Full text: Mapping without the sun

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 
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