Biomedical Engineering Reference
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The template image is shown with the ground-truth transformation (blue) and an
estimated transformation (red) in Fig.
2.3
a. The average endpoint error
e
from
Eq. (
2.89
) between the two grids is shown in Fig.
2.3
d (scaled between 0 and 25 in
pixel units). It can be seen that the estimated transformation differs from the ground-
truth transformation at the corners of the images, where the intensities are almost
zeros in the images
. We thus restrict the quantitative error analysis to the
region where the images have an intensity value above 1. The error
e
restricted to this
area is shown in Fig.
2.3
e and is 0.47 pixels on average with a maximum error
e
max
from Eq. (
2.90
) of 1.39 pixels. The reference image is shown in Fig.
2.3
b and the
resulting image after applying the estimated transformation is shown in Fig.
2.3
c.
Line profiles are given in Fig.
2.3
f. The dotted line profile after mass-preserving
motion estimation is almost indistinguishable from the reference line profile.
The same experiment is performed for the standard transformation model defined
in Eq. (
2.2
)andisshowninFig.
2.4
. The estimated grid in Fig.
2.4
a is subject to
major errors which results in an erroneous transformed image in Fig.
2.4
c. The error
T
and
R
2D example for the standard transformation model. The template image
T
Fig. 2.4
in (
a
)is
R
registered to the reference image
in (
b
) with the standard transformation model in Eq. (
2.2
)
resulting in (
c
). The average endpoint error
e
between the estimated transformation
y
std
and the
ground-truth transformation
y
GT
is visualized in (
d
). The same plot restricted to a mask where
T
and
have an intensity above 1 is shown in (
e
). The color map for both error plots is given in-
between. Line profiles are shown in (
f
). (Colored figures are only available in the online version.)
R
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