Image Registration Methods in MRI - Advance Image Processing in Magnetic Resonance Imaging - page 198

Crossover point

Parent 1

Parent 2

f3/ftot f0/ftot

f2/ftot

New 1

f1/ftot

New 2

(a) (b)

FIGURE 7.6 (A) Roulette wheel selection for genetic algorithms and (B) crossover.

of two or more parents extracted from the population. “Roulette wheel” selection
is often used to perform this task. Figure 7.6A shows how roulette wheel selection
works in the case of six individuals with fitness f 0 , ,f 5 . A circle (the wheel) is

divided into six sectors with a width proportional to the normalized fitness ( ftot
means the sum of f 0 ,

…

,f 5 ). A angle is randomly extracted (the arrow in the figure),
and the individual corresponding to the sector indicated by the arrow is selected
for reproduction. In this way, all the individuals have a probability to reproduce,
and the probability is proportional to the chromosome fitness. The process is
repeated twice for each new individual to be produced in order to select the two
parents involved in the reproduction process. The chromosomes of the two parents
are usually combined using the random selection of a crossover point (Figure 7.6B).
Genetic algorithms are generally more robust in respect to the presence of subop-
timal maxima in the fitness function. The main disadvantage is the great computa-
tional complexity; in fact, the fitness function has to be evaluated for each individual
in each iteration. However, genetic algorithms are inherently parallelizable, and the
time required for optimization is independent of the number of parameters of the
fitness function. Therefore, they can be effectively applied to registration problems
involving complex transformations such as the elastic ones, and in global registra-
tion of multiple data sets.

…

7.6 REGISTRATION OF MULTIPLE DATA SETS

MRI data sets are often composed of a large number of parallel slices that cover
a 3-D region inside the body. Slices can be acquired in different times, so patient
movement, breath, or poor EEG synchronization in cardiac imaging can lead to
image misalignment along the slices. Reconstruction of such data sets into 3-D
volumes, via the registrations of 2-D sections, is often needed in order to perform
correct 3-D visualization and morphometric analysis (e.g., surface and volume
representation) of the structures of interest. Consecutive slices may differ signif-
icantly owing to the fact that they represent different anatomical locations, and
the difference along slices is more pronounced when the distance between images