ANATOMY GUIDED HYBRID DEFORMABLE MODEL FOR RECONSTRUCTION OF BRAIN CORTEX FROM MR IMAGE

Somojit Saha Rohit Kamal Chatterjee Sarit Kumar Das Avijit Kar

Department of CSE Department of CSE Department of Mechanical Engineering Department of CSE Jadavpur University BIT Mesra IIT Madras Jadavpur University

Kolkata, India Kolkata, India Chennai, India Kolkata, India somojitsaha@yahoo.co.in rkchatterjee@bitmesra.ac.in skdas@iitm.ac.in avijit_kar@cse.jdvu.ac.in

ABSTRACT This paper presents an Anatomy Guided Hybrid Deformable Model (AGHD) for fully automatic reconstruction of outer cortical surface of brain from MR image. Apart from its fully automatic nature, the algorithm requires tuning of the least number of parameters and avoids all kinds of assumption and approximation. This strength of the algorithm is a derivative of rich tissue specific information of the images acquired with signal attenuation from the gray matters.

Using signal nulling effect the acquisition protocol has enhanced the intensity difference between white and gray matters in the reconstructed MR image. This leads to the generation of a histogram where pixel values of different anatomical structures are distributed around separate dominant modes. An algorithm for automated multilevel thresholding for partitioning specific modes into initial brain contour has been highlighted.

Finally AGHD model has hybridized the essence of traditional “snake” model and the Generalized Gradient Vector Flow deformable contour with precise neuroanatomical guidance for accurate reconstruction of CSF/gray matter interface. The algorithm has been tested on a large dataset with great success and validated by a robust index with highly encouraging outcome. KEY WORDS Magnetic resonance imaging, Image segmentation, Deformable model, Cortical reconstruction

1. Introduction Human cerebral cortex reconstruction from MR image is one of the challenging problems in computational neuroanatomy because of its highly convoluted complex structures and marked variability within and across individuals. Apart from these inherent biological attributes of the anatomic shapes of interest, in case of MRI data, post-hoc processing is limited by factors like image contrast, resolution, SNR, RF field inhomogeneity, sampling artifact etc. which render the boundaries of the structures indistinct and discontinuous [1, 2]. That is why to integrate the cortical boundaries into a coherent mathematical description using model-free, low level image processing technique such as thresholding, edge detection and linking, region growing, relaxation labeling and mathematical morphology operations produce inefficient results since they consider local information only and highly

suffer from manual interpretations [1, 3, 4]. Deformable model-based segmentation approaches consider an object boundary as a whole and can make use of a priori knowledge to constrain the segmentation problem and thereby it can overcome many of the limitations of traditional image processing techniques [3]. Among two types of deformable models, parametric deformable models represent curves and surfaces explicitly in its parametric form and its popularity in medical image analysis is credited to the work of “snake” by Kass et al. [5, 6]. Other variant of deformable models is geometric deformable model which is based on the theory of curve evolution and geometric flow, represents curves and surfaces implicitly as a level set of an evolving scalar function and used as a powerful technique for computing interface motion [1, 4, 6]. A number of groups have attempted to implement both types of deformable models in cortical reconstruction as it is a fundamental step for brain image registration [7, 8], image-guided neurosurgery [9, 10], brain geometry analysis [11, 12] and functional mapping [13, 14]. Davatzikos and Prince used a ribbon for mapping the cortex [15]. Davatzikos and Bryan used a deformable surface model to obtain a shape representation of cortex and proposed an active contour algorithm for determining the spine of such a ribbon [16]. McDonald et al. designed an iterative algorithm for simultaneous deformation of multiple surfaces to segment MR brain images using cost function minimization [17]. Kapur et al. also used a snake approach, along with EM segmentation and mathematical morphology [18]. Teo et al. incorporated knowledge of cortical anatomy with deformable models, in which white matter and CSF regions were first segmented, then the connectivity of the white matter was verified. Finally, a connected representation of the gray matter was created by growing out from the white matter boundary [19]. Xu et al. proposed the generalized gradient vector flow (GGVF) deformable surface in conjunction with tissue membership functions for reconstructing the central cortical layer halfway between the gray/white and gray/CSF boundaries [4, 20]. McInerney and Terzopoulos developed topologically adaptive snakes (T-snakes) and implemented to segment gray/white interface in MR brain image slice [21]. Apart from these parametric deformable models, Zeng et al. implemented geometric deformable models by developing a coupled surfaces approach for automatically segmenting a volumetric cortical layer from 3D image. They used a set of coupled differential equations, with each equation

