2.1 Introduction
The process of automatically constructing a spatially unbiased template can bedescribed in followingsteps, which is depicted in Fig. 2.1.
1. Nonuniformity correction
2. Selection of representative brain
3. Determination of unbiased stereotaxic space
4. Transformation and averaging
First, we use Non-parametric Non-uniform intensity Normalization (N3) [26] tech-nique, provided by Montreal Neurological Institute, to correct the nonuniformity of image.
In the following steps, we use the corrected images to be processed. Second, because every brain images should be registered to a stereotaxic space before calculating the unbiased space, a reference brain is needed. We choose a brain volume, which is one subject of the image set and has the minimum variation of deformation magnitude to the other subjects, as the representative brain. Then we will define the unbiased space based on this repre-sentative brain. Thirdly, we compute the unbiased space according to the reprerepre-sentative brain and all other brain images. Finally, we normalize all images to the unbiased space and average them to generate the brain template.
2.2 Nonuniformity Correction 15
Figure 2.1: Flow chart of template construction. This figure describes the processed flow chart of the template construction. First, nonuniformity correction is performed to acquire images with better qualities. Second, a representative brain is selected among the data set to serve as the reference volume. Thirdly, the unbiased space is determined based on the selected representative brain and all other images. Finally, all images are transformed to this unbiased space and averaged to become the brain template.
2.2 Nonuniformity Correction
An intensity artifact, which the signal intensity vary smoothly across an image, is often seen in MR images. Variously referred to radio frequency (RF) inhomogeneity, shading ar-tifact, or intensity non-uniformity, it is usually attributed to poor RF field uniformity. How-ever, the image nonuniformity may significantly degrade the performance of automatic segmentation and interfere in quantitative analysis. Therefore, the removal of intensity nonuniformity (“bias”) from MRI images is an essential prerequisite for the quantitative analysis of MRI brain volumes. Fig. 2.2 shows the nonuniformity of MR images of a sub-ject in our database.
Non-parametric Non-uniform intensity Normalization (N3) [26] technique have been
Figure 2.2: Nonuniformity of MR images. This figure shows the nonuniformity of MR images of a subject. There are four different slices in axial view of an individual brain. We can see the nonuniformity appeared, which the posterior white matter (in yellow region) is lighter than the anterior white matter.
devised in order to correct this intensity nonuniformity without requiring supervision. With-out anatomy model assumptions, an iterative approach is employed to estimate both the multiplicative bias field and the distribution of the true tissue intensity in N3 method. It models the low-frequency spatial variations in the data to maximize high-frequency infor-mation in the intensity histogram of the corrected volume. The N3 algorithm was demon-strated a high degree of stability [2], represents an elaboration of tissue signal analysis.
Also N3 substantially improve the accuracy of anatomical analysis techniques such as tis-sue classification, cortical surface extraction [26] and grey matter segmentation for voxel-based morphometry [1]. An executable version of the N3 algorithm was provided by Dr.
A. C. Evans at the Montreal Neurological Institute, and program default values were used for all run-time parameters.
2.3 Image Registration
Registration of structural brain images typically include affine transformation and non-linear deformation. In general, affine transformation, or called global normalization, is composed of zero or more linear transformations, including translation, rotation, scaling and shearing. Further, nonlinear deformation is used to match the subject to the target
im-2.3 Image Registration 17
Figure 2.3: Affine registration and nonlinear registration. This figure shows the affine registration and nonlinear registration results. (a) This is the source image which is nor-malized to the target image. (b) This is the target image. We can tell the different brain size and shape between the source and the target. (c) The affine registered image of the source image is presented. The source image now is roughly registered to the target with the brain size. (d) The nonlinear registered image of the source image is showed. We can see the anatomical structure of the source brain is now registered to the target image, especially the corpus callosum region.
age on a regional level. The registration method adopted in this study is proposed by Liu et al. [18]. In their study, simulation data were used for validations and experiment results showed that the proposed registration approaches can efficiently register brain images with high accuracy compared to other algorithms, such as SPM2, AIR5 and ART. Fig. 2.3 shows the affine registration and nonlinear registration results of a subject in our database.
