The model-based brain tissue classification framework presented here was setup to analyze MR signal abnormalities in neuropathological disorders in large sets of multispectral MR data in a reproducible and fully automatic way. The overall strategy adopted was to build statistical models for normal brain MR images, with emphasis on accurate intensity models. Signal abnormalities are detected as model outliers, i.e., voxels that cannot be well explained by the model. Special attention has been paid to automatically estimate all model parameters from the data itself to eliminate subjective manual tuning and training.
As discussed in section 1.1.1, geometry-driven and intensity-driven methods are the two main paradigms for model-based segmentation. In this chapter, both paradigms are used in a sequential order. Complex intensity models are developed that automatically fit to the data. As a result, multispectral MR data are segmented fully automatically without prior knowledge about the appearance of the different tissue types in the images. Bias fields are automatically corrected for, and the partial volume effect is explicitly taken into account. The intensity models are complemented with image-based brain atlas models of prior tissue probabilities. These atlases are first iconically matched to the images and subsequently used as constraints during the tissue classifications. The matching was originally limited to affine transformations between atlas and study image (see also , but was later extended to nonrigid transformations as well (see also [14, 50, 75, 80]).
These attempts to combine the ability of intensity-driven methods to capture local shape variations with the general description of global anatomy provided by geometry-driven methods have been limited to a sequential use of both methods in separate processing steps. Atlas maps of prior distributions of the different tissue classes are first geometrically aligned to the images to be segmented. These transformed maps provide an initial approximate segmentation to initialize the classification algorithm but also provide an estimate of the prior class probabilities for each voxel during further iterations.
In  an attempt was made to intertwine statistical intensity-based tissue classification and nonlinear registration of a digital anatomical template to segment both normal and abnormal anatomy. The algorithm iterates between a classification step to identify tissues and an elastic matching step to align a template of normal anatomy with the classified tissues. The alignment of the anatomical template is usedto modify the classification to produce a spatially varying, rather than a global classification. The steps are iterated until the matched anatomy and the classification agree. However, this method currently needs manual supervision, and it still needs to be investigated how reliably this method can be automated. Moreover, the iterative procedure is not derived as the solution of an optimization problem. As a result, there is no guarantee that convergence, if at all, to a plausible solution can be obtained.
Wyatt and Noble , on the other hand, suggested a joint solution to the linked processes of segmentation and registration. They cast this as a maximum a posteriori (MAP) estimation of the segmentation labels and the geometric transformation parameters and pose the solution using MRF. Their results indicate that the addition of spatial priors (in the form of intermediate segmentation maps) leads to substantially greater robustness in rigid registration and the combination of data via registration improves the segmentation accuracy. However, their formulation is poorly suited for generalization to nonrigid registration.
D'Agostino et al.  explored the possibility of nonrigid image registration by maximizing an information theoretic measure of the similarity of voxel object labels directly, rather than of voxel intensities. Applied to intersubject MR brain image matching, such labels are obtained by the intensity-based tissue segmentation presented in this chapter, assigning each voxel a probability to belong to a particular tissue class. Using class labels as features for nonrigid image registration opens perspectives for integrating registration and segmentation as two cooperative processes in a single framework, by considering one of the images as an atlas that is nonrigidly warped onto the other and that provides a priori tissue distribution maps to guide the segmentation of the other image. The possibilities of such a method are enormous, since it would allow fully automated partial volume segmentation and bias correction of multispectral MR images with unknown tissue contrast, while deforming a label atlas at the same time. The quantification of intensity abnormalities could be confined to anatomical regions of interest. The brain could be automatically segmented into relevant substructures, allowing the quantification of changes in shape and volume, over time in one individual patient, or between populations. Knowledge of the deformation of the label atlas would allow nonrigid multimodal registration of images of different patients and provide a common reference frame for population studies. Deriving realistic statistical models for the shape of the human brain is, therefore, a major challenge for further research.
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