DOI: 10.2316/P.2010.728-015

Proceedings of the IASTED International Conference

November 1 - 3, 2010 Cambridge, Massachusetts, USAComputational Bioscience (CompBio 2010)

599

determining the evolution or propagation of a surface within a level set framework [22, 23]. Despite so many attempts and approaches, fully automated reconstruction of the outer cortical surface is still a big challenge. Though all approaches address the challenge with success to a great extent, question of automation, close initialization of the deformable models and validation of the end result are still under investigation. All approaches suffer from varied amount of human interaction, approximation and assumption, heuristically tuning of several parameters and above all the questionable representation of the true surface. In case of deformable ribbon of Davatzikos et al. close initialization and human interaction are needed to force the ribbon into the sulcal folds [1, 15, 16]. Algorithm of McDonald et al. is not only computationally expensive but also requires tuning a number of weighting factors in the cost function [1, 17]. Although volume measurement may be reliable with the approach of Kapur et al., the shape of the outer surface is poorly representative of the true surface [1, 18]. GGVF deformable surface of Xu et al. retrieves central cortical layer, not the outer cortical surface. It may be useful for feature based image registration but it can not meet the other purposes like functional mapping or morphometric analysis. Besides this, the method depends on human interaction to extract intracranial tissue from entire brain image, to compute an initial estimate of the cortical surface and depends on tuning of a number of parameters empirically [4, 20]. T-snake segments the gray/white interface not the gray/CSF interface of outer cortical surface. In approach of Zeng et al. coupling between the surfaces incorporates the notion of an approximately fixed thickness separating the surfaces everywhere in the cortex. Since three layered granular type heterotypical cortex of postcentral gyrus, superior temporal gyrus and part of hippocampal gyrus or agranular type heterotypical gyrus of precetral gyrus differs in thickness from six layered homotypical neocortex of the remaining area [24, 25, 26], this approximation does not reflect the true scenario. Considering all these shortcomings of the existing deformable models for segmentation of the cortical outer surface from MR image of brain we have developed a novel Anatomy Guided Hybrid Deformable (AGHD) Model to make it fully automated and accurate. For this purpose we tried to identify the basis of the drawbacks of all existing models. Actually all deformable models with or without incorporation of a priori knowledge of brain anatomy highly depends on parameters derived from image information namely pixel values of the classified tissues, relative differences of their pixel values, edge maps, gradient and so on. Apart from the structural variability of the complex brain structure, common source of error is lack of specific information from a particular tissue class. Different tissue classes may share the same information, most importantly the pixel value. If specific non-overlapping information does not resides in the image at acquisition level mere post-hoc processing is not enough to distinguish different tissue classes depending on the image information. In spite of advancement of post hoc processing, image acquisition plays the central role to meet the objectives. Once the objective is

defined, image acquisition should be done in a way that leads to minimum computational overheads with maximum accuracy. For this application we have focused on the highest contrast between white and gray matters as well as CSF and gray matters at acquisition level to explicitly delineate the CSF/gray interface without any post-hoc enhancement. The acquisition protocol has been detailed in [27]. The resulting images of this protocol have brilliant gray-white contrast which is evident by the unique feature of the histogram. In the histogram, pixels of specific brain structures namely CSF, gray and white matters, background and bones have so distinct gray levels that they group into dominant modes with prominent valleys in between. CSF is confined in the lowermost range of the gray scale and the gray matter, background, white matter and bones are distributed in that order towards the lighter direction of the gray scale [27, 28, 29]. Using this histogram feature automated thresholding in conjunction with prior knowledge of brain anatomy segments the brain with thin layer of CSF encapsulated by the meninges [28, 29]. In this way, we have designed a fully automated algorithm for extraction of intracranial tissues including brain, CSF and meninges. Salient features of the algorithm have been mentioned in section 2 with illustration. External boundary of the meninges serves as the initial estimator of the deformable contour. Then we have hybridized the parametric classical snake of Kass et al. with GGVF proposed by Xu et al. to exploit the power of greater capture range and greater progression into boundary concavity [4, 20, 30, 31] along with precise anatomical guidance. Detail of the algorithm is discussed in section 3. Result of the proposed AGHD model for segmentation of CSF/gray interface is not only encouraging but also holds some unique merits. The most outstanding feature of the algorithm is complete automation without any assumption or approximation. Accuracy of the result has been evaluated quantitatively by a robust index proposed by Zizdenbos et al. [32] with highly positive outcome. 2. Determination of the Initial Estimator As T1-weighting produces better contrast between white and gray matters and inversion-recovery sequence generates greater T1 contrast [33], we used inversion-recovery spin echo sequence to generate T1-weighted coronal view of the brain. A consistent unique feature has been identified in the histogram of MR image of brain acquired with the proposed protocol for better visulization of the target gray structures. This leads to generation of a histogram where pixel values of different anatomical structures are distributed around separate dominant modes. Global multilevel thresholding of the histogram by heuristic approach, based on visual inspection on an image is illustrated in Fig. 1. From this illustration it is evident that CSF, gray matter, background, white matter and bones are distributed respectively in the lighter direction of the gray scale. This unique feature of the histogram has been combined with the prior knowledge of inherent anatomy of brain to develop an algorithm for automated multilevel thresholding of the histogram for partitioning specific modes into brain contour.

