Image Processing Reference
In-Depth Information
n4
n3
n4
n3
w2
w1
p
p
w3
w4
n1
n2
n1
n2
n4
n3
w2
w1
p
w3
w4
n1
n2
arg min
d
(
p
,
n i
) =
n 3
Σ i w i
= 1
n i
n 3 )
B
(
p
) =
Σ i w i
B
(
n i
)
B
(
p
) =
B
(
h ( A ( p ), B ( p )) + = 1
h ( A ( p ), B ( p )) + = 1
Σ i w i
= 1
i
:
h
(
A
(
p
),
B
(
n i
)) + =
w i
FIGURE 7.4 Three types of interpolation for the evaluation of the joint histogram.
interpolation, updates the joint histogram for each voxel pair in the two images.
Instead of interpolating new intensity values, the contribution of the image inten-
sity of each voxel to the joint histogram is distributed over all the intensity values
of the neighboring voxels, using the same weights as for trilinear interpolation.
Figure 7.4 shows the previously described interpolation algorithms. Nearest
neighbor interpolation and trilinear (bilinear, in the present 2-D example) inter-
polation find the reference image intensity value at position p and update the
corresponding joint histogram entry at p, whereas PV interpolation distributes
the contribution of this sample over multiple histogram entries defined by its NN
intensities, using the same weights as for bilinear interpolation.
To explain the differences among the three methods, we propose an experiment
on a synthetic data set. A metric related to image voxel values (i.e., the mean square
difference [MSD]) and a metric related to voxel statistic distribution, such as MI,
were tested. Two different interpolation techniques were adopted, trilinear interpo-
lation (TRI) and trilinear partial volume distribution (PV). The method of the exper-
iment has been tested on a simulated data set that reproduces a real heart shape.
Search WWH ::




Custom Search