Los Principios Contables desde la perspectiva del Derecho Financiero: La unidad de

EM segmentation involves the accurate modelling of the intensities of the whole space covered by the different regions of the brain. In the standard EM segmentation, every region is assumed to follow a Gaussian distribution over the intensities of the voxels. This section describes the subdivision of regions that need to be described with more than one Gaussian distribution. The subdivision is performed in the space of the image to be segmented by splitting the spatial priors propagated from the atlases.

As the manual segmentation protocol (Gousias et al., 2012) did not divide the WM/CGM structures of the brain into CGM and WM, these regions contain both tissues. Therefore, in order to describe each structure with a single Gaussian intensity model, each WM/CGM structure was divided into its corresponding tissue parts (WM, CGM) using a soft segmentation. The prior probability of each WM/CGM structure in the individual subject space is multiplied with a WM and a CGM probability map to define the corresponding WM and CGM parts. The required subject-specific tissue probabilities are obtained as the posteriors of a simple EM scheme with 4 classes (CSF, GM, WM and extra-cranial space) in the intensity domain. In this EM scheme, the means and standard deviations are initialised using k-means clustering (Macqueen, 1967). The k-means clustering is performed in the intensity space with k=4 clusters. An alternative approach would be to segment the WM/CGM structures of the atlases into WM and CGM and use the modified atlases for the propagation of the CGM,WM components of these structures. However, the registration between different neonatal brains does not align accurately the cortical ribbon (Figure 4.11.A. demon- strates this effect). The term-equivalent atlases have very different cortical complexity from early neonatal brains and the registration can not capture the large deformations occuring as a result of the rapid development. There- fore, we have chosen to differentiate between the tissue types in the space of the target image with intensity clustering.

The background of the manual segmentations contains the extra-cranial space, CSF, as well as parts of the subcortical GM space as can be seen

in Figure 4.1. The background prior probability is subdivided accordingly into three parts. The CSF and extra-cranial space are defined from the tissue probability maps. The ventricles were further excluded as separate regions from the CSF. The subcortical background mainly represents the internal capsule and is segmented by masking the background with a deep grey matter binary map (obtained by transforming and thresholding the subcortical GM map of Serag et al. (2012)).

The ventrolateral nuclei of the thalamus deviates significantly in terms of intensity from the rest of the thalamus (Counsell and Rutherford, 2002). To account for this, the right and left thalamus were subdivided into the low intensity (in T2 space, inversely for the T1 space) part of the thalamus that represents the ventrolateral nuclei and the rest of the thalamus, with another simple EM scheme initialised with a 2 cluster k-means technique.

The remaining subcortical structures retain their propagated definitions from the atlases. It should be noted that the subcortical GM background and the thalamus parts are segmented using a hard segmentation in the atlas space and then propagated to the subject image, as these regions are difficult to differentiate in early preterm brains. The initial labels and the ones resulting from the subdivision are presented in Figure 4.3. The 50 atlas labels are subdivided into 87 labels. Once the EM estimation has converged, the subdivided parts of the structures are merged.

4.3.4 Markov Random Field regularization

MRF regularization is modelled as in the previous chapter (Equation 3.6). The spatial proximity is automatically defined from the atlases. A pair of structures is defined as ”neighboring” if the structures have neighboring voxels in at least one set of atlas labels. Since the atlases did not differentiate the WM/CGM structures into WM, CGM, these parts were automatically subdivided prior to the definition of the neighboring structures.

Subcortical structure 1 Subcortical structure 2 Subcortical structure 16 Extra-cranial space Subcortical background CSF Background WM/CGM structure 1 (CGM part) WM/CGM structure 1 (WM part) WM/CGM structure 1 WM/CGM structure 2 (CGM part) WM/CGM structure 2 (WM part) WM/CGM structure 2 WM/CGM structure 32 (CGM part) WM/CGM structure 32 (WM part) WM/CGM structure 32

Left ventrolateral nuclei

Left thalamus without the ventrolateral nuclei Left thalamus

Right ventrolateral nuclei

Right thalamus without the ventrolateral nuclei Right thalamus

Subcortical structure 1 Subcortical structure 2 Subcortical structure 16

Atlas labels Labels after brain subdivision (87)

(50 + background)

Figure 4.3: Initial labels of the atlases and labels after the subdivision.

Here Akj is defined as:

Akj =                           

0, if structure k is the same as j a, if structure k is neighbouring j,

and both k and j belong to WM/CGM b, if structure k is neighbouring j,

and either k or j do not belong to WM/CGM c, if structure k is distant from j

with a < b < c. To preserve the propagated anatomical information at the boundaries between the WM/CGM structures while removing isolated voxels, a weak smoothing is allowed here to alter the boundaries between these structures. The connectivity strength parameters were empirically set to a = 1, b = 3, c = 5.