600

Fig. 1: Histogram analysis: 1st row shows histogram and the original image, following rows illustrates histogram with faded out thresholded region on left and the segmented image on right.

At first third mode of the histogram that is background is thresholded out automatically using histogram statistics [34]. Pixels containing the gray value lower than the lower threshold of the background must be part of CSF and the gray matters (Cortical and subcortical) as first and second mode of the histogram representative of CSF and gray matter respectively. So, mere global thresholding of the entire image with lower threshold of the background produce boundary of

the intracranial tissue consist of CSF and cortical gray matter. Since meninges shares the same gray value as gray matter, the segmented brain contour is encapsulated with meninges of varied thickness. Though this global thresholding produce perfect result for posterior and middle part of the brain, nasal cavity is misclassified as brain tissue in frontal area. This non-brain region is strategically eliminated after identification of the erroneous slices. Position of the centroid of the bony skull in the brain bounding box plays a deterministic role in this strategy [28, 29]. Thus, the brain contour surrounded by CSF and encapsulated by meninges is extracted automatically. One pixel thick outer boundary of the meninges serves as the con- tour initialization for cortical reconstruction. End results of this automated histogram based segmentation spanning the entire brain from posterior to anterior are depicted in Fig 2. 3. AGHD Model for Cortical Segmentation After computation of the initial contour three stepped Anatomy Guided Hybrid Deformable (AGHD) model has been implemented for finding out the CSF/gray interface in each slice. In first step, classical energy-minimization snake of kass et al. [5] is implemented to drive the contour towards inner margin of the meninges. In next step, under guidance of topological distribution of CSF, snake is reinitialized in the vicinity of the cortex after elimination of thick meningeal fold and finally it is deformed according to GGVF model of Xu et al. [4, 31]. The detail steps are as follows: 3.1 Classical Energy-Minimizing deformable model In this approach, initially the contour is one pixel thick outer most margins of the meninges derived from automated histogram based segmentation described in section 3. Idea of implementing the classical energy-minimizing snake [1,4,5,6] is to drive the initial contour towards inner margins of the meninges that is meninges/CSF interface. The deformable contour is represented in the image

plane 2),( ℜ∈yx as Τ= ))(),(()( sysxsv , where x and y

are the coordinate functions and ]1,0[∈s in the parametric domain. The shape of the contour is typically determined by variational formulation expressed as

.))(())((int dssvsv extsΕ+Ε=Ε � (1)

The functional can be viewed as a representation of the energy of the contour, and the final shape of the contour corresponds to the minimum of this energy. The first term prescribes a priori knowledge about the model such as its elasticity and rigidity and can be expressed as

.)()(2

2

2

2

1

0

2

1intds

sv

swsv

sw∂∂+

∂∂= �Ε (2)

w1(s) and w2(s) two parameters dictate the simulated physical characteristics of the contour. The second term in (1) is the external force which couples the snake to the image. In accordance with the calculus of variations, the contour v(s) that minimizes the energy E must satisfy the Euler-Lagrange equation

601

Fig 2: Initial contour: Initial contour for deformable model derived by automated histogram based segmentation

