Accurate Partial Volume Estimation of MR Brain Tissues

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1 Aurate Partial Volume Estimation of MR Brain Tissues Author Liew, Alan Wee-Chung, Yan, Hong Published 005 Conferene Title Proeedings of the Asia-Paifi Worshop on Visual Image Proessing Copyright Statement 005 IEEE. Personal use of this material is permitted. However, permission to reprint/ republish this material for advertising or promotional purposes or for reating new olletive wors for resale or redistribution to servers or lists, or to reuse any opyrighted omponent of this wor in other wors must be obtained from the IEEE. Downloaded from Lin to published version Griffith Researh Online

2 ACCURATE PARTIAL VOLUME ESTIMATION OF MR BRAIN TISSUES ALAN WEE-CHUNG LIEW 1, HONG YAN,3 1 Department of Computer Siene and Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong Department of Eletroni Engineering, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon Tong, Hong Kong 3 Shool of Eletrial and Information Engineering, University of Sydney, NSW 006, Australia wliew@se.uh.edu.h, h.yan@ityu.edu.h Abstrat: Aurate estimation of tissue volume has important appliations in brain diagnosti and morphologi studies. In this paper, we show how partial volume estimation of brain tissues from 3D MR brain images an be performed using the reently proposed adaptive spatial FCM algorithm. The effiay of the proposed algorithm is demonstrated eperimentally using simulated MR images with nown ground truths. Keywords: Magneti resonane imaging; partial volume estimation; brain tissue segmentation 1. Introdution Aurate segmentation of MR images of the brain is of interest in the study of many brain disorders [1], []. However, automati MRI brain tissue lassifiation has proven diffiult sine MR images are often degraded by various artifats, notably the intensity non-uniformity (INU) artifat [3] and the partial volume averaging (PVA) artifat [4]. The INU artifat arises due to the inhomogeneity in the magneti field or the non-uniform sensitivity in the reeiver oil. PVA artifat ours when multiple tissues are present in one voel due to the limited resolution of the image. The intensity of a voel affeted by PVA is a weighted average of the intensities of the different tissues in the voel, and fine anatomial strutures are lost. PVA affets the auray of delineation and volume estimation of different tissue. Various approahes have been proposed for partial volume (PV) estimation [4], [5], [6]. In these approahes, every voel is assumed to be onsisted of a miture of pure tissue lasses. The objetive of PV estimation is then to determine the relative fration of eah tissue lass that is present within every image voel. This tas is in ontrast to tissue segmentation, where a voel is lassified to only one tissue type. Sophistiated statistial estimation tehniques are often used to estimate the miture parameters. In [7], the MRI brain tissue lasses are modeled as finite Gaussian mitures with Marov random field regularization and a priori digital brain atlas initialization. The Gaussian miture modeling of the tissue allows PV estimation to be performed during the segmentation proess. In [8], we proposed a novel algorithm alled the adaptive spatial fuzzy C-means lustering (ASFCM) algorithm for 3D MR brain image segmentation. Our algorithm is able to aurately reover the bias field assoiated with the INU artifat, while giving very good segmentation results ompares to several state-of-the-art algorithms. In this paper, we show that the soft segmentation framewor used in our algorithm an also be used to perform aurate PV estimation of brain tissues.. Partial Volume Estimation The ASFCM algorithm we proposed for 3D MR brain image segmentation has two novel features: (1) the inorporation of loal spatial ontet into the lustering proess, and () the suppression of the INU artifat in MR images via the simultaneous reovery of the bias field. We briefly outline the algorithm here, and interested readers are referred to [8] for details. The ost funtion of the ASFCM algorithm is given by J ( U, v, w) = I = 1 subjet to the onstraint = = inde m u, D + βη ( ) + γϕ( ) u 1 (1) 1. The dissimilarity D measures the dissimilarity between the voel s( and the -th luster entroid v as follow, where 1 [ d y + d y (1 λ y ] D = λ ) () ℵ y ℵ ℵ is the ardinality of the neighborhood onfiguration, and the sigmoid weighting fator λ, with y

3 range between zero and one, ontrols the degree of influene of the neighboring voels s( ℵ on the enter voel s (. Through this novel dissimilarity inde, loal spatial ontet is utilized in the lustering proess. When there is no INU, the distane d between s( and is given by the Eulidean distane. When INU is present, the MR data is ompensated for the bias field by letting ~ ~ d = s / b ( v, where b ( ) is the estimate for, ( ) the unnown bias field. In [8], we proposed to estimate the ~ bias field b ( ) in the log domain, suh that d ˆ ˆ, s( w( v, =, where w ( is the log bias field, s ˆ( = log s( and vˆ = log. The 3D log bias field w( surfaes v is modeled as a sta of oupled D ubi B-spline { }. The two regularizing terms, w z η( w ) z = + y + ddy v y ϕ ( ) = ddy (4) z are used to impose intra- and inter-slie ontinuity of the bias field. Through iterative update of the ASFCM variables, we an reah a loal minimum of the objetive funtion. The final segmentation is obtained by a hard thresholding operation on the membership maps. The ASFCM algorithm is able to perform a soft segmentation of the MR images, where the tissue membership value indiates the ontribution of eah tissue to a voel. Thus, it would be possible to perform PV estimation using the returned membership values. We model the PVA artifat as s( = t ( g (, = 1 with onstraints = t =,. Here, is ( 1 t 1 ( 0 t ( the ontribution of tissue at loation, g ( is the true intensity of tissue at loation, and is the number of tissue lasses. Hene, the entroids and membership values returned by the ASFCM algorithm ould be interpreted as orrespond to g ( and (, respetively. t In 3D volume segmentation, the interfae between two tissues forms a surfae, whereas the interfae between three tissues forms a urve. PVA is therefore muh more probable (3) between two tissue types, espeially for highly onvoluted brain tissues. In addition, the anatomial struture of the brain tissues indiates that PVA most frequently ours between GM/WM interfae and CSF/GM interfae, and also between WM/CSF at the interfae between the orpus allosum and lateral ventriles [9]. We therefore assume that PVA eists between two tissue types. We modify the final membership values returned by the ASFCM algorithm by setting, at eah voel loation, the smallest membership value to zero, and proportionately sale the remaining two membership values suh that they add up to one. This simple post-proessing step on the membership maps is able to give very good PV estimation as our simulation results show net. 3. Eperiments For evaluation purpose, we perform PV estimation on the simulated MR brain image obtained from BrainWeb ( [10]. The simulated MR brain image has the following settings: T 1 modality, ICBM protool, slies thiness of 1 mm (1 mm 3 voels), 3% noise level and 40% INU. The fuzzy tissue models for gray matter (GM), white matter (WM), and erebrospinal fluid (CSF) from BrainWeb are used as ground truths. The voel value in the fuzzy tissue models reflets the proportion of tissue present in that voel and ranges between zero and one. The seond to fifth row of Figure 1 shows the results of soft segmentation for GM, WM, and CSF from our algorithm, the FCM algorithm, and the EM-MRF algorithm [7] without and with MRF regularization, respetively. By omparing to the ground truth at the first row, it is lear that our algorithm an estimate the PV muh more aurately than the other three algorithms. The PV estimations given by the FCM algorithm suffer from INU artifat and noise, whereas the PV estimations given by the EM-MRF algorithm either do not model the PVA aurate enough or suffer from perimeter shading. The perimeter shading is partiularly notieable in the GM PV estimation given by the EM-MRF algorithm with MRF regularization, and the CSF PV estimation given by the EM-MRF algorithm with and without MRF regularization. For quantitative evaluation, we alulated the root mean square error (RMSE) in the PV estimation, as shown in Table 1. The RMSE for eah tissue lass is given by the square root of the mean squared differene between the estimated tissue volume and the true volume, omputed over the orresponding tissue support. The tissue support is defined as the union of all voels with a non-zero value for that tissue. It an be seen that our algorithm has the best

4 performane. Table shows the estimated tissue volume for GM, WM, and CSF, omputed over the orresponding tissue support. It an be seen that our algorithm has the best overall performane: in both the WM and CSF volume estimations, it is the losest to the true value, whereas in the GM volume estimation, it is the seond losest to the true value. The EM-MRF algorithm is good at estimating the PV for GM. However, its performane is signifiantly poorer for WM and CSF, where an underestimation of more than 0% has been observed for CSF. Interestingly, our algorithm and the FCM algorithm give the best PV estimation for CSF, even though the CSF is usually the hardest to segment aurately for most eisting algorithms. Table 1. RMSE in PV estimation, omputed over the orret tissue type GM WM CSF Our Alg FCM No MRF With MRF Referenes [1] S. M. Lawrie, and S. S. Abumeil, Brain abnormality in shizophrenia - A systemati and quantitative review of volumetri magneti resonane imaging studies, British Journal of Psyhiatry, Vol. 17, pp , [] J. L. Tanabe, D. Amend, N. Shuff, V. DiSlafani, F. Ezeiel, D. Norman, G. Fein, and M. W. Weiner, Tissue segmentation of the brain in Alzheimer disease, AJNR Amerian Journal of Neuroradiology Vol. 18, No. 1, pp , [3] J. G. Sled, and G. B. Pie, Understanding intensity nonuniformity in MRI, Pro. Medial Image Computing: Computer Assisted Intervention MICCAI 98. Leture Notes in Computer Siene, Springer-Verlag, Berlin, Germany, Vol. 1496, pp , [4] D. H. Laidlaw, K. W. Fleisher, and A. H. Barr, Partial-volume Bayesian lassifiation of material mitures in MR volume data using voel histograms, IEEE Trans. Med. Imag., Vol. 17, No. 1, pp , Table. Estimated tissue volume ( 10 ), omputed over the [5] D. W. Shattu, S. R. Sandor-Leahy, K. A. Shaper, orret tissue type. Perentage value in braet indiates the level of over or under segmentation D. A. Rottenberg, and R. M. Leahy, Magneti resonane image tissue lassifiation using a partial GM (8.99) WM (6.639) CSF (3.71) volume model, NeuroImage, Vol. 13, No. 5, pp. Our Alg (-4.8%) 6.83 (.9%) 3.70 (-0.%) , 001. FCM 8.48(-5.7%) 6.37 (-4.0%) 3.77 (1.8%) No MRF 9.44 (5.1%) (-1.1%) (-6.6%) With (-3.7%) MRF (-1.8%) (-30.0%) 4. Conlusions Due to the limited resolution of the imaging devie, it is possible that multiple tissues are present in one voel, giving rise to the PVA artifat. Aurate partial volume estimation is an important problem in MRI tissue volume estimation. We proposed here a simple post-proessing of the fuzzy tissue membership maps returned by the adaptive spatial FCM segmentation algorithm for PV estimation and show that good results ould be obtained in spite of the simpliity of the approah. Anowledgements This wor is supported by the IEEE Systems, Man and Cybernetis Soiety, Hong Kong Chapter. [6] A. Noe, S. Kovai, and J. C. Gee, Segmentation of erebral MRI sans using a partial volume model, shading orretion, and an anatomial prior, Pro. of SPIE, Medial Imaging 001: Image Proessing, Vol. 43, pp , 001. [7] K.V. Leemput, F. Maes, D. Vandermeulen, and P. Suetens, Automated model-based tissue lassifiation of MR images of the brain, IEEE Trans. Med. Imag., Vol. 18, pp , [8] A. W. C. Liew, and H. Yan, An Adaptive Spatial Fuzzy Clustering Algorithm for MR Image Segmentation, IEEE Trans. Med. Imag., Vol., No. 9, pp , 003. [9] M. Brandt, T. Bohan, L. Kramer, and J. Flether, Estimation of CSF, white and gray Matter volumes in hydroephali hildren using fuzzy lustering of MR images, Computerized Medial Imaging and Graphis, Vol. 18, pp. 5-34, [10] R. K. S. Kwan, A. C. Evans, and G. B. Pie, An etensible MRI simulator for post-proessing evaluation, Visualization in Biomedial Computing (VBC'96). Leture Notes in Computer Siene, Springer-Verlag, Vol. 1131, pp , 1996.

5 Figure 1: Soft segmentation as an estimation of PV for GM, WM, and CSF. The top row is the true PV for GM, WM, and CSF. The seond to fifth rows are the PV estimation from our algorithm, FCM algorithm, EM-MRF without MRF regularization, and EM-MRF with MRF regularization, respetively.