Figure 1.4: A 3-D magnetic resonance image of a human head. It is shown in the coronal, sagittal and axial views.
ical treatments. Moreover, this imaging uses magnetic fields and non-ionizing radiation.
According to current knowledge, they do not have potential harmful effects to humans. In comparison with some other scanning methods like CT, it is very safe. Another advantage of MR imaging, probably the most important character, is the flexibilty of data acquisition and the outstanding contrast resolution. Therefore, it can be used as spectroscopic imag-ing, diffusion-weight imagimag-ing, angiogarphic imagimag-ing, and functional imaging. That makes MR images able to provide much respectable information and endow the thecnique with superior scientific and dianostic values [4].
Because of the clear contrast resolution, MR images are often used to observe patho-logic tissues from normal tissues, and help doctors to diagnose medical conditions and disorders of the brain. However, such a manual diagnosis is very subjective and time-consuming, especially when the amount of images is large. Thanks to the advances in com-puter, computerized approaches can help to deal with the huge and complex data. Many morphometric analysis methods were proposed to quantitatively analyze MR images by computers.
1.3 Morphometrics
By using MR images, a number of in vivo anatomical studies of the human brain have been done. Most studies are based on the defined regions of interests (ROIs), and then analyze each tissue volumes [5–7] in ROI. However, this method has some limitations. It wastes a lot of time to define the ROIs, especially when there are large amount of subjects [8]. In addition, when analyzing a certain disease, users have to know the most concerned regions [9] before selecting ROIs. It makes ROI-based analysis inconvenient to be used in practice.
Therefore, another kind of automatic morphometric methods, involving the technique of spatial normalization, to characterize neuroanatomical differences has been developed.
These methods broadly fall under two categories: (1) ones handle macroscopic differences in shape of brain, and (2) ones handle microscopic differences in brain tissue as the shape differences have been discounted. When connecting these with the technique of spatial nor-malization, the first kind of methods analyzes the parameters or the deformation fields used during the normalization; and the second kind of methods analyzes resulting normalized images after normalization.
The first family of morphometric method includes the pattern-theoretic approach [10], deformation-based method [11, 12], tensor-based method [13, 14], and factor analytic ap-proach [15]. These methods quantify brain shape by using deformation fields obtained from nonlinear registration. This kind of methods can potentially obtain a precise estimation of the brain shape, but it is very sensitive to the accuracy of the underlying normalization approach. Consequently, there are some limitations in practice [9].
The second family of morphometric methods characterizes anatomy in brain tissue by estimating voxel intensities of normalized images. Because this type of methods makes use of images after normalization, the differences in the brain shape are eliminated. Thus, it is
1.4 Motivation 9
suitable for analyzing local and subtle differences in brain tissue. A common-used method, voxel-based morphometry [16], is belong to this family. Besides, the RAVENS [9] is also a kind of these methods.
This thesis emphasizes the second family of morphometric methods. The targeted im-ages are all normalized. Now, the voxel-based morphometry (VBM) is the most popular method applied to analysis of structural brain discrepancy between different groups of im-ages. For each and every voxel from the normalized images, it makes a standard statistical test to examine if there exists a significant difference of brain structure on the location of this voxel. Although VBM is an intuitional and simple approach, it has a fatal defect so that its sensitivity to some kind of group differences is bad. Our goal is to propose a method to ameliorate this lack. In the following, we will briefly indicate the main drawbacks of the VBM analysis, and try to improve according to the fundamental cause of it. It goes into details in chapter 2.
1.4 Motivation
Although VBM is one of most popular morphometric method and has been applied successfully in many instances, there are still limitations that make VBM disable to detect particular anatomical differences in some situations. These limitations are caused by the inherent defect of this approach. It is because VBM is a voxel-by-voxel manner, i.e. a univariate method, to analysis differences by using standard statistical tests at each distinct voxel. That means when VBM tests group difference at a particular voxel, it only takes measurements of images at this voxel in account at a time, and discards potential informa-tion carried by other voxels adjacent to this voxel. The way of VBM to analyze the brain structures makes this method simple to use. However, from the spatial point of view, such the voxel-wise manner to find anatomical differences appears improper, because it treats each voxel as an independent object. Adjacent brain tissues should have relations to each
other. As a result, this method is criticized for its capability to estimate widely-distributed, continuous and subtle changes in brain structure [17].
In this work, we proposed a novel method that can consider interrelations between voxels, called the multivariate volumetric morphometry (MVM). In this method, a high-dimensional classification technology is employed. It seeks the most discriminative hyper-plane that separates populations by minimizing the scatter within each individual group and simultaneously maximizing the scatter between groups. The discriminative hyper-plane not only has the ability to classify different groups, but also is appropriate to be used in this application of characterizing the anatomical group discrepancy. Besides, before using this classification technique to find brain differences, a recombination of the spatial and frequency signals is performed for the multiresolution analysis. Our method is built on the classification and the data recombination techniques.
In this thesis, we not only demonstrate the effectiveness of the proposed method, but also develop an efficient computational implementation to save time for analysis. More-over, a part of idea of this method has been proved in this work. Experimental results showed that the multivariate volumetric morphometry (MVM) indeed has a better sensitiv-ity to subtle and distributed changes of brain structures. So, it is very useful to characterize early symptoms of a disease especially. The details of the reason why we need a multivari-ate approach and the proposed method are described in the chapter 2 and 3, respectively.
In the following chapters, we introduce the voxel-based morphometry and its drawbacks in chapter 2, and then our method in chapter 3. In chapter 4, some experiments are used to estimate the accuracy of the proposed method, and the comparison between the results of MVM and VBM is performed. Finally, we will bring up some issues about our method MVM in chapter 5, and conclude this work in chapter 6.