In image registration, two images are performed by serious deformations in order to make one image identical to the other. The result is stored in a deformation field, a vector field which records the magnitude and direction required to deform a point in the source
image to the appropriate point in the target image. The deformation function is
xT = xS+ dST(xS) (2.1)
, which xT is a point in the target image, xSis a point in the source image and dST(xS) is the deformation vector of the point x.
2.4 Selection of Representative Brain
Because every brain images should be registered to a stereotaxic space before calculat-ing the unbiased space, a reference brain is needed [16]. There are several choices to select a reference volume such as the MNI305 template and the ICBM152 template. However, these different ethnic templates may cause large deformation while registering Taiwanese subject to them. Large deformation often conduct inaccuracy or instability of registration.
Thus, we choose a brain volume, which is one subject of the image set and has the mini-mum variation of deformation magnitude to the other subjects, as the representative brain.
In other words, the representative brain is defined to be the brain that is closer to all the brains than others. The definition of representative brain is as follows:
R = arg min
i {var(kdij(xi)k))|, ∀j 6= i, xi ∈ brain area, (2.2) where dij(xi) is the deformation vector from subject i to subject j at position xiin the space of subject i. The subject which has the minimum cost function, variation of deformation magnitude, with all the other subjects is chose as representative brain R. We describe this idea in Fig. 2.4.
2.5 Determination of Unbiased Stereotaxic Space
Our goal is to create an unbiased space, the template, in which the structure location at the template denoted as xT should be equal to the expected location of that structure
loca-2.5 Determination of Unbiased Stereotaxic Space 19
Figure 2.4: The sketch map of selection of the representative brain. Suppose there are eight subjects in the data set, S1, S2, . . . , S7 and SR. When we register SRto other seven subjects, we will obtain seven deformation fields dRi(xR), which i = 1, 2, . . . , 7. SRwill be the selected representative brain if it has the minimum value of var(kdRi(xR)k) compared with other subjects.
tion at subject i, denoted as xi, across all individuals N (a similar argument in Diedrichsen J. et al. [8]) [12] [14]:
xT = E{xi}, (2.3)
where i = 1, 2, . . . N . That is, the expected deformation vector between xT and xi is zero.
However, we can regist representative brain R to subject i to get the deformation field.
Referring to equation 2.1, dRi(xR) is the deformation vector from representative brain R to subject i at position xR. Thus,
xi = xR+ dRi(xR), (2.4)
which xR+ dRi(xR) is the location in the space of subject i. Trivially,
E{xi} = E{xR+ dRi(xR)} = xR+ ¯dR(xR), (2.5) where dRis the average deformation field which calculated by
d¯R(xR) = 1
Figure 2.5: The sketch map of transforming representative brain to the unbiased space. Suppose there are eight subjects in the data set, S1, S2, . . . , S7 and R. When we register representative brain R to other seven subjects, we will obtain seven deformation fields dRi(xR), which i = 1, 2, . . . , 7. Then we use the equation 2.6 to derive the average deformation field ¯dR. By applying the average deformation field ¯dR to the representative brain R to result the unbiased template space T.
Therefore, referring to equation 2.3 and equation 2.5, the template space can be defined as
xT = xR+ ¯dR(xR), (2.7)
which means that applying the average deformation field to the representative brain R to result the unbiased template space T. We describe this notation in Fig. 2.5.
The representative brain is registered to each nonuniformity-corrected image. We ob-tain each deformation field dRi(xR) and average them to become the average deformation field ¯dR. It is notable that the deformation vectors, stored in the average deformation field, record the vector required to deform points, called voxels, in representative brain to the appropriate voxels in unbiased space. This unbiased space is our template space.
However, due to the sub-voxel accuracy of the average deformation field ¯dR, the in-tensity of each voxel xT is not trivially known. We illustrate the concept with Fig. 2.6.
2.5 Determination of Unbiased Stereotaxic Space 21
Figure 2.6: The sketch map of interpolating the mapping coordinate in the unbiased space. The intensity profile of the representative brain is shown as I(xR). When compress-ing the profile of representative to become the profile of the template, the ideal profile of template is shown as I(xT) (green profile). x1R and x3R plus the average deformation vec-tors, ¯dR(x1
R)and ¯dR(x3
R)to the sub-voxel position in unbiased space. However, the intensity of x2T must not be derived by simply averaging the intensity of I(x1R) and I(x2R), which is 0.7. Instead of averaging the intensity, it should calculate the corresponding position in the xR, which is x2Rin this case, and finally derive the intensity of x2T, which is 1.0.
