Group MRF for fmri Activation Detection

Transcription

1 Group MRF for fmri Activation Detection Bernard Ng, Rafeef Abugharbieh The University of British Colubia 9 West Mall, Vancouver, BC VT Z bernardn@ece.ubc.ca, rafeef@ece.ubc.ca Ghassan Haarneh Sion Fraser University 8888 University Drive, Burnaby, BC VA S haarneh@cs.sfu.ca Abstract Noise confounds present serious coplications to accurate data analysis in functional agnetic resonance iaging (fmri). Siply relying on contextual iage inforation often results in unsatisfactory segentation of active brain regions. To reedy this, we propose a novel Group Marov Rando Field (Group MRF) that extends the neighborhood syste to other subects to incorporate group inforation in odeling each subect s brain activation. Our approach has the distinct advantage of being able to regularize the states of both intraand inter-subect neighbors without having to create a stringent one-to-one voxel correspondence as in standard fmri group analysis. Also, our ethod can be efficiently ipleented as a single MRF, hence enabling activation aps of a group of subects to be siultaneously and collaboratively segented. We validate on both synthetic and real fmri data and deonstrate superior perforance over standard analysis techniques.. Introduction Iage noise reains a aor challenge to accurate segentation. In scenarios with only a oderate level of sparsely distributed noise, regularization approaches that exploit contextual iage inforation, such as Marov Rando Fields (MRF), typically perfor well in segenting the obects of interest []. However, if the aority of iage voxels are corrupted by strong noise, MRFs ay not be effective due to the lac of reliable neighbors. The heart of the proble is that, in certain cases, there ay siply be insufficient inforation within a single iage to enable reliable segentation. Additional inforation is thus needed in these situations. If ultiple iages containing obects of the sae class are available, one can exploit coon features shared aong the iages to enhance the segentation of each iage. This general idea of incorporating group inforation is widely used in any areas including recognition [], registration [], and reconstruction []. A popular approach is to build a odel or teplate fro a set of training iages that is then used to segent new iages []. Alternatively, one ay use ultiple teplates to generate candidate labels that are subsequently reconciled using e.g. aority voting to fuse these labels into a single segentation []. Generating representative odels, however, can be quite difficult for certain applications, such as edical iaging where even experts oftenties cannot provide consistent, accurate ground truth segentations. Under such circustances, unsupervised approaches are needed. A few recent unsupervised approaches have alluded to the iportance of aggregating inforation over a set of candidate segentations. A notable approach called enseble clustering that cobines outputs fro ultiple clustering algoriths has shown superior perforance over using each algorith separately []. In [7], Ward and Haarneh proposed extracting seletons fro a group of iages and applied aority voting to prune each seleton with robust results deonstrated. In this wor, we extend this fundaental idea of drawing consensus across iages to the analysis of functional agnetic resonance iaging (fmri) data, where the highly coplex noise structure and the lac of ground truth segentation render group-wise unsupervised approach particularly attractive. In a typical fmri experient, ultiple subects (usually - ) are recruited to perfor a certain tas, e.g. finger tapping, while three diensional (D) MRI scans of their brains are acquired at regular tie intervals. Neurons within brain regions involved will fire in response to tas stiulus, which alters the oxygenation level in nearby tissues, resulting in an intensity change in the MR signal. This induced signal contrast is referred to as blood oxygen level dependent (BOLD) contrast, which is widely used as a basis for inferring brain activation. However, confounds such as scanner noise, head otion, and oxygen level changes arising fro the cardiac and respiratory cycles have perplexing effects on the BOLD signal, which greatly coplicates accurate analysis of fmri data. The standard way of analyzing fmri data involves exaining the intensity changes of each voxel over tie and statistically coparing each voxel s intensity tie course against a hypothesized response. A general linear odel (GLM) is typically used for this purpose, where statistics reflecting the degree of siilarity between the stiulus and voxel tie courses are generated and assebled into an activation statistics ap [8]. A threshold is then applied to identify the activated voxels. Since each voxel is analyzed

