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In-Depth Information
allow to quantify the location, size and shape of anatomical structures observed in
medical images without making use of advanced image analysis techniques, such as
segmentation. In the case of 3D spine images, the most relevant geometrical
properties of the spine as the observed anatomical structure can be represented by
the spine curve and axial rotation of vertebrae. To enable a proper geometrical
representation of the spine in a 3D image, image-based and spine-based coordinate
systems are introduced (Sect.
2.1
), the spine-based coordinate system is formally
de
ned (Sect.
2.2
), and methods for automated determination of the spine-based
coordinate system are presented (Sect.
2.3
).
2.1 Coordinate Systems
Given a 3D image of an anatomical structure, the image-based coordinate system
(Sect.
2.1.1
) describes the acquisition of the image with respect to the observed
anatomical structure. However, several 3D anatomical structures (e.g. spine, colon,
arteries) have geometrical properties that enable the introduction of the structure-
based or anatomy-based coordinate systems, which can be in the case of the spine
as the observed anatomical structure termed spine-based coordinate system
(Sect.
2.1.2
).
2.1.1 Image-Based Coordinate System
The image-based coordinate system is the coordinate system of the acquired image.
In the case of 3D images, it is de
3
I
ned by a 3-tuple
ð
x
;
y
;
z
Þ2
R
of mutually
orthogonal axes x, y and z, represented by unit vectors e
Ix
¼½
I
, e
Iy
¼½
1
;
0
;
0
0
;
1
;
0
I
and
I
, respectively. In the case of 3D spine images, the image-based
coordinate system usually corresponds to the coordinate system of the imaging
device (i.e. CT or MR scanner), in which the body is longitudinally aligned. The
image-based coordinate system is, in general, aligned with the coordinate system of
the body, and therefore its axes represent the following anatomical directions:
^
e
Iz
¼½
0
;
0
;
1
the sinistro-dexter axis x represents the direction
^
e
Ix
from the left to the right part
of the body,
the ventro-dorsal axis y represents the direction
^
e
Iy
from the anterior to the
posterior part of the body,
the cranio-caudal axis z represents the direction
e
Iz
from the superior to the
inferior part of the body (i.e. the longitudinal axis of the body).
As a result, the following three imaging 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 body, therefore
dividing the body into left and right sections (the sagittal plane that passes
ð
y
;
z
Þ