Suppose the image signal is a one dimensional signal, and the intensity profile of the repre-sentative brain is shown as I(xR). The point x1R and x3Rare deformed to sub-point position in template space. In that case, the intensity of point x2T in template space is not to know.
However, the intensity of x2Tmust not be derived by simply averaging the intensity of I(x1R) and I(x2R). Instead of averaging the intensity, it should calculate the corresponding position in the xR, which is x2Rin this case, and finally derive the intensity of x2T.
In this thesis, we propose a interpolation method to calculate the corresponding position in the xR. A voxel xTin the unbiased space, or said template space, is corresponding to xTR in the representative space. Then the intensity of xT is I(xT) is defined as:
I(xT) = I(xTR). (2.8)
We interpolate the xTR position by the following equation :
In equation 2.9, w is the Gaussian weight which defined as
f (x, y, z) = Ae−( equation 2.8 and equation 2.9, we finally derive the intensity of all voxels in the unbiased space.
2.6 Average Template in Unbiased Space
After we derive the unbiased space, we normalize all MR T1-images, which have been corrected the intensity inhomogneity, to the unbiased space. Then we average them to become the average template. However, because this unbiased space is derived from the representative brain, the brain size and orientation of the generated template is significantly dependent on the representative brain. Suppose the representative brain is not located in the center of the MR image, then the brain template will not located in the center of the MR image. Fig. 2.7 describes the processed flow chart of the average template.
2.7 Brain Tissue Templates
Brain tissue could be classified into three different types, gray matter (GM), white mat-ter (WM) and cerebral spinal fluid (CSF). Inthe thesis, GM, WM and CSG tissue templates are generated by the following steps:
2.7 Brain Tissue Templates 23
Figure 2.7: Flow chart of average template construction. This figure describes the pro-cessed flow chart of the average template. The average template in unbiased space in con-structed by normalizing all individual images to the unbiased space then averaging them to become the average unbiased template.
(1) Segment each individual brain into three tissue classes (GM, WM and CSF).
(2) Register each T1-weighted image to the unbiased template and obtain its deforma-tion field.
(3) Normalize every tissue segment of all individuals by their own deformation field in step 2.
(4) Average all these normalized tissue segments and finally form the templates of three tissue classes.
Figure 2.8: Flow chart of tissue templates construction. This figure describes the pro-cessed flow chart of the tissue templates. First, we segment each individual brain into GM, WM and CSF by FMRIB’s Automated Segmentation Tool (FAST). Then we register each T1-weighted image to the unbiased template and obtain its deformation field. After we obtain the deformation field, we normalize every tissue segment of each individual by ap-plying its own deformation field. Finally, the tissue templates are generated by averaging all these normalized tissue segments.
Segmentation are performed by FMRIB’s Automated Segmentation Tool (FAST) [27]
[13]. The tissue templates procedure is shown in Fig. 2.8.
2.8 Mapping to Talairach Coordinate System
Talairach coordinate system is widely used as a reference with Brodmann cytoarchi-tectonic areas and other structural and functional labels. Therefore, we should provide the mapping method between our template and the Talairach coordinate system. In other words, we intend to create a transformation to apply to the coordinates from the our brain template, to give matching coordinates in the TB. However, because there is no MRI scan
2.8 Mapping to Talairach Coordinate System 25
for the Talairach brain, we are incapable of using computerized registration to simply trans-form our template to Talairach brain.
Since there are already tools that can transform a coordinate in the MNI template space to the Talairach space [6], we use MNI template as the bridge to Talairach space by trans-forming the coordinate in our template to MNI template first. Thus, the mapping coordi-nate in Talairach space will be calculated by the second transformation from MNI305 to Talairach space.
To implement the method illustrated above is registering our template to the MNI tem-plate to obtain the deformation field. This deformation field stores the appropriate mapping coordinate in MNI template space of every voxel in our template. Then we derive Talairach coordinates from mni2tal script (http://www.mrc-cbu.cam.ac.uk/ ˜matthew/abstracts/ MNI-Tal/mnital.html) , a tool commonly used to map MNI coordinates to Talairach coordi-nates [3]. Also we register MNI template to our template and transform the coordinate in Talairach space to out template space.