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spines, and applied automated region growing segmentation to obtain reference
points, such as the center of the vertebral canal, the center of the sternum at the T5
vertebra and the center of the anterior half of the vertebral body, which were used to
de
ne the axial vertebral rotation. Axial vertebral rotation was studied in both CT
and MR images of whole spines also by Vrtovec et al. [
83
,
86
]. In CT images [
83
],
circular cross-sections that were orthogonal to the spine curve were
rst automat-
ically extracted, and axial vertebral rotation was then de
ned from the line that
bisected the cross-section and resulted in the maximal correlation of image inten-
sities in the bisected regions. For MR images [
86
], the rotation was de
ned in an
optimization procedure that searched for the orientation angle of the line of sym-
metry in each axial-cross section, and then smoothed with a polynomial function
along the whole spine using the least-trimmed-squares regression technique. The
same authors also combined both approaches into a method that was modality-
independent, i.e. applicable to both CT and MR images [
87
]. Basing on the pre-
de
ned location of the vertebral body center in 3D, they obtained the relation
between the image-based and vertebra-based coordinate systems by matching
image intensity gradients that de
ned the best available symmetry of vertebral
anatomical structures. The method was thoroughly evaluated and compared to
established manual methods when applied to CT [
91
] and MR [
90
] images of
normal and scoliotic spines. To segment vertebral bodies in both CT and MR
images,
Š
tern et al. [
79
] proposed to use a parametric model based on superquadrics
that, among several shape parameters, included also the axial rotation of the
vertebral body, and which was later used to perform quantitative vertebral mor-
phometry in CT images of normal and fractured vertebrae [
80
]. Axial vertebral
rotation was determined from the symmetry of vertebral anatomical structures also
in the study of Forsberg et al. [
18
], who for each vertebra in CT images extracted a
cross-section that was orthogonal to the spine curve and passed through the center
of the vertebral body, and then minimized the sum of absolute differences in image
intensities over the line that bisected the cross-section at the evaluated rotation
angle. The same group of authors also developed a method for segmentation of
vertebrae by registering a spine model to CT spine images, and then measured axial
vertebral rotation from landmarks that were placed at distinctive anatomical loca-
tions in the spine model and mapped to each CT image by using the obtained
registration transformation
fields [
17
].
2.3.3 Examples of Automated Determination of the Spine Curve
and Axial Vertebral Rotation
ð
Þ
Among automated methods for the determination of the spine curve cðiÞ
i
and/or
axial vertebral rotation
uð
Þ
i
, the following approaches are presented in detail:
automated determination of the spine curve and axial vertebral rotation in CT
images [
83
] (section
Automated Determination of the Spine Curve and Axial
Vertebral Rotation in CT Images
),