2 independently, voxel interactions are ignored despite that each voxel is unliely to function in isolation. Therefore, soe have proposed odeling activation statistics aps as MRFs to incorporate contextual iage inforation [9], while others eployed Bayesian approaches to directly integrate neighborhood inforation into the activation statistics estiates []. Encouraging neighboring voxels to have siilar labels (e.g. active or non-active) helps reduce the nuber of isolated voxels falsely declared as active. However, solely relying on contextual iage inforation is often inadequate to deal with the inherently low signal-to-noise (SNR) of fmri data. Thus, pooling additional inforation fro other subects ay prove beneficial []. In ost fmri studies, the standard approach for aggregating inforation across subects is to first non-rigidly register the anatoical iage of each subect onto a coon brain teplate with the sae transfor applied to the activation statistics ap. Statistical testing is then applied to activation statistics assebled across subects to delineate the coonly active voxels. The resulting group ap is then taen as representative of all subects. The iplicit assuption is that a one-to-one correspondence exists between the active voxels across subects and that the voxels are perfectly aligned in the teplate space. However, due to the large anatoical inter-subect variability, rarely can the anatoical iages be perfectly aligned to the teplate. Hence, registration errors pose aor liitations to the standard analysis approach. In fact, even if one anages to align the anatoical iages perfectly, whether a one-to-one functional correspondence exists between voxels is debatable. The considerable functional inter-subect variability observed in past studies [] suggests that such voxel correspondence does not liely exist. Nevertheless, active voxels within brain regions involved with the experiental tass are often consistently found across subects, though the exact locations are usually different []. The question thus becoes whether the observed functional variability is due to noise or true intersubect differences. If the observed variability ainly arises fro noise, incorporating group inforation to segent each subect s activation statistics ap ay better reveal intersubect coonalities. In this paper, we propose exploiting group inforation in fmri analysis by odeling the activation ap of each subect as an MRF with the neighborhood syste extended to other subects. Our approach thus ointly accounts for the states of both intra- and inter-subect neighbors in estiating the state of each voxel. Also, by incorporating group inforation in segenting each subect s activation ap, as opposed to estiating a group ap, both inter-subect coonalities as well as differences can be studied. In our proposed forulation, MRFs of all subects can be ointly and cooperatively solved as a single MRF. We thus refer to our proposed ethod as Group MRF.. Proposed ethod Our proposed ethod iics a neurologist s expertise deployed in deciding if a voxel is active. Specifically, to deterine if voxel in subect i is active, one ay first exaine the spatial neighbors of voxel. However, if the neighboring voxels are found to be too noisy or unreliable, one ay have to consider voxels of other subects located in proxiity to voxel. Since only voxels proxial to each other are hypothesized to be in a siilar state, the stringent requireent for a one-to-one voxel correspondence is alleviated. Instead, a relaxed condition of requiring only the brain structures of the subects to be approxiately aligned is in place. Based on this intuition, we propose to odel each subect s activation statistics ap as an MRF whose neighborhood syste extends to other subects (Fig. ). Since the vast anatoical variability in real fmri data renders accurate whole-brain registration difficult, we eploy an alternative approach, where we define regions of interest (ROIs) and perfor alignent at the regional level. This approach ensures that no brain structures will be istaenly declared as part of another structure as often encountered with whole-brain registration. voxel subect i voxel p subect subect N s voxel q Fig.. Proposed Group MRF. Each subect s ROI activation ap is odeled as an MRF with its neighborhood syste extended to other subects to incorporate group inforation... Group MRF Let G i = (V i,e i ) be a graph, where E i = ε i U ε ~i, V i and ε i are the sets of voxels and edges within subect i s ROI, and ε ~i is the set of edges between subect i and other subects. Also, let pε i be the intra-subect edge between voxels and p and qε ~i be the inter-subect edge between voxel and q. Delineation of subect i s ROI activation statistics ap can be forulated as the following MRF energy iniization proble:

