Image Registration Methods in MRI - Advance Image Processing in Magnetic Resonance Imaging - page 197

population is formed. This is motivated by the hope that the new population will
be better than the old one. The process is repeated until some condition (for
example a certain population or improvement of the best solution) is satisfied.
The technique can be summarized thus: (1) a population of individuals
encoded as chromosomes propagates (2) copies of these individuals based on
external fitness criteria, creating (3) a generation of new individuals by mutating
chromosomes and recombining members of the population. Genetic algorithms
for the solution of a registration problem are typically implemented as follows:

1. A similarity function is chosen that describes the fitness of any potential

solution. The similarity function will be selected from a number of
parameters, depending on the registration algorithm.

2. A population of candidate solution is initialized. Typically, each solu-

tion is described by a vector x , called a chromosome , with elements
called genes . In the case of a 3-D rigid registration, the chromosome
is a six-element vector.

3. Each chromosome is used to evaluate the fitness function (i.e., to

perform a roto-translation of the floating image). The value of the
fitness function (e.g., the mutual information value between the refer-
ence image and the roto-translated one) is used as a fitness score.

4. We assign to each chromosome a probability of reproduction, depend-

ing on the fitness score. The reproduction probability will be propor-
tional to the fitness of the chromosome in respect to the fitness of the
others in the population.

5. A new population of chromosomes is generated by taking into account

the reproduction probability defined in the previous task. The new
population is generated recombining the chromosomes of the existing
population.

6. A random mutation of the chromosomes is introduced.

7. The process is halted if a suitable solution has been found. Otherwise,

the process returns to step 3.

The key issues in the implementation of the genetic algorithm are the rules
for producing the new generation and the amount of random mutation to be
introduced. Regarding the latter, the mutation probability should be very small
(10 4 is a typical value) to avoid damaging the good solutions that evolve during
the iterative process. The role of the random mutation is to explore new search
regions by avoiding premature convergence of the algorithm to suboptimal solu-
tions.
Several rules for creation of the new generation have been proposed in literature.
Usually, a percentage of old individuals (i.e., the ones with the best fitness) are
saved and included in the new generation. New individuals are then created to build
a population with the same size. A probability of reproduction is assigned to each
individual, depending on the fitness of the individual in respect to the fitness of the
others in the population. New individuals are created combining the chromosomes