Information Technology Reference
In-Depth Information
In contrast
to the image-based coordinate system, which is de
ned in the
Euclidean space, the spine-based coordinate system is de
ned in a non-Euclidean
space, and therefore morphometric measurements based on Euclidean metrics can
not be obtained directly from the spine-based coordinate system.
2.3 Automated Determination of the Spine-Based Coordinate
System
The spine-based coordinate system can be manually determined by identifying
distinctive anatomical points on each vertebra (e.g. the centers of vertebral bodies)
and the corresponding rotation of vertebrae, and then interpolating through these
points to obtain a continuous description of both the spine curve and axial vertebral
rotation along the whole length of the spine. However, navigation through 3D spine
images is time-consuming and subjective, moreover it is practically impossible to
manually de
ne the plane orthogonal to the spine curve, in which axial vertebral
rotation is de
ed anatomical points on each vertebra.
As a result, several automated and semi-automated methods based on image pro-
cessing and analysis techniques were proposed to determine the spine curve and/or
axial vertebral rotation in 3D spine images.
ned, basing only on the identi
2.3.1 Automated Determination of the Spine Curve
In the past, the only possibility for measuring the geometrical properties of the spine
curve was based on examining the antero-posterior and/or lateral radiographs. As a
result, the spine curve in 3D was observed as its projection in 2D in the form of
coronal and sagittal spinal curvatures. Moreover, these curvatures were usually
evaluated by one-dimensional measures including angles of curvature (e.g. the
Ferguson angle, the Cobb angle, the tangent line angle) and indices of curvature
(e.g. the Greenspan index, the Ishihara index). A detailed review of methods for
the determination of spinal curvature was performed by Vrtovec et al. [
89
].
With the development of 3D imaging techniques, methods that captured the
3D nature of the spine started to emerge, followed by application of computerized
techniques that automatically or semi-automatically (i.e. with minimal observer
interaction) determined the spine curve in 3D images. Due to the continuous course
of the spinal curvature, a number of studies attempted to model the spine curve with
a mathematical curve in stereoradiographic (i.e. in multiple radiographs acquired
at different angles), CT or MR spine images. Different functions were used
for modeling, such as harmonic functions (i.e. sines, cosines or Fourier series)
[
13
,
15
,
27
,
58
,
74
], spline functions [
6
,
33
,
55
,
82
] and standard polynomial
functions [
56
,
83
,
85
,
86
], as well as statistical interpolation techniques, such as
kriging [
59
].