3 E i ( x ) ( x ) p ( x, x p ) V i p i, () q ( x, xq ) q ~ i where x r L = { K} is the label assigned to voxel r, indicates the experiental tas, θ (x ) denotes a unary potential, and p ( x, x p ) and q( x, xq ) are intra- and intersubect pairwise potentials. α is used to adust the contribution of the pairwise potentials while γ balances the contribution of intra- and inter-subect pairwise potentials... Unary potential Let t be the activation statistic of voxel. If voxel has a low probability of being activated during tas, we penalize labeling x as active, and vice versa. Our unary potential is thus defined as: ( x ) p( x t ), () where p(x = t ) is the probability of x being assigned label given t, estiated using a constrained Gaussian ixture odel (CGMM) [], as detailed in Section.... Pairwise potentials The proposed extended neighborhood syste consists of an intra- and an inter-subect coponent. For the intra-subect coponent, we use the Pott s odel potential: p ( x, x p ) ( x x p ), () where δ(y) = if y = and otherwise, and edges are added between the - and -connected spatial neighbors for the D and D case, respectively. For the inter-subect coponent, we also use the Pott s odel potential: q ( x, xq ) ( x xq ). () Edges are added between voxel of subect i and its c nearest inter-subect neighbors for every subect pair... Algorith ipleentation The proposed ethod can be ipleented as a single MRF by treating the voxels of all subects as a single set and adding edges within and between all subects in the anner described in Section.. Since we are labeling the voxels as either active or non-active (i.e. K = ) as in [], globally optial labels for this Group MRF s energy function () can be estiated using binary graph cut []. N s E ( x ) p ( x, x p ) i V i p i, (). q ( x, xq ) q ~ i where N s is the nuber of subects and. is introduced to avoid penalizing each inter-subect edge twice. By using this ipleentation strategy, activation statistics aps of all subects can be ointly and collaboratively segented. We set α in () to /N s to scale the cuulative contribution of the subects to a level siilar to that of a single subect, and thus ensures that the pairwise potentials will not doinate over the unary potential. The choice of γ depends on the degree of inter-subect variability, which is unnown a priori. We have thus set γ to. to weight subect i s own inforation ore than that of other subects. Nevertheless, varying γ by ±. (i.e. ±%) did not significantly affect the results. To copute p(x = t ) in (), we first estiate t using a GLM [8]: y X, () t / se( ), (7) where y is the intensity tie course of voxel, ω is assued to be white Gaussian noise, β is a vector containing the estiated effects β for the various tass, and se(β ) is the standard error of β []. X is a design atrix with boxcar functions (tie-loced to tas stiuli) convolved with the heodynaic response (HDR) as regressors [8]. Based on t, p(x = t ) can be estiated using a CGMM [], as shown graphically in Fig.. η τ a b α µ K π t z N v σ Fig.. Graphical depiction of constrained GMM for coputing the unary potential θ (x ). In CGMM, t is assued to be generated fro a ixture of K Gaussian distributions with ixing coefficients π, eans µ, and variance. Conugate priors are used to constrain the odel paraeters µ,, and π : t K K ~ N (,, (8) ) ~ N (, ), (9) ~ IG( a, b), () ~ Dir( ), () where IG(a,b) and Dir(α) denote inverse Gaa and Dirichlet distributions. Adding priors itigates the singularity proble in axiu lielihood solutions, i.e. µ collapsing onto t with approaching, thus assigning infinite probability at t. Also, having priors allows us to encode our nowledge of µ into the odel. Specifically, we now that t of non-active voxels should theoretically be and the threshold used for delineating the active voxels given t is roughly between and based on Gaussian Rando Field

4 (GRF) theory [8]. This prior nowledge is encoded into η with τ set to. As for, we use an uninforative prior by setting both a and b to. [], since little is nown about this paraeter. α is set to /K assuing equal prior probabilities of being assigned any one of the K labels. Gibbs sapling is eployed to copute p(x = t ) []: Nv, Nv, K p( z, ) Dir z,, K z, () p( t, z ) Nv, z t Nv, z p( t, z, a, b) N v N, v IG a.z, b.z, Nv, z, ( t ), (), () p( z t,,, ) N (, ), () where N v is the nuber of voxels in subect i s ROI and z, is an indicator variable set to if voxel during tas is estiated to be in state, and otherwise. For the intersubect pairwise potential, we have epirically set c to, but increasing c to or had little effects on the results.. Synthetic data experients To validate our proposed ethod, we generated synthetic datasets, each consisting of ten subects. The activation pattern coprised three clusters (Fig. ). The signal intensity of the active voxels (ared with circles in Fig. ) was set to decrease exponentially as a function of distance fro the respective activation centroid of each cluster. The saller cluster was added to test whether Group MRF can detect spatially isolated active voxels that are consistently present across subects. The synthetic tie courses of active voxels were generated