The rest of this thesis is organized as follows. Chapter 2 introduces the proposed im-plicit deformable model as well as the application in brain extraction. The registration techniques presented in Chapter 3 comprise an affine and a non-rigid approaches. Chap-ter 4 introduces the morphometric analysis conducted to examine the neuropathological substrates of bipolar I and II disorders. Finally, Chapter 5 concludes the researches pre-sented in this dissertation.
Brain extraction
2.1 Background and related works
Brain extraction is essential or beneficial to many neuroimaging applications. For ex-ample, removal of the non-brain tissues facilitates the correction of intensity non-uniformity for MR images [20]. Tissue segmentation algorithms for separating brain regions into GM, WM, and CSF usually incorporate brain extraction as a preprocessing step to simplify the segmentation problem [33–35]. Extraction of brain regions can improve the accuracy of brain image registration by avoiding the interference of inter-subject variation of non-brain structures [36], including affine and non-rigid methods [37–39]. In the past decade, VBM [11] has been extensively applied to statistically reveal regions with significant struc-tural discrepancy between image groups [1,3,40–42]. Recent studies indicated that accurate brain extraction can improve the validity of VBM results because of better tissue segmen-tation and brain registration [20,43].
Brain extraction algorithms can be classified into four major classes: (1) threshold-ing/clustering based methods, (2) boundary-based methods, (3) deformable model meth-ods, and (4) hybrid methods. Thresholding/clustering based methods extract brain regions according to the phenomenon that intensities of the voxels belonging to the same tissue are similar. Lemieux et al. proposed a fine-tuned algorithm which utilizes several inten-sity thresholds and morphological operations to remove non-brain areas [44]. Analysis of Functional NeuroImages (AFNI) fits a Gaussian mixture model to the intensity histogram of a brain image and estimates an intensity range to segment the brain areas in a slice-by-slice manner [45, 46]. Hahn and Peitgen presented a watershed algorithm which uses a connectivity criterion, pre-flooding height, to group image voxels with similar intensities and then regards the largest connected component as the brain volume [47]. More exam-ples can be found in [48–53]. Methods of this type are usually sensitive to image scanning parameters and image artifacts, such as noise and intensity inhomogeneity. Therefore, user intervention is usually required to determine proper parameters.
Boundary-based methods locate brain boundaries using the edge information obtained from image derivatives. Bomans et al. presented a semi-automated algorithm in which the brain region was manually labelled from the connected components detected with the Marr-Hildreth operator [54]. Brain Surface Extractor (BSE) method improved the work of Bomans et al. by adaptively smoothing the noisy regions, detecting structure edges, and au-tomatically determining the brain volume [35,55]. In contrast to the thresholding/clustering based approaches, these methods are less sensitive to intensity inhomogeneity and scanning parameters. However, automated methods of this type may encounter difficulties in differ-entiating true boundaries from the false ones. For example, the GM/WM edges are usually very close to the target boundaries, the CSF/GM edges, and thus may perplex the determi-nation of the brain volume.
Extraction methods using deformable models segment brain volumes by evolving con-tour or surface toward the target. Deformable model can be characterized by its repre-sentation method, implicit or explicit, and the evolution scheme [56, 57]. An explicit model directly describes the brain contour or surface and the fitting process is usually rapid [24,33,58,59]. On the other hand, implicit model can easily change the model topol-ogy, for example, to split or merge objects, but the computational complexity is usually high. The level set method adopted in Zhuang et al.’s work [26] is an example of this kind of methods. Brain extraction using deformable model is generally more robust and accu-rate compared to the thresholding/clustering based and boundary-based methods [24–26].
Moreover, incorporation of constraints or prior knowledge about the brain shape is rela-tively easy for this kind of methods. Therefore, they are more robust to both image artifacts and boundary discontinuities and can achieve subvoxel accuracy [56].
Hybrid approaches integrate the methods of different types with the anticipation to draw on the specific strengths at the expense of more computational cost [60–65]. S´egonne et al.
applied the watershed algorithm [47] to generate an initial brain volume and incorporated the prior information of the brain shape into a deformable model to refine the extraction
results [25]. Rehm et al. integrated the extraction results obtained from atlas registration [36], intensity thresholding, and the BSE algorithm [35,55] by means of voting in the brain volume [66].
For large-scale studies, both accuracy and efficiency are important issues when con-sidering brain extraction algorithms [19]. The level set methods, which use implicit de-formable models, are superior in accuracy and robustness, but the computational complex-ity of these methods is usually very high. On the contrary, methods using explicit models are generally more efficient. However, the discretization process in this kind of meth-ods needs to compromise between the extraction accuracy and evolution efficiency. Finer (coarser) discretization employs more (fewer) sampling points to model object boundaries and can achieve more precise (rougher) results at a relatively slow (rapid) evolution speed.
In this work, we designed a new deformable model and developed an automated brain extraction method. The deformable model is implicitly represented by a set of Wend-land’s RBFs and can efficiently evolve toward the target boundary by iterative updates of RBF locations. Because of the use of RBFs, the new model can smoothly represent object boundaries though each RBF keeps a distance to the neighboring ones. Brain contours of 2-D coronal and sagittal slices are individually fitted. The results of these two views are generally complementary and thus can be integrated to obtain accurate 3-D brain volumes.
According to our experiments, the proposed brain extraction method outperformed others when jointly considering extraction accuracy and robustness.