Biomedical Engineering Reference
In-Depth Information
Gemini, respectively, [32]. Given this hardware approach to image registration,
the question arises as to the continued need for software registration techniques.
It is our opinion however, that software image registration will continue to play
a vital role in many instances and that the development of registration algo-
rithms shall remain an important research area for years to come. In many
cases, hardware registration is impractical or impossible and one must rely on
software-based registration techniques. For example, when monitoring treat-
ment effectiveness over time, software image registration is necessary since the
single or multimodality images are acquired at different times. In addition, appli-
cations involving intersubject or atlas comparisons require software registration
since the images originate from different subjects. Other applications for soft-
ware registration include the correction of motion that occurs between sequen-
tial transmission and emission scans in PET and SPECT as well as the position-
ing of patients with respect to previously determined treatment plans. The need
to offer multiple different combinations of imaging modalities (i.e., PET/MR,
SPECT/MR, PET/CT, etc.) would be impractical. As most researchers agree, the
hybrid devices will likely play a major role primarily in radiation oncology.
The remainder of this chapter is organized as following: section 10.2 defines
all three measures and discusses how they can be used in an image registra-
tion context. Section 10.3 addresses the implementation issues. Section 10.4
details the experimental setup to test cross-entropy, reversed cross-entropy,
and symmetric divergence image registration by both maximization and mini-
mization. Section 10.5 presents the registration results, along with a discussion.
Section 10.6 concludes with a brief summary.
10.2
Cross-Entropy, Reversed Cross-Entropy,
and Symmetric Divergence
Cross-entropy, reversed cross-entropy, and symmetric divergence can be defined
for pdfs of any-dimensional random variables. To make it relevant to the image
registration context, in the following equations only a vector variable (
u
,v
)is
considered. In these equations,
u
and
v
are voxel gray values at corresponding
points in two images,
f
(
x
,
y
,
z
) and
g
(
x
,
y
,
z
) that are known as the reference
image and the floating image, respectively. This gray value pair is considered in
