Information Technology Reference
In-Depth Information
2.1.2 Spine-Based Coordinate System
The spine-based coordinate system [
84
] is the coordinate system of the spine as the
observed anatomical structure. In the case of 3D spine images, it is de
ned by a
3
3-tuple
ð
u
;
v
;
w
Þ2
R
S
of mutually orthogonal axes u, v and w, represented by unit
vectors e
Su
¼½
S
, e
Sv
¼½
S
and e
Sw
¼½
S
, respectively. The spine-
based coordinate system is aligned with the spine, and its axes represent
1
;
0
;
0
0
;
1
;
0
0
;
0
;
1
the
following structural directions:
^
the anatomical axis u represents the direction
e
Su
from the left to the right part of
the spine,
^
the anatomical axis v represents the direction
e
Sv
from the anterior to the
posterior part of the spine,
the anatomical axis w represents the direction e
Sw
from the superior to the
inferior part of the spine (i.e. the longitudinal axis of the spine).
As a result, the following three anatomical (structural) planes can be de
ned:
a sagittal or lateral plane
is any plane that passes from the anterior to the
posterior, and from the superior to the inferior part of the spine, therefore
dividing the spine into left and right sections,
ð
v
;
w
Þ
a coronal or frontal plane
is any plane that passes from the left to the
right, and from the superior to the inferior part of the spine, therefore dividing
the spine into anterior and posterior sections,
ð
u
;
w
Þ
an axial or transverse plane
is any plane that passes from the left to the
right, and from the anterior to the posterior part of the spine, therefore dividing
the spine into superior and inferior sections.
ð
u
;
v
Þ
The spine-based coordinate system is therefore a right-handed Cartesian coor-
dinate system with a standard orthonormal basis (Fig.
2
).
2.2 De
nition of the Spine-Based Coordinate System
To de
ne the spine-based coordinate system, two geometrical properties of
the spine have to be determined, namely the spine curve (Sect.
2.2.1
) and axial
vertebral rotation (Sect.
2.2.2
), which serve to de
ne the transformation from the
image-based to the spine-based coordinate system (Sect.
2.2.3
).
2.2.1 Spine Curve
The spine curve C is the curve that follows the curvature of the spine along its entire
longitudinal length. If i is an independent parameter that denotes an arbitrary
location on the spine, then c
ð
i
Þ
is the parametrization of the spine curve C:
