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Mapping without the sun
Zhang, Jixian

The theory and the algorithms of the image fusion have been
studied widely, including those using several different multi
scale transforms and those using no transforms (e.g. additive
(ADD) fusion which weights the two source images directly).
The tests included the most frequently employed MSD fusion
approaches: the Laplacian pyramid algorithm (LPT), and the
gradient pyramid (GP) and the ratio-of-low-pass pyramid
(RoLP) are the same kind; the morphological (MORPH)
pyramid algorithm [8]; the discrete wavelet transform (DWT)
algorithm and the shift invariant DWT (SiDWT) fusion
algorithm. For each basic algorithm configuration, multiple
alternatives for the activity level measurements, grouping
methods, combining methods, and consistency verification
methods from the framework described in [6] were considered.
After registering the same region of SAR and optical images
as well as possible, based upon the preliminary judging and
testing, some promising fusion approaches are proposed. The
alternative of the combining method is employed at the lowest
frequency band for the pyramid transform-based fusion, and
low-low band for DWT fusion. In the process of determining
the methods in the test, many algorithms were eliminated
because some of them performed quite poorly. For example,
consider the contrast pyramid (CONTR) and the ratio of low
pass pyramid fusion (RoLP) [9] is the similar and too many
algorithm-created spots in the fused images. Therefore, we
substitute the CONTR fusion and the RoLP fusion algorithm
with LPT algorithm. Many other methods were eliminated for
similar reasons (poor performance in a reasonable number of
cases) or because they always performed similarly to other
At each sample position, a decision made on how the MSD
representations of the source images should be used to construct
the MSD representation of the fused image. This decision is
based on a quantity called the activity-level measurement. The
activity level of an MSD coefficient reflects the local energy in
the space spanned by the term in the expansion corresponding
to this coefficient. There are three methods to computer the
activity level just as [6] expatiate: coefficient-based activity
(CBA); window-based activity (WBA); and region-based
activity (RBA).
When determining the coefficients of the MSD, these
coefficients may be associated with each other or not.
Determining these coefficients together or not is called no
grouping (NG) schemes. If the corresponding coefficients in the
same decomposition scale are jointly constrained to take the
same decision, we call this a single scale grouping (SG) scheme.
So a multi-scale grouping (MG) is that consider the different
frequency coefficients together. For example the LAP fusion
algorithm, the NG and SG are the same since there is only one
frequency band in each decomposition level.
Then we must consider how to combine the source MSD
coefficients to produce the composite MSD representation.
There are at lease two alternatives, the choose-max (CM)
scheme and the weighted average (WA) scheme, which they
appear most frequently in the documents. In the paper we
emphasize on using adaptive multi-objective optimization to
search the Pareto optimal weights of the model and compared
the results with other methods.
J. Kennedy and R. C. Eberhart brought forward particle
swarm optimization (PSO) inspired by the choreography of a
bird flock in 1995 [10]. Unlike conventional evolutionary
algorithms, PSO possesses the following characteristics:
1) Each individual (or particle) is given a random speed and
flows in the decision space;
2) Each individual has its own memory;
3) The evolutionary of each individual is composed of the
cooperation and competition among these particles. Since the
PSO was proposed, it has been of great concern and become a
new research field. PSO has shown a high convergence speed in
single objective optimization, and it is also particularly suitable
for multi-objective optimization [4], [11].In this article, we use
so called “Adaptive Multi-objective Optimization” (AMO) to
combine, in which not only an adaptive mutation operator is
used to avoid earlier convergence, but also a crowding distance
operator is used to improve the distribution of nondominated
solutions along the Pareto front and maintain the population
diversity[3], and an adaptive exponent inertia weight is used to
raise the searching capacity.
In the paper, the algorithm is definite as follows: first,
initialize the population and algorithm parameters, then
execution the optimal cycles.
1) Initialize the position of each particle: pop[i], where
i=l, '".AT 5 , NP is the particle number, in the circumstance we
use 150; the speed of each particle: vel[i]=0; the record of each
particle: pbests[i] =pop[i\\Evaluate each of the particles in the
POP: fun[i,j],where j= 1, “‘,NF, and NF is the objective number,
in here we use 5. Then store the positions that represent
nondominated particles in the repository of the REP according
to the Pareto optimality.
2) Before the maximum number of cycles is reached, do
update the speed of each particle using function as below.
vel[ i] = W- vel[ i] + c, • ranc{ • (pbesL{ i] - pop[ i])
+c 2 ■ rand^ ■ (rep[ h] - pop[ i])
where W is the inertia weight [12]; cl and c2 are the learning
factors [13], randl and rand2 are random values in the range [0,
1], the inertia weight of Wmax is 1.2, and Wmin is 0.2; the
learning factor of cl is 1, and c2 is 1; the maximum cycle
number of Gmax is 1QQ,pbests[i\ is the best position that the
particle i has had; h is the index of the maximum crowding
distance in the repository that implies the particle locates in the
sparse region, as aims to maintain the population diversity;
pop[i] is the current position of the particle 7. Update the new
positions of the particles adding the speed produced from the
previous step pop[i] =pop[i] + vel[i],
3) Maintain the particles within the search space in case they
go beyond their boundaries. When a decision variable goes
beyond its boundaries, the decision variable takes the value of
its corresponding boundary, and its velocity is multiplied by -1.
4) Adaptively mutate each of the particles in the POP at a
probability of Pm. Evaluate each of the particles in the POP.
Then update the contents in the REP, and insert all the current
nondominated positions into the repository.
5) Update the records, when the current position of the
particle is better than the position contained in its memory, the
particle’s position is updated.
pbests[i] = pop[i\
6) Increase the loop counter of g.
In the whole algorithm the sum of the weights at each
position of two source images is limited to 1. All approaches
are run for a maximum of 100 evaluations.
For the RS application, the ideal image is always unknown.
Without an ideal or reference image, designing objective
metrics that describes what the perfect scheme would produce is
a very difficult
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