by convolving a box-car function, having the sae stiulus tiing as in our experient (Section.), with a canonical HDR [8] and adding Gaussian noise. We introduced additional inter-subect variability to eulate two potential cases. In the first case, which we refer to as the coon cluster location (CCL) case (Fig. (a)-(d)), the location of the clusters were fixed but the placeent of the activation centroids (i.e. location away fro which the signal of the active voxels decrease) were varied across subects and peritted to be anywhere within the clusters. This case eulates the situation where the active regions copletely overlap between subects but the location at which the BOLD signal concentrates varies. Hence, it will appear that there is little overlap between the active regions of the subects. In the second case, which we refer to as the varying cluster location (VCL) case (Fig. (e) & (f)), we randoly varied the locations of the two larger clusters across subects. This case odels the situation where the active regions of the subects do not copletely overlap. The axiu cluster isalignent was set to two voxels (~% of the cluster width) in both the vertical and horizontal directions. The axiu SNR was set as. for both cases in Fig., i.e. voxels near the activation centroids had an SNR close to., whereas voxels away fro the activation centroids had an SNR below.. For coparisons, we also tested the following ethods: (i) GLM with Gaussian soothing and a threshold based on GRF theory for a p-value of. [8], (ii) MRF separately applied to each subect s t ap, and (iii) second level GLM (i.e. substituting spatially soothed β of all subects into y in () and setting X as a colun of ones) with a GRF threshold [8]. We refer to ethods (i), (ii), and (iii) as individual GLM (iglm), individual MRF (imrf), and group GLM (gglm), respectively... Coon cluster location Fig. (a)-(d) shows the qualitative results for the CCL case. Only results fro four of the ten subects in one of the synthetic datasets are plotted due to space liitations. Using iglm issed ost of the active voxels away fro the activation centroids, whereas using imrf resulted in ore active voxels identified, although active voxels with t below were largely undetected. Also, the saller cluster was issed due to lac of intra-subect active neighbors. Using gglm detected ore ildly activated voxels, but the spatial soothing required for using GRF threshold resulted in any false positives. Using Group MRF detected ost of the active voxels, including those with t well below. Also, Group MRF consistently detected the saller cluster in all subects. To quantify the perforance, we coputed the average Dice siilarity coefficient (DSC) over the synthetic datasets (Fig. ). TP DSC, () TP FP FN where TP, FP, and FN denote the nuber of true positives, false positives, and false negatives, respectively. As evident fro the low DSC for iglm and imrf, a single subect s inforation ay be insufficient to obtain satisfactory segentation at low SNR, even when contextual inforation is considered. This result confirs our arguent for incorporating additional inforation. Solely relying on group inforation, however, can also be probleatic as apparent fro the gglm results, where increasing SNR reduced DSC. This counter-intuitive finding can be explained as follows. Since the locations of the activation centroids are randoly varied across subects, β at each voxel location will thus be different between subects. Considering that the range of β values is governed by the SNR, increasing SNR will increase inter-subect variability in β, which decreases TP, hence a reduction in DSC. In contrast, using Group MRF resulted in higher DSC for all SNR levels copared to the other ethods. Also, unlie gglm, the DSC of Group MRF increased

5 - - (a) iglm with Gaussian spatial soothing and threshold estiated based on GRF theory (coon cluster location) (b) imrf separately applied to each subect (coon cluster location) - - (c) gglm with Gaussian spatial soothing and threshold estiated based on GRF theory (coon cluster location) (d) Proposed Group MRF (coon cluster location) (e) gglm with Gaussian spatial soothing and threshold estiated based on GRF theory (varying cluster location) (f) Proposed Group MRF (varying cluster location) Fig.. Synthetic data results. t plotted with dots and circles indicating detected and ground truth active voxels. t aps along each colun correspond to the sae subect s activation ap for each test case, but appears different due to spatial soothing eployed in GLM. For the CCL case, Group MRF (d) detected the aority of active voxels, whereas iglm (a) and imrf (b) failed to obtain such delineation. gglm (c) also detected ost of the active voxels, but included any false positives. For the VCL case, Group MRF (f) was able to adapt to the cluster variations, whereas the single group ap approach of gglm (e) does not facilitate such adaptation.

