Biomedical Engineering Reference
In-Depth Information
and define the vector
W
=
(
w
1
,w
2
,...,w
n
) and the coefficients
α
1
,
α
x
,
α
y
, and
α
z
by the equation
L
−
1
Y
=
(
W
|
α
1
α
v
α
w
)
T
.
α
u
Third, use the elements of
L
−
1
Y
to define a function
f
(
u
,v
,w
) everywhere
in the entire volume:
i
=
0
w
i
|
P
i
−
(
u
,v,w
)
|
.
n
f
(
u
,v
,w
)
=
α
1
+
α
u
u
+
α
v
v
+
α
w
w
+
Thus, any voxel (
u
i
,v
i
,w
i
) in the floating volume is transformed to a new coordi-
nate (
u
i
,v
i
,w
i
) and a warped volume can be obtained by trilinear interpolation.
Additional algorithm details are now described. For both VOI optimization
and rigid body registration, we use trilinear interpolation. Optimization of sim-
ilarity ends either when the maximum number of calculations is reached (typ-
ically 500) or the fractional change in the similarity function is smaller than a
tolerance (typically 0.001). We use IDL as the programming language.
3.3.3
Registration Evaluation
We used the multiple visualization features of RegViz to visually evaluate reg-
istration results. First, we manually segmented prostate boundaries in image
slices and copied them to corresponding slices from the other volume. This en-
abled visual determination of the overlap of prostate boundaries over the entire
volume. We applied the same method to evaluate pelvic registration. Second,
color overlay displays were used to evaluate overlap of structures. One image
was rendered in gray and the other in the “hot-iron” color scheme available in
IDL. To visualize potential differences, it was quite useful to interactively change
the contribution of each image using the transparency scale. Third, we used a
sector display, which divided the reference and registered images into rectan-
gular sectors and created an output image by alternating sectors from the two
input images. Even subtle shifts of edges could be clearly seen [1].
Voxel gray value measures were calculated as indicators of registration qual-
ity. Mutual information and correlation coefficient between registered volumes
were computed. Since volumes to be registered were acquired using the same
acquisition parameters, high absolute CC values were obtained when registra-
tion was good [41]. Because voxel intensities were comparable, we created