02

2

22

2

1 =Ε∇−���

����

�

∂∂

∂∂−�

�

���

�

∂∂

∂∂

extsv

wss

vw

s (3)

A numerical solution of (3) is found by discretizing the equation and solving the discrete system iteratively. 3.1.1 Anatomical guidance to define external force field The basic objective of classical deformable model is to bring the initial contour in the area containing CSF. For this reason, we have designed an external force field by using topological guidance of distributed CSF. For this purpose, topological distribution of CSF is segmented out. Since we have the image with very distinct pixel values for different tissue types, a binary image of CSF and the background has been produced by automated optimal global thresholding [35, 36] of first two mode of the histogram. Lower threshold of the third mode of the histogram is determined by the background removal algorithm [34] as follows: In reconstructed MR data, background noise is normally distributed white noise and has a Rayleigh distribution in the image histogram [37] and expressed as

2

2 2( ) exp2noise

f fP f

σ σ� �

= −� �� �

(4)

where σ is the standard deviation of the channel noise. Global maxima or height of any Rayleigh curve

maxr is

related toσ as max0.607 rσ = (5)

All maxima ( )ih f of the histogram function ( )h f and the

corresponding gray values if are traced. Using this value of

( )ih f in (5), initially a Rayleigh curve ( )ir f is generated at

each maximum. Similarity of ( )ir f in the range iσ to the cut

off value 2c if σ= is measured quantitatively with the

original histogram in the same range using a similarity index derived from the Kappa statistic as proposed by Zijdenbos et al. [32]. If area under ( )ir f in the mentioned range is

denoted asiR and area under the original histogram in the

same rang is denoted asiH , then the similarity index

iS

becomes

2 i ii

i i

R HS

R H=

+�

(6)

where { }0...1iS ∈

The relevant ( )ir f for the highest iS is considered as the

Rayleigh for the noise distribution ( )noiser f . Peak of the

curve ( )noiser f coincides with the noise peak of the original

histogram. Then, ( )noiser f is scaled by a constant K and a least square fit is performed by minimizing the error expression

2

2

2 20

( ) exp2

cf

f

f fh f K

σ σ=

� �� �− −� �� �� �

� �� �� (7)

to get the best fit Rayleigh curve ( )r f . Lower threshold of ( )r f is considered as the lower threshold of the third mode

that is image background. Part of the histogram below this threshold is clearly bimodal with well-defined peaks and valley for our image dataset. First mode is of CSF and the second mode is of gray matter. Because of this distinct bimodal distribution, automated optimal global thresholding of the histogram up to lower threshold of the third mode by the algorithm proposed by Otsu [35, 36] efficiently segment out the distributed CSF in the given image. Fig. 3 shows an example of segmentation of CSF with intermediate result of lower threshold of the third mode at gray level 146 and optimal global thresholding at gray level 66. Logic operation of this binary image of CSF with the original image produces uniform gray value of zero for entire CSF region instead of a range of gray values. Thereby it produces a sharp distinct boundary at meninges/CSF interface and CSF/gray matter interface with enhanced gradient. Now, external potential is designed whose local minima coincide with step edges and expressed

as 2

),(),( yxIyxext

∇−=Ε (8)

As meninges has got spatially varied thickness, depending on the sharpness of the edge gradient and the chosen parameters for the internal force, it may fail to come completely inside the meninges. Besides these, in some area, cortical surface may be attached to the meninges leaving no visible subarachnoid space for CSF. Fig. 4 shows the end result of this step. To overcome these entire problems, topological guidance along with a prior knowledge of neuroanatomy has been incorporated in the next step.

602

(a)

(b) (c)

Fig. 3: CSF distribution: Histogram with best fit Rayleigh curve, faded out part for optimal global thresholding and the threshold for CSF distribution (a) applied on the image (b)

and the segmented CSF distribution (c)

3.2 Incorporation of anatomical guidance and reinitialization of the deformable contour CSF map which has been designed to enhance the gradient across the edge adjacent to CSF, also provides topological guidance to eliminate the thick part of meninges as well as helps to design external force field for GGVF in the following steps.

