Image Processing Reference
In-Depth Information
Algorithm: General RECA Algorithm Flow
Data: Input Image
Result: Optimal Threshold Value
1. Create X population with Size random N -level solutions (chromosomes)
repeat
forall chromosomes of X do
calculate their rough entropy measure values RECA
Fuzzy Rough Entropy Measure
end
create mating pool Y from parental X population
apply selection, cross-over and mutation operators to Y population
replace X population with Y population
until termination criteria ;
Algorithm: Crisp-Crisp Difference RECA Approximations
foreach Data object x
i
do
Determine the closest cluster center center(C
i
) for x
i
Increment Lