Biomedical Engineering Reference
In-Depth Information
Chapter 9
Elastic Registration for Biomedical
Applications
3
Jan Kybic
1
and Michael Unser
2
9.1
Introduction
The task of
image registration
is to find homologous (corresponding) points
in two images that we shall call
reference
and
test
. These images depict the
same or similar objects but are not identical. See an example in Fig. 9.1. We see
immediately that the task is not trivial, since some zones in one image do not have
any corresponding region in the other image. This illustrates some vagueness
of the registration problem which we will have to address. A multimodality
biomedical registration task, Fig. 9.2, presents another difficulty: Although the
images represent exactly the same object, the same slice of the same brain, the
visual appearance of the tissues is radically different in both.
For us, the output of the image registration is
correspondence function
g
such
that
x
t
=
g
(
x
r
), mapping a coordinate
x
r
of an arbitrary point in the reference
image to a coordinate
x
t
of a corresponding point in the test image.
If we are considering image registration as an inverse problem, then
image
warping
(image deformation) is the corresponding forward part (see Fig. 9.3).
