MR brain image segmentation by growing hierarchical SOM and probability clustering
(BMU) for the input vector xi are adjacent units [5]: te =
A. Ortiz, J.M. Go´rriz, J. Ramı´rez and D. Salas-Gonzalez
Introduction: Magnetic resonance imaging (MRI) provides valuable clinical information regarding tissue distribution on the brain for diagnosing brain disorders such as schizophrenia or Alzheimer’s disease. Segmentation consists in partitioning an image into its constituent parts. Thus, segmentation of a brain MRI provides different regions corresponding to different tissues. Then, having separated the different regions, it is possible to perform a quantitative evaluation of the distribution of the tissues on the brain. However, the difference among the amount of pixels corresponding to each tissue makes the segmentation process difficult to be accurate. On the other hand, the evaluation of the different tissues found on a brain MRI is usually done through visual ratings performed by experts and other subjective steps, which are time consuming and prone to error. A fully computer-aided segmentation system for the automatic segmentation of brain magnetic resonance (MR) images is presented in this Letter. Hence, the segmentation process has been split into two phases. The first step consists in extracting the more discriminant features from the MRI in order to maximise the classifier performance. The second phase uses a classifier to figure out the different tissues present on the MRI. For the classification task, previous approaches are based on the intensity values of the whole brain image (histogrambased methods) [1], clustering techniques such as K-means [2] or classic self-organising maps [3]. In this work we use a classifier based on growing hierarchical self-organising maps (GHSOM). The main advantage of this classifier is the ability to discover the inherent hierarchy of the data. Moreover, we use a probabilistic model over each map for labelling the neurons. The result is a fully unsupervised segmentation tool which does not need to use any a priori information to segment brain images. Feature extraction and selection: In the first stage, first order and second order as well as moment and scale invariants are extracted from the image using overlapped 2D windows. These features are computed by using the extracted windows as independent 2D images. Then, the intensity feature corresponds to the central pixel on each window. Second-order features are computed from the grey level co-occurrence matrix (GLCM) [4]. Moreover, moment and scale invariants provide independence with the orientation and the size of an image. Once the features on each window are calculated, a feature vector is stored and associated to the central pixel on the window. The features are normalised by subtracting the mean and dividing by the standard deviation in order to avoid one feature being more important than others for the classifier. The resultant matrix comprises the input space of the classifier. Nevertheless, a feature selection stage is necessary in order to supply the classifier with the more discriminant ones. This is accomplished by multiobjective optimisation, which maximises the goodness of the classifier. Let xi = (x1 , x2 , . . . , xn ) be the data vector belonging to the unit Cj , and xk the kth feature computed. Then, two error measurements can be performed for an SOM classifier. The first evaluates the average distance from the input vectors to the prototypes v m . This is the quantisation error and is defined for a map unit m as v m − xi (1) qem = xi [Cj
On the other hand, the topological error for a map with N neurons measures the topology preservation. This measurement uses the u(xi ) function which is 1 if the first and the second best matching unit
(2)
Note that making qe and te as low as possible, the classifier will perform better. Then, multiobjective optimisation is accomplished in order to minimise both measurements at the same time. This is done by composing a fitness function as Fqtp = (0.5∗ qe + 0.5∗ te )
(3)
for the BMU path p. This BMU is computed for a map m as j Um (xi ) = arg min xi − v
(4)
The BMU path calculation is shown in Fig. 1. Thus, only the features that result in more discriminants for the classifier are stored in a new feature vector. 1.0 0.9 Tanimoto's performance
A fully automatic tool to assist the segmentation of brain magnetic resonance images (MRI) is presented. Thus, the figured out regions can be evaluated for the diagnosis of brain disorders. The main problem to be handled consists in discovering different regions on the image without using a priori information. The new approach consists in hybridising multiobjective optimisation for feature selection with a growing hierarchical self-organising map (GHSOM) classifier and a probability clustering method. The segmentation results yield average overlap metric values of 0.32, 0.75 and 0.69 for white matter, grey matter and cerebrospinal fluid, respectively, over the Internet Brain Segmentation Repository database. These results mean an improvement over the values reached by other existing techniques.
N 1 u(xi ) N i=1
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0.3 0.2 0.1 0 RLGHSOM CGMM
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Fig. 1 Averaged Tanimoto’s coefficient comparison calculated over set of 20 real brain scans from IBSR repository Results for grey matter (GM) and white matter (WM) Manual segmentation results correspond to four brains averaged over two experts
Tissue classification by GHSOM: A GHSOM-based model is used to classify the computed feature vectors. GHSOM [6] is a hierarchical SOM model, which has the ability to build an SOM hierarchy. The depth of the created hierarchy and the breadth of the generated maps are adapted to the input data to keep the quantisation error of each map unit below a defined threshold. Moreover, the breadth limit of each map and the hierarchy depth can be limited by two parameters t1 and t2 , respectively. After the training process, each discovered class is labelled. However, some map units may remain unlabelled if they do not correspond to any BMU for the input data (i.e. the GHSOM is oversized). We can take advantage of this by applying a majorityvoting scheme for labelling the unlabelled units on each map when new data is presented to the GHSOM. This is accomplished by using a 2D-Gaussian kernel s centred on the BMU unit u of width 1, defining the neighbourhood of an unlabelled BMU. Thus, the probability of successfully labelling an unlabelled BMU is defined as Pl =
Ms(u,1) (u) 1
(5)
Then, the unlabelled BMU is labelled with the most occurring label inside the Gaussian kernel. As a result, new clusters are defined on each hierarchy level. Experiments: The experiments were performed over the images provided by the Internet Brain Segmentation Repository (IBSR) database [7]. This database is widely used in the literature for evaluating the segmentation algorithms since it also provides manually segmented volumes. On the other hand, the results shown in the IBSR website are referred to the average of 20 coronal brain scans. Initially, the 256 × 256 × 64-voxel IBSR brain images are split by using overlapped windows of 7 × 7 pixels on each 2D slice. Then, features from each image slice are extracted and each of the coronal, axial and sagittal slices are segmented separately. After that, we compute an n × m × 3 matrix containing the features of the three slices, where n is the number of extracted windows, and m is the number of features selected by multiobjective optimisation. Then, the Jaccard/Tanimoto coefficient [7] averaged over 20 coronal brain scans is calculated. Fig. 1 shows the average overlap metric (averaged Jaccard/Tanimoto index) obtained by using our segmentation method with the probability-based labelling for white matter (WM), grey matter (GM) and cerebrospinal fluid (CSF) calculated over a set of 20 real coronal brain scans from the IBSR. Fig. 2 shows the segmentation results figuring out the WM, GM and CSF
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for coronal, axial and sagittal planes, and the ground truth provided by the IBSR database. Fig. 2 shows the comparison between an image segmented by our algorithm and the ground truth from the IBSR database [7]. axial plane, RLGHSOM segmented
coronal plane, RLGHSOM segmented
sagital plane, RLGHSOM segmented
axial plane, ground truth
coronal plane, ground truth
sagital plane, ground truth
Fig. 2 Segmentation example for three planes, coronal, axial and sagittal, of image 100_23, slice 128, 30, 66 from IBSR database White segment corresponds to white matter (WM), light grey to grey matter (GM) and dark grey to cerebrospinal fluid (CSF)
average overlap
Fig. 3 provides a comparison among average overlap metric data for the segmentation algorithms shown on the IBSR website and the results from our algorithm (RLGHSOM). These results are calculated over the 20 real coronal brain scans. As shown in Fig. 3, our results clearly outperform the results obtained by the algorithms published on the IBSR web page [7] as well as other algorithms such as CGMM [8], especially for CSF and GM tissues. 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
RLGHSOM CGMM marro tskm mlc map fuzzy CSF
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Fig. 3 Average overlap metric calculated over 20 real brain scans from IBSR repository Results for CSF (cerebrospinal fluid), GM (grey matter) and WM (white matter) Dashed line corresponds to authors’ algorithm (RLGHSOM)
Conclusions: A computer-aided segmentation tool for figuring out the three basic tissues on an MRI brain image in an unsupervised way is presented. The system was developed by performing feature extraction and selection using multiobjective optimisation, which reduces the feature space. Then, the most important features feed a classifier based on
GHSOM, which has the ability to discover hierarchical relationships among the data. A probability-based labelling model is used over each map on the GHSOM, which improves the performance of the classifier. As a result, an accurate method for labelling the classifier units is obtained. Thus, our approach reaches 1, 0.32, 0.75 and 0.69 average overlap metric for background (BCK), WM, GM and CSF, respectively, for the IBSR database volumes. These values clearly outperform the results obtained by other segmentation algorithms taken from the IBSR website. Moreover, the average overlap metric comparison shown in Fig. 3 makes clear that the segmentation method based on GHSOM presented in this Letter outperforms the results obtained by other segmentation, especially for CSF and GM tissues. Acknowledgments: This work was partly supported by the Spanish Government under the PETRI DENCLASES (PET2006-0253), TEC2008-02113, NAPOLEON (TEC2007-68030-C02-01) projects and the Consejerı´a de Innovacio´n, Ciencia y Empresa (Junta de Andalucı´a, Spain) under the Excellence Project (TIC-02566). # The Institution of Engineering and Technology 2011 1 February 2011 doi: 10.1049/el.2011.0322 One or more of the Figures in this Letter are available in colour online. A. Ortiz (Departamento de Ingenierı´a de Comunicaciones, Universidad de Ma´laga, Spain) E-mail:
[email protected] J.M. Go´rriz, J. Ramı´rez and D. Salas-Gonzalez (Departamento Teorı´a de la Sen˜al, Telema´tica y Comunicaciones, Universidad Granada, Spain) References 1 Kovacevic, N., Lobaugh, N., Bronskill, M., Levine, B., Feinstein, A., and Black, S.: ‘A robust method for extraction and automatic segmentation of brain images’, NeuroImage, 2002, 17, (3), pp. 1087–1100 2 Vapnik, V.: ‘Statistical learning theory’ (Wiley, New York, 1998) 3 Fan, L., and Tian, D.: ‘A brain MR images segmentation method based on SOM neural network’. IEEE Int. Conf. on Bioinformatics and Biomedical Engineering, Wuchang, People’s Republic of China, 2007 4 Haralick, R.M., Shanmugam, K., and Dinstein, I.: ‘Textural features for image classification’, IEEE Trans. Syst. Cybern., 1973, 6, pp. 610– 621 5 Kohonen, T.: ‘Self-organizing maps’ (Springer, 2001) 6 Rauber, A., Merkl, D., and Dittenbach, M.: ‘The growing hierarchical self-organizing map: exploratory analysis of high-dimensional data’, IEEE Trans. Neural Netw., 2002, 13, (6), pp. 1331–1341 7 Internet Brain Segmentation Repository (IBSR). http://www.cma.mgh. harvard.edu/ibsr 8 Greenspan, H., Ruf, A., and Goldberger, J.: ‘Constrained Gaussian mixture model framework for automatic segmentation of MR brain images’, IEEE Trans. Med. Imaging, 2006, 25, (9), pp. 1233– 1245
ELECTRONICS LETTERS 12th May 2011 Vol. 47 No. 10