(a) (b)

Fig. 4: Removal of meninges: Classical deformable model started with initial contour over outer boundary of the

meninges (a) and the final contour, red line in (b) resides over inner boundary of the meninges

3.2.1 Removal of thick part of meninges This part is designed to overcome the failure of classical energy-minimizing snake in attempt to eliminate the meninges completely. Since we have clear distribution of CSF, the final contour of the classical snake is scanned pixel

by pixel along its length with inspection of surrounding eight neighbors of each pixel. If any neighbor of the scanned pixel contains the pixel value zero, it must be part of CSF and the corresponding CSF set is traced by extraction of connected component of pixel value zero [38]. If two pixels on the length of the contour are adjacent to the common CSF set, connected component of non-zero pixel value in between them is identified and turned into zero in order to eliminate those sets. In the thick meningeal fold where the classical snake could not touch the meninges/CSF interface, eliminated in this way on letting the cerebrum and cerebellum the only tissue with non-zero pixel value. 3.2.2 Reinitialization of deformable contour Before implementation of GGVF deformable model of Xu et al., presence of the initial estimator must be ensured in the capture range of the gradient vector field. For this purpose, boundary of the cluster of non-zero pixel set (containing cerebrum and cerebellum) is approximated by a polygon with a method for finding minimum perimeter polygons proposed by Kim and Sklansky [38, 39]. In this procedure boundary of the cluster is enclosed by a set of two pixels thick concatenated cells and the boundary is considered as rubber band contained within the walls of a cell. If the rubber band is allowed to shrink, it produces a polygon of minimum perimeter that fits the geometry established by the cell strip. This minimum perimeter polygon serves as the initial contour for the final step of GGVF model. 3.3 GGVF deformable contour Finally GGVF deformable model has been implemented for extraction of CSF/gray matter interface by exploiting its properties of greater capture range and superior convergence of boundary concavity in comparison to the classical snake model. The method is started by defining an edge map f(x) derived from the gray-level image. In our application we have used Canny edge detector [40] to define the edge map with very high gradient at CSF/gray matter interface because of distinct topological guidance of distributed CSF as described in section 4.1.1. The gradient of the edge map f∇ has vectors pointing towards the edges, which are normal to the edges. With help of this edge map, GGVF field v is defined as the equilibrium solution of the following vector partial differential equation

( ) ( )( )fvfhvfgvt ∇−∇−∇∇= 2 (9)

In (9) the first term is considered as the smoothing term, since it alone produces a smoothly varying vector field. The second term is referred as data term since it encourages the vector field to be close to f∇ computed from the edge map.

Spatially varying weighting functions )(⋅g and )(⋅h are applied to the smoothing and data term. For better progression of the deformable contour in long, thin indentation along the cortical boundary where two edges are in close proximity, weighting functions are selected such that

603

)(⋅g gets smaller as )(⋅h becomes larger [4, 30, 31]. For this application, the weighting functions are as follows:

( )2

exp ���

����

� ∇−=∇

κf

fg (10)

( ) ( )fgfh ∇−=∇ 1 (11)

The specification of κ determines to some extent the degree of tradeoff between field smoothness and gradient conformity. Once the GGVF is designed it acts as an external force field and replaces the potential force extE∇− in (3). Then the equation is solved numerically by discretization and iteration, in identical fashion to the traditional deformable contour.

4. Test Results and Validation Checking The proposed algorithm has been tested with 24 datasets of coronal views of proposed acquisition protocol with excellent accuracy. Fig. 5 shows final contour of the AGHD model overlaid on the original image with intermediate outcome of reinitialized deformable model for GGVF (discussed in section 4.2.2) along with edge map for external force and initial estimator. For validation study, some slices were selected such that the entire range of the image volume from anterior to posterior was covered. A domain expert traced the target manually on each slice and it was compared with the automatically drawn head and brain contour using the similarity index described by Zijdenbos et al.[32]. In case of segmented brain images of the coronal view manually segmented cortical outer contour was highly comparable to the automated ones and it is reflected by high similarity indices, approximately 0.98 or more. Index for

exactly similar pattern is 1 and index of more than 0.7 is considered as very good agreement [41].

