Information Technology Reference
In-Depth Information
Fig. 10 a A circular domain of radius d and centered at the point on the spine curve cðiÞ,
ð
i
Þ
,de
ned
in the plane orthogonal to the spine curve cðiÞ.
ð
i
Þ
. b For a bisecting line that is inclined for an angle
u
against the direction of e
Iy
, image intensities s
A
and s
B
at mirror point pairs are used to evaluate the
similarity between the two halves of the circular domain
P
J
; uÞ
; uÞ
; uÞÞ
P
1
ð
s
A
ð
i
;
j
s
A
ð
i
; uÞÞð
s
B
ð
i
;
j
s
B
ð
i
j
¼
s
R
AB
ð
i
; uÞ
¼
;
ð
32
Þ
P
J
j¼1
ð
s
A
ð
i
;
j
; uÞ
s
A
ð
i
; uÞÞ
J
j¼1
ð
s
B
ð
i
;
j
; uÞ
s
B
ð
i
; uÞÞ
2
2
J
P
j¼1
s
A
ð
J
P
j¼1
s
B
ð
1
1
where
are the mean
image intensities in parts A and B, respectively, of the circular domain. It is
important to note that features other than image intensities can be extracted at
mirror points (e.g. image intensity gradients), and similarity measures other than the
correlation coef
s
A
ð
i
; uÞ
¼
i
;
j
; uÞ
and
s
B
ð
i
; uÞ
¼
i
;
j
; uÞ
cient can be computed (e.g. mutual information) for the corre-
sponding circular domain halves. Nevertheless, the domain must be circular so that
irrespectively of inclination
u
, the same points are taken into account for the
computation of the in-plane similarity. The optimal polynomial parameters b
u
that
de
finally obtained in an optimi-
zation procedure that searches for the combination of parameters that corresponds
to the maximal sum of correlation coef
ne the axial vertebral rotation
uð
i
Þ
(Eq.
26
) are
cients along the spine curve:
!
X
N
b
u
¼
argmax
b
u
R
AB
ð
i
; uÞj
b
u
:
ð
33
Þ
i¼1
Similarly as in the case of the spine curve, optimization can be designed hier-
archically and performed on multiple levels. However, in the case of the axial
vertebral rotation, on the
first level the optimization starts with a zero degree
polynomial, i.e. K
u
¼
0, meaning that the
initial axial vertebral rotation is constant and equal to zero along the whole length of
0, and with polynomial parameter b
u;
0
¼
