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coordinate system, the following types of MPR can be applied to 3D images of the
spine:
orthogonal MPR, where the sampling plane is orthogonal to one of the axes of
the image-based coordinate system (Sect. 3.1.1 ),
￿
oblique MPR, where the orthogonal sampling plane, de
ned in the image-based
coordinate system, is rotated about the axes of the image-based coordinate
system (Sect. 3.1.2 ).
￿
The common characteristic of all types of MPR is that sampling planes are
3
de
ned on the basis of the image-based coordinate system
I .
R
3.1.1 Orthogonal Multi-planar Reformation
The most common MPR is orthogonal, meaning that the sampling plane is
orthogonal to one of the axes of the image-based coordinate system. By applying
orthogonal MPR to a 3D spine image, the following orthogonal multi-planar cross-
sections can be obtained:
sagittal orthogonal multi-planar cross-sections are obtained by sampling the 3D
image on selected sagittal planes de
￿
ned in the-based coordinate system (sec-
tion Sagittal Orthogonal Multi-planar Cross-Sections ),
coronal orthogonal multi-planar cross-sections are obtained by sampling the
3D image on selected coronal planes de
￿
ned in the image-based coordinate
system (section Coronal Orthogonal Multi-planar Cross-Sections ),
axial orthogonal multi-planar cross-sections are obtained by sampling the 3D
image on selected axial planes de
￿
ned in the image-based coordinate system
(section Axial Orthogonal Multi-planar Cross-Sections ).
I ,
By selecting a point p c ¼ ð
x c ;
y c ;
z c Þ
in the image-based coordinate system
R
exactly one sagittal (x
¼
x c ), one coronal (y
¼
y c ) and one axial (z
¼
z c ) orthogonal
multi-planar cross-section can be de
ned through p c .Ifp c is located on the spine
, the obtained cross-
sections show, depending on the shape of the spine, parts of the spinal anatomy.
curve c
ð
i
Þ
, e.g. at point i
¼
i p so that p c ¼
c x ð
i p Þ;
c y ð
i p Þ;
c z ð
i p Þ
Sagittal Orthogonal Multi-planar Cross-Sections
Sagittal orthogonal multi-planar cross-sections are obtained by sampling the 3D
image on selected sagittal planes that are orthogonal to axis x of the image-based
coordinate system. The sagittal orthogonal multi-planar cross-section M x¼x c
is
¼
therefore obtained by selecting a
x c , and sampling the 3D
image I along coordinates y and z in the image-based coordinate system:
fixed coordinate x
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