Automated Determination of the Spine-Based Coordinate System for an Efficient Cross-Sectional Visualization of 3D Spine Images - Spinal Imaging and Image Analysis - page 268

Fig. 17 A sagittal oblique multi-planar cross-section M x¼x c ;c ¼ c p of a 3D CT image of a scoliotic
spine, shown in a 3D view, b left sagittal view, c posterior coronal view and d superior axial view
of the image-based coordinate system (Note The image-based coordinate system and the spine
curve correspond to Figs. 1 and 7 )

coordinate z z c that is additionally rotated for angle a ¼ a p about axis x and/or for

angle b ¼ b p about axis y of the image-based coordinate system:

¼

M z¼z c ;a ¼ a p ;b ¼ b p ð x ; y Þ ¼I ð R ða p ; b p ; 0 Þ ½x ; y ; z c Þ; ð 64 Þ

with the center of rotation at point p c ¼ ð x c ; y c ; z c Þ (Eq. 57 ). The rotation angles

2 ½

4 ; þ 4

must be on the closed interval , otherwise the cross-section

turns into a coronal or sagittal oblique multi-planar cross-section. However, in
practice only one rotation is usually applied:

a p ; b p