5. Conclusion In this paper we have tried to meet the basic challenge of reconstruction of outer cortical surface from MR image of brain by developing a novel AGHD model which is hybridization of traditional deformable model with GGVF deformable contour along with prior precise anatomical knowledge. The proposed algorithm claims its excellence in terms of fully automation, tuning of the least number of parameters and avoidance of any assumption or approximation. No step of the algorithm, from elimination of bones and soft tissues or initialization of the deformable contour to final localization of AGHD model requires an iota of human interpretation. Essence of the algorithm resides in the rich non-overlapping tissue specific information in the acquired datasets. Though the algorithm is specific for the proposed acquisition protocol, the protocol is highly applicable for the basic purposes of cortical reconstruction viz. image registration, image-guided neurosurgery and functional mapping when co-registered with functional imaging modalities like SPECT, PET or fMRI since it produces markedly different gray values for different class of tissue.

In our data sets, though the signal from the gray matters has been attenuated, it could not be nullified because of hardware limitations and unavoidable computational constraints [27]. However, the gray-white contrast is markedly improved evidenced by distinct intricate cerebral and cerebellar gray structures. Analysis of the histogram reestablishes this subjective evaluation. The unique feature of the histogram is that modal distribution of the gray values directly correlated with a specific anatomical structure. From the histogram one can easily identify a mode actually representing a given anatomical structure. That is why

Fig. 5: Cortical segmentation: Initial estimator for classical deformable model in first column, edge map for external force with superimposed reinitialized minimum perimeter polygon (red line) for GGVF deformable model in second column and

final contour of GGVF model with segmentation of CSF/gray matter interface (red line) in last column.

604

determination of the initial contour is easily be made by global thresholding only. Actually, using global thresholding, segmentation of the brain is possible only because of high contrast of the adjacent tissues as well as full control to manipulate it to meet the objective. As in our dataset pixel values of CSF and gray matter are consistently lower than the background noise, lower threshold of the background is confidently chosen for the upper threshold for segmentation of the initial brain boundary. As the brain is bounded by the bony skull and the background noise never overlaps the distribution of the bones, the chance of misclassification of the bony part as brain is virtually eliminated. The only shortcoming of the global thresholding is that the nasal cavity is erroneously included in the segmented contour. This has also been successfully eliminated by incorporating spatial information of the intricate anatomy [28, 29]. As structural organization of the bony cranium is more consistent than any soft tissues we intend to shift the centroid towards bony region to set a criterion. Sphenoid and the bony orbit help to identify the anterior slices with coronal section of the frontal lobe of the brain attached to the nasal cavities. No imprecise morphological operations have been used in this algorithm since our primary objective is measurement of subcortical gray matters as well as quantitative study of cognition. The initial brain contour derived in this way is surrounded by CSF and encapsulated by meninges with spatially varying thickness. Meninges is eliminated by using traditional “snake” model and thus the deformable contour is brought to the inner boundary of meninges. To design the exernal force field we again exploit the unique feature of the histogram that is modal distribution of the specific tissue class for segmentation of topological distribution of CSF in the image. By assigning the zero value to the distributed CSF map and logic operation with the original image we actually tries to have zero valued CSF and nonzero valued intracranial tissues like cerebrum and cerebellum. This step is the most crucial for success of the algorithm. By this way gradient of CSF/meninges interface and CSF/gray matter interface becomes very high which helps to define the external force field for traditional snake as well as GGVF field in next step. Besides this, it provides precise anatomical guidance to eliminate thick meningeal folds which can not be eliminated by the traditional snakes. Though some zero valued CSF remain distributed in the ventricles, being far away of the cortical gray matters they do not affect the following steps of the algorithm anyhow.

Final contour of the traditional snake is scanned pixel by pixel for its adjacency to the zero-valued CSF. In case of any thick isolated meningeal fold, final contour of the traditional snake passes arbitrarily through mid portion and may not be adjacent to CSF. But first and last pixel of the fold must be adjacent to the same CSF set. On checking this condition after tracing these extreme points, non-zero set in between is identified and turned into zero value to eliminate it. This situation is more vivid around superior sagittal sinus. This checking is made strategically not to affect the part of the cortical folds which are attached to the meninges leaving no CSF in between them. Thus all discrete non-zero valued meningeal folds turns into zero selectively and the brain

remains as a set of non-zero value. Polygon of minimum perimeter of that set serves as initial contour for GGVF deformable contour and this initialization ensures starting of the deformable contour in the capture range of the force field. In our GGVF model, we have chosen a pair of weighting function for better convergence of boundary concavity which is very essential for our application to reconstruct the highly convoluted cortical surface. The GGVF field computed using this pair of weighting functions will conform to the edge map gradient at strong edges, but will vary smoothly away from the boundary. Despite medialness of the GGVF deformable model, in this application the final contour perfectly lies over CSF/gay matter interface, since the contour faces a very high gradient at this interface when approaches externally. This has occurred due to anatomical guidance of CSF distribution. Instead of having a range of gray values, distributed CSF posses gray value zero and gray matter distribution in the gray scale is far away from zero. This produces very high gradient at their interface and helps to segment out that interface. The result is highly encouraging and this 2D deformable contour is to be implemented as 3D surface for reconstruction of the entire cortical surface. 7. References

