Biomedical Engineering Reference
In-Depth Information
are generally well understood. That means that they are versatile with a variety of
different possible configurations (e.g., intensity or gradient distance measures).
One of the main differences between image registration and optical flow, as
presented in this topic, is the numerical realization. While image registration is
based on a discretize-then-optimize strategy, optical flow follows an optimize-then-
discretize strategy. The optimization in the case of optical flow includes a Taylor
approximation whereas image registration relies on the exact computation of all its
components. The Taylor approximation makes, e.g., the incorporation of non-linear
hyperelastic regularization into the optical flow functional in Eq. (
2.70
) challenging.
Hyperelasticity would thus transform into something like linear elasticity, which is
only suitable for small deformations.
Fig. 2.9
in (
b
) leading to the overlaid transformation grid
in (
a
). The transformed template image is shown in (
c
). A magnification with a comparison of the
estimated vectors (
red
) and the ground-truth vectors (
blue
)isshownin(
d
). (Colored figures are
only available in the online version.)
MPOF:
T
in (
a
)isregisteredto
R
2.3.1
Comparison
Despite the fundamental differences, the basic idea of MPOF and V
AMPIRE
is
the same. Hence, we will derive the mass-preserving optical flow equations from
the V
AMPIRE
model in the following. For this purpose, let us recall the concept
of mass-preservation as introduced in Sect.
2.1.4
. The idea of mass-preserving
image registration is the preservation of the total intensity of an image due to a
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