Image Processing Reference
In-Depth Information
as the centroid of the three best points in the simplex (i.e., all vertices
except
x
3
).
Reflect:
Compute the
reflection
point
x
r
,
xx xx
r
=+ −
α
(
)
3
Evaluate f(
x
r
). If f(
x
0
) f(
x
r
)>f(
x
4
), accept the reflected point
x
r
and termi-
nate the iteration.
Expand:
If f(
x
r
) > f(
x
0
), compute the
expansion
point
x
e
,
xx
=+ −
β
(
xx
)
e
r
r
If f(
x
e
)
f (
x
r
), accept
x
e
and terminate the iteration; otherwise, accept
x
r
and terminate the iteration.
Contract:
If f(
x
r
)
>
<
f(
x
3
−
1), perform a contraction between
x
and
x
n
:
xx xx
e
=+ −
ζ
(
)
3
If f(
x
e
)
x
n
) accept
x
e
and terminate the iteration.
Shrink simplex:
Evaluate f() at the three new vertices:
≥
xx
=+ −
0
η
(
xx
)
i
i
0
0.5.
The simplex algorithm is often used in the solution of the registration problem
due to its small computational complexity. This allows work on large data sets to
be completed in a reasonable time. Another application of the simplex algorithm
is to perform a preliminary registration followed by a more effective registration
executed with a more complex search strategy. In the last paragraph, an application
of the Nelder-Mead algorithm, together with the Powell algorithm, will be
described.
The suggested values for the parameters are:
α
=
1,
β
=
1,
ζ
=
0.5, and
η
=
7.5.2
G
ENETIC
A
LGORITHMS
Genetic algorithms are inspired by Darwin's theory of evolution, and use an
evolutionary process to find the best solution of an optimization problem. Algo-
rithms begin with a set of individuals (represented by chromosomes) called a
population
. Each set of chromosomes represents a possible set of parameters of
the function to be optimized. The value of the function (i.e., the similarity function
in the registration problem) for a certain chromosome set is called
fitness of the
corresponding individual
. Selecting the individuals with the best fitness, a new
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