6 DSC iglm imrf gglm Group MRF SNR Fig.. DSC of the four contrasted ethods for the CCL case at various SNR levels. Group MRF consistently outperfored all the other ethods. Note: DSC of iglm = at SNR =.. with increasing SNR. The reason is that Group MRF does not directly copare t across subects. Instead, group inforation is integrated by first assigning a label to each voxel and then estiating the state of a voxel based on consensus of labels between the intra- and inter-subect neighbors. Note that at higher SNR where ore reliable inforation is available within each subect, adding group inforation still iproved results over using iglm and imrf alone. Moreover, increasing the nuber of subects increased DSC as shown in Fig.. DSC Nuber of Subects SNR. SNR. SNR.7 SNR. Fig.. DSC vs. nuber of subects for the CCL synthetic test using Group MRF at varying levels of SNR. Increasing the nuber of subects consistently increased DSC... Varying cluster location Qualitative results for the VCL test case are shown in Fig. (e)-(f). iglm and imrf resulted in siilar perforance as in the CCL case, since neither ethod depends on group inforation. Therefore, we oitted these results fro Fig.. Using gglm, any active voxels near the cluster borders were issed due to cluster isalignents. In contrast, Group MRF was able to adapt to the intersubect differences with ore active voxels identified and fewer false positives declared. This adaptability arises fro the fact that, unlie gglm, Group MRF does not solely rely on group consensus but also uses subectspecific inforation to segent each subect s t ap. Thus, the ore pronounced inter-subect differences were preserved. Quantitative results show that Group MRF again outperfored all other ethods (Fig. ). We note that increasing the nuber of subects did not increase DSC initially (Fig. 7), due to difficulties in drawing consensus across subects with the added cluster isalignents. Nevertheless, after adding seven subects, DSC began and continued to increase, thus deonstrating Group MRF s robustness to inter-subect variability. DSC SNR iglm imrf gglm Group MRF Fig.. DSC of the four contrasted ethods for the VCL case at various SNR levels. Group MRF again outperfored all other ethods. Note: DSC of iglm = at SNR =.. DSC Nuber of Subects SNR. SNR. SNR.7 SNR. Fig. 7. DSC vs. nuber of subects for VCL case using Group MRF. DSC decreased initially due to cluster isalignents, but eventually increased when enough subects were deployed.. Real data analysis.. Materials After obtaining infored consent, fmri data were collected fro healthy subects ( en, 7 woen, ean age 7. years). Each subect used their right hand to squeeze a bulb with sufficient pressure to aintain a bar shown on a screen within an undulating pathway. The pathway reained straight during baseline periods and becae sinusoidal at a frequency of. Hz (slow),. Hz (ediu) or.7 Hz (fast) during tie of stiulus. Each session lasted s, alternating between baseline and stiulus of s duration. Functional MRI was perfored on a Philips Gyroscan Intera. T scanner (Philips, Best, Netherlands) equipped with a head-coil. T*-weighted iages with BOLD contrast were acquired using an echo-planar (EPI) sequence with an echo tie of.7 s, a repetition tie of 98 s, a flip angle of 9, an in plane resolution of 8 8 pixels, and a pixel size of.9.9. Each volue consisted of axial slices of thicness with a gap. A D T-weighted iage consisting of 7 axial slices was further acquired to facilitate anatoical localization of activation. Slice tiing and otion correction were perfored using Brain Voyager (Brain Innovation B.V.). Further otion

7 correction was perfored using otion corrected independent coponent analysis (MCICA) []. The voxel tie courses were high-pass filtered to account for teporal drifts and teporally whitened using an autoregressive AR() odel. No whole-brain registration or spatial soothing was perfored. For testing our proposed ethod, we selected the left priary otor cortex (M) as the region of interest, since the left M is nown to activate during right-hand otor oveents (Fig. 8). Anatoical delineation of the left M was perfored by an expert based on anatoical landars and guided by a neurological atlas. The segented ROIs were resliced at fmri resolution for extracting preprocessed voxel tie courses within each ROI. The anatoical ROIs were rigidly aligned (Fig. 8) using a ethod that odels each ROI point cloud as a Gaussian ixture and registers the ROIs by aligning the ixture distributions []. Enhanced robustness to noise and outliers was shown over standard techniques []. Fig. 8. Hounculus. Hand area of M is circled in Hounculus diagra. Approxiate corresponding area in the rigidly aligned ROIs is indicated. Hounculus courtesy of thebrain.cgill.ca... Results and discussion Results obtained with Group MRF applied to real data are shown in Fig. 9. Again for coparisons, we tested iglm, imrf, and gglm. For gglm, we too the union of the ROI point clouds (Fig. 8) to create an ROI teplate, interpolated β in the teplate space, spatially soothed the β with a 8 full-width half-axiu Gaussian ernel, and applied a second level GLM to copute t [8]. For both iglm and gglm, a GRF threshold at a p-value of. was used. [8]. Note that activation changes in M ay be very subtle between the tas and baseline conditions, since both required otor squeezing. We thus expect a low SNR for the t aps. Only t of the fast condition is plotted due to space liitations. Due to low SNR, iglm issed ost voxels in the hand region (Fig. 8). In contrast, imrf detected any voxels in the hand region, but also falsely declared wide areas adacent to the hand region as active. We suspect these falsely detected areas arose fro insufficient inforation in each subect s t ap to correctly deterine which voxels were truly active. For gglm, we interpolated the group ap bac onto each subect s ROI to facilitate clearer coparisons. gglm detected the hand region in general. However, closely coparing the t aps (Fig. 9(a)) with the thresholded aps (Fig. 9(d)) showed that a nuber of voxels directly adacent to the detected region had t above soe of the voxels within the detected region but were falsely declared as non-active. These voxels, in addition to the hand region, were correctly detected using Group MRF despite the apparent high degree of inter-subect variability (Fig. 9(a)). Thus, the results again show that Group MRF has the highly desired capability of identifying subect coonalities, while preserving the ore pronounced inter-subect differences.. Conclusions We proposed a novel ethod that incorporates group inforation for accurate segentation of fmri activation aps. By odeling activation aps of a group of subects as a Group MRF, all subects inforation is ointly exploited. Also, our presented forulation enables all subects activation aps to be siultaneously segented using binary graph cut, which guarantees global optiality. Moreover, our proposed approach perits group inforation to be integrated without having to establish a one-to-one voxel correspondence as in conventional fmri group analysis. Applying Group MRF to synthetic data for a range of SNR showed superior perforance over standard techniques. On real data, Group MRF was able to consistently detect active voxels in regions nown to be involved with the experiental tas eployed, whereas techniques relying on single subect failed. Our results thus indicate great proise for the proposed group-wise approach in handling noisy data. References [] S. Gean and D. Gean. Stochastic Relaxation, Gibbs Distributions and the Bayesian Restoration of Iages. IEEE Trans. Pat. Anal. Mach. Intel., ():7-7, 98. [] W. Zhao, R. Chellappa, A. Rosenfeld, and P.J. Phillips, Face Recognition: a Literature Survey. ACM Coputing Surveys, ():99-8,. [] F. Wang, B. Veuri, and T. Syeda-Mahood. Generalized L-divergence and its Application to Shape Alignent. In: Proc. Info. Proc. Med. Iaging, 7-8, 9. [] T. Yu, N. Xu, and N. Ahua. Reconstructing a Dynaic Surface fro Video Sequences Using Graph Cuts in D Space-tie. In: Proc. Intl. Conf. Pat. Rec., :-8,. [] X. Artaechevarria, A. Munoz-Barrutia, and C. Ortiz-de- Solorzano. Cobination Strategies in Multi-Atlas Iage Segentation: Application to Brain MR Data. IEEE Trans. Med. Iaging, 8(8):-77, 9. [] V. Singh, L. Muheree, J. Peng, and J. Xu. Enseble Clustering using Seidefinite Prograing. In: Proc. NIPS, 7. [7] A. Ward and G. Haarneh. The Groupwise Medial Axis Transfor for Fuzzy Seletonization and Pruning. IEEE Trans. Pat. Anal. Mach. Intel., 9. (PrePrint) DOI:.9/TPAMI.9.8

8 (a) Non-soothed t-aps separately estiated for each subect using GLM (b) iglm with Gaussian soothing and threshold estiated based on GRF theory (c) imrf separately applied to each subect (d) gglm with Gaussian soothing and threshold estiated based on GRF theory (e) Proposed Group MRF Fig. 9. Real data results for all subects. Blue in (b)-(d) indicates detected active voxels in the left M. iglm(b) failed to detect the hand region shown in Fig. 8, whereas imrf(c) detected the hand region but also falsely declared adacent areas as active. gglm (d) detected the hand region, but neglected several adacent voxels that were oderately active. Exaples of such voxels (that can be easily identified in the ROI orientation shown) are indicated with a red arrow. Group MRF (e) correctly detected the hand region including the oderately active voxels neglected by gglm, thus deonstrating Group MRF s ability to adapt to inter-subect differences. [8] K.J. Friston, A.P. Holes, K.J. Worsley, J.B. Poline, C.D. Frith, and R.S.J. Fracowia. Statistical Paraetric Maps in Functional Iaging: A General Linear Approach. Hu. Brain Mapp., ():89-, 99. [9] X. Descobes, F. Kruggel, and D.Y. von Craon. Spatio- Teporal fmri Analysis Using Marov Rando Fields. IEEE Trans. Med. Iaging, 7:8-9, 998. [] W.D. Penny, N.J. Truillo-Barreto, and K.J. Friston. Bayesian fmri Tie Series Analysis with Spatial Priors. Neurooage, :-,. [] D.R. Bathula, L.H. Staib, H.D. Tagare, X. Papadeetris, R.T. Schultz, and J.S. Duncan. Multi-Group Functional MRI Analysis Using Statistical Activation Priors. In: Proc. Med. Ig. Coputing and Coputer Assit. Intervention fmri Data Analysis Worshop, 9. [] M.W.G. Vandenbrouce, R. Goeoop, E.J.J. Dusche, J.C. Netelenbos, J.P.A. Kuier, F. Barhof, Ph. Scheltens, and S.A.R.B. Robouts. Interindividual Differences of Medial Teporal Lobe Activation during Encoding in an Elderly Population Studied by fmri. Neuroiage, :7-8,. [] S. Mani, P. Ciuciu, J. Idier, and J.B. Poline. Joint Detection-Estiation of Brain Activity in Functional MRI: A Multichannel Deconvolution Solution. IEEE Trans. Sig. Processing, (9):88-,. [] Y. Boyov, O. Vesler, and R. Zabih. Fast Approxiate Energy Miniization via Graph Cuts. IEEE Trans. Pat. Anal. Mach. Intel., ():-9,. [] W.W. Daniel. Biostatistics: A Foundation for Analysis in the Health Sciences, 9 th Ed. Wiley, 8. [] R. Liao, J.L. Kroli, and M.J. McKeown. An Inforationtheoretic Criterion for Intrasubect Alignent of fmri Tie Series: Motion Corrected Independent Coponent Analysis. IEEE Trans. Med. Iaging, ():9-,.