**4. Results**

12 Will-be-set-by-IN-TECH

182 Advances in Brain Imaging

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Opening by reconstruction size

(a)

(b)

(c)

Fig. 7. Size election of structuring element to attenuate the skull. a) Graph of structures size vs volume on the image *<sup>γ</sup><sup>μ</sup>* <sup>−</sup> *<sup>γ</sup><sup>μ</sup>*+1, b) Original image , eroded size 3 and opening by reconstruction size 3; c) Original images, eroded size 6, and opening by reconstruction size 6

Fig. 8. Opening by reconstruction size *μ* = 1 applied to images in Fig. 6(a).

0 0,01 0,02 0,03 0,04 0,05 0,06 0,07 0,08 0,09 0,1

volume

In particular, we consider three main groups of clear and dark structures. These groups take into account the size of the structuring element (the structuring element used in this paper is a square, see subsection 2.1).

*Group 1(Small structures).-*In this group the structures within the sizes 1 and 2 of the structuring element are comprised. *Group 2(Medium structures).-* This group contains the structures located in the size interval 3 to 6 of the structuring element. *Group 3(Large structures).-*Finally, this group comprises structure sizes 7-17 of the structuring element.

#### *i) Clear and dark regions analysis from graphics in Fig. 10 for DHD case.-*

In both clear and dark regions, a great variation in the curves of DHD subjects is observed with respect to the CS, mainly in medium and large sizes. This indicates the lack of smooth transitions between the analyzed structures.

*ii) Clear and dark regions analysis from graphics in Fig. 10 for SSAV case.-* Main changes in clear structures are observed in large size structures; while dark structures vary for all sizes.

Curves in Fig. 10 indicate the existence of important variations in clear and dark structures in the DHD and SSAV subjects with respect to the CS. However, clear and dark structures are mixed, and results difficult to infer, since it is not possible to determine whether the predominance or the absence of some structures sizes is due to clear or dark components. This situation occurs because WM and GM have different intensities, and the morphological transformations used to build equations 3 and 4 are not autoduals, i.e, they do not try clear and dark structures in a separate form; this causes that, some clear and dark components are mixed during the processing.

Trying to avoid this inconvenience, WM and GM will be analyzed in separate ways with the purpose of finding some morphometric differences between CS and SS.

#### *iii) WM and GM analysis from graphics in Fig. 12 for DHD case.-*

From graphs in Fig. 12, for WM and GM in the SS case, we observe the following: a) a lack of small components with respect to CS; b) the existent small components are thin; and c) medium and large structures predominate in WM and GM.

DHD vs CS case:

SSAV vs CS case:

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

Mean volume Mean volume Mean volume Mean volume

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Opening size

Dark regions granulometric pattern

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Closing size

Fig. 10. Mean volume of clear and dark structures corresponding to SS and SC.

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Clear regions granulometric pattern

from Normal and Dissociated Strabismus Subjects Through Morphological Transformations

<sup>185</sup> Comparison of Granulometric Studies of Brain Slices

Opening size

Dark regions granulometric pattern

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Closing size

Clear regions granulometric pattern

> CS Mean SSAV1 SSAV2

CS Mean SSAV1 SSAV2

CS MEAN DHD1 DHD2

CS Mean DHD1 DHD2

Fig. 9. Procedure to obtain granulometric patterns. In step A the graphics obtained for one slice of each of the two CS and for one SS case are illustrated. In step B, a common mean pattern is obtained for both CS and one SS. Finally, in step C, a mean pattern is obtained for the two CS.