[1] Isaac N. Bankman, Handbook of Medical Imaging Processing and analysis, Academic Press, 2000 [2] Marijn E. Brummer, Russell M. Mersereau, Robert L. Eisner, & Richard R. J. Lewine, “Automatic Detection of Brain Contours in MRI Datasets”, IEEE Transactions on Medical Imaging, 12(2), pp.153-166, 1993 [3] Tim McInerney and Demetri Terzopoulos, “Deformable models in medical image analysis: a survey,” Medical Image Analysis, 1(2), pp. 91-108, 1996 [4] C. Xu, “Deformable Models with Application to Human Cerebral Cortex Reconstruction from Magnetic Resonance Images”, Ph.D. thesis, The Johns Hopkins University, Baltimore, MD, January 1999 [5] M. Kass, A. Witkin and D. Terzopoulos, “Snakes: Active contour models”, International Journal of Computer Vision, 1(4), pp. 321-331, 1988. [6] S. Osher and N. Paragios, “Geometric level set methods in imaging, vision and graphics,” Springer-Verlag, 2003 [7] G. E. Christensen, S. C. Joshi and M. I. Miller, “Volumetric Transformation of Brain Anatomy”, IEEE Transactions on Medical Imaging, 16(6), pp.864-877, 1997 [8] Chris A. Davatzikos, “Spatial transformation and registration of brain images using elastically deformable models”, Computer Vision and Image Understanding, 66, pp. 207-222, 1997 [9] W. E. L. Grimson, G. J. Ettinger, T. Kapur, M. E. Leventon, W. M. W. III and R. Kikinis, “Utilizing segmented mri data in image-guided surgery”, Int. J. Pattern Recog. Artif. Intell., 11(8), pp. 1367-1397, 1996 [10] M. Vaillant, C. Davatzikos, R. H. Taylor and R. N. Bryan, “A path-planning algorithm for image-guided neurosurgery”, in Lecture Notes in Comp. Sci.: CVRMed-MRCAS’97, 1205, pp.467-476, 1997

605

[11] S. Joshi, J. Wang, M. I. Miller, D. C. V. Essen and U. Grenander, “On the differential geometry of the cortical surface,” in Proc. Of the SPIE: Vision Geometry IV, 2573, pp. 304 -311, Aug. 1995 [12] L. D. Griffin, “The intrinsic geometry of the cerebral cortex”, Journal of Theoretical Biology, 166(3), pp. 261-273, 1994 [13] A. M. Dale and M. I. Sereno, “Improved localization of cortical activity combining EEG and MEG with MRI cortical surface reconstruction: A linear approach”, Journal of Cogn. Neuroscience, 5(2), 162-176, 1993. [14] H. A. Drury and D. C. V. Essen, “Functional specializations in human cerebral cortex analyzed using the visible man surface-based atlas”, Human Brain Mapping, 5, pp.233-237, 1997 [15] Chris A. Davatzikos and Jerry L. Prince, “An Active Contour Model for Mapping the Cortex”, IEEE Transactions on Medical Imaging, 14(1), pp.65-80, 1995 [16] Chris A. Davatzikos and R. N. Bryan, “Using a deformable surface model to obtain a shape representation of cortex”, IEEE Transactions on Medical Imaging, 15(6), pp.785-795, 1996 [17] D. MacDonald, D.Avis and A. C. Evans, “ Multiple surface identification and matching in magnetic resonance images,” in SPIE Proc. VBC’94, 2359, pp. 160-169, 1994 [18] T. Kapur, W. Grimson, W. Wells and R. Kikinis, “ Segmentation of brain tissue from magnetic resonance images”, Medical Image Analysis, 1, pp.109-128, 1996 [19] P. C. Teo, G. Sapiro and B. A. Wandell, “Creating connected representations of cortical gray matter for functional MRI visualization”, IEEE Transactions on Medical Imaging, 16(6), pp.852-863, 1997 [20] C. Xu, D. L. Pham, M. E. Rettmann, D. N. Yu and J. L. Prince, “Reconstruction of the human cerebral cortex from magnetic resonance images”, IEEE Transactions on Medical Imaging, 18(6), pp.467-480, 1999 [21] Tim McInerney and Demetri Terzopoulos, “ T – snakes: Topology adaptive snakes”, Medical Image Analysis, 4, pp.73-91, 2000 [22] X. Zeng, L. H. Staib, R.T. Schultz and J. S. Duncan, “Volumetric Layer segmentation using coupled surface propagation” in Computer vision and Pattern Recognition, pp. 708-715. IEEE Comp. Soc., Los Alamitos, 1998 [23] X. Zeng, L. H. Staib, R.T. Schultz and J. S. Duncan, “ Segmentation and measurement of the cortex from 3D MR images using coupled surface propagation”, IEEE Transactions on Medical Imaging, 18(10), 1999 [24] R. S. Snell, “ Clinical Neuroanatomy for Medical Students,” Lippincott-Raven Publishers, Fourth edition, 1997 [25] M J T FitzGerald and Jean Folan-Curran, “ Clinical Neuroanatomy and Relate Neuroscience,” W.B. Saunders, Fourth edition, 2002 [26] R.H. S. Carpenter, “Neurophysiology”, Arnold, Fourth edition, 2003 [27] Somojit Saha, Sarit K. Das, Avijit Kar, “High Resolution MR Image of Brain With Signal Attenuation of Gray Matter”; IST, IEEE Instrumentation and

Measurement Society, Thessaloniki, Greece, pp. 311-315, 2010 [28] Somojit Saha, Sarit k Das, Avijit Kar; “Segmentation of MR Image of Brain: A New Method Using Unique Histogram Features and Prior Knowledge of Brain Anatomy,” IPCV , WORLDCOMP, Las Vegas, Nevada, USA,2010 [29] Somojit Saha, Sarit k Das, Avijit Kar; “A New Segmentation Technique for Brain and Head from High Resolution MR Image Using Unique Histogram Features,” IPTA (IEEE & EURASIP), Paris, France, 2010 [30] C. Xu and J. L. Prince. “Snake, shape, and gradient vector flow,” IEEE Transaction on Image Processing, 7(3), pp. 131-139, 1998 [31] C. Xu and J.L. Prince, “Generalized gradient vector flow external forces for active contours,” Signal Processing, An International Journal, 71(2), pp. 131-139, 1998 [32] A. Zijdenbos, B. Dawant, R. Margolin, & A. Palmer, “Mophometric analysis of white matter lesions in MR images: Method and Validation”; IEEE Transactions on Medical Imaging, 13(4), pp. 716-724, 1994 [33] Zhi-Pei Liang, & Paul C. Lauterbur, Principle of Magnetic Resonance Imaging – A signal processing perspective, IEEE Press, 2000 [34] Somojit Saha, Sarit k. Das, Subhajit Das, Avijit Kar; “An improved algorithm for automated segmentation of the head contour from MR image”, VIIP, IASTED Cambridge, UK, pp. 25-32, 2009 [35] N. Otsu “ A threshold selection method from gray level histogram”, IEEE transaction on systems, man, and cybernetics, SMC 9, pp 62-66, 1979 [36] R. M. Haralick and L. G. Shapiro, “Computer and Robot Vision, vol. 1, Addison-wesley Publishing company, 1992 [37] M. Henkelman, “Measurement of signal intensities in the presence of noise in MR images”, Medical Physics, 12(2), pp. 232-233, 1985 [38] Rafael C. Gonzalez, & Richard E. Woods, Digital Image Processing 2nd ed. (Prentice-Hall, 2002). [39] C. E. Kim and J. Sklansky, “Digital and cellular convexity,” Pattern recognition, 15(5), pp. 359-367, 1982 [40] J. F. Canny, “A computational approach to edge detection,” IEEE Transaction on Pattern Analysis and Machine Intelligence,” 8(6), pp. 679-698, 1986 [41] John J. Bartko, “Measurement and Reliability: Statistical Thinking Considerations”; Schizophrenia Bulletin, 17(3), pp. 483-489, 1991

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