentation Result

Fig. 6. Segmentation results and ground truth for the sagital plane, volume 100 23,slice 128:30:166. (a) White Matter, (b) Gray Matter and (c) Cerebrospinal Fluid.

(a) WM (b) GM (c) CSFGround Truth

(d) WM (e) GM (f) CSFSegmentation Result

Fig. 7. Segmentation results and ground truth for the coronal plane, volume 100 23,slice 128:30:166. (a) White Matter, (b) Gray Matter and (c) Cerebrospinal Fluid.

56 A. Ortiz et al.

Fig. 8. Average overlap metric for different segmentation algorithms and for our ap-proach for the 100 23 volume (Data from the IBSR web site)

Jd(A, B) =TP,AB + TP,BA

TP + TP,AB + TP,BA(8)

This similarity measurement is widely used in the literature. Moreover, the IBSRweb provides this data for different segmentation algorithms. Thus, we calculatethe Jaccard coefficient for each pair of images, the ground truth segment andthe automatically segmented by our algorithm.

In Fig. 7 we present the overlap average metric for the volume 100 23 onthe IBSR database. At the same time, the overlap average comparison withother segmentation algorithms provided by the IBSR web site is depicted. Asshown in Fig. 7, our proposal outperforms the segmentation techniques found inthe IBSR database. Although there is a new segmentation proposal [19] whichprovides higher values for the overlap average metric, our algorithm outperformsit when classifying CSF pixels.

6 Conclusions

In this paper, we presented a segmentation method based on four basic stages:feature extraction, feature classification, training and segmentation. In order toselect the more discriminant features which maximize the classifier performance,we use multiobjective optimization. The selected set of features is used to traina classifier consisting on a supervised version of SOM which uses an associativelayer to build an effective classifier. Once the system has been trained with a

MRI Brain Image Segmentation with Supervised SOM 57

percentage of the pixels present on a volume, it may classify pixels belonging toother volumes. The experimental results performed with volumes from the IBSRdatabase shows that our proposal outperforms the segmentation algorithms pub-lished in the IBSR web page. However, there are more recent proposals whichprovide better results for WM and GM, but our algorithm clearly outperformsit when classifying CSF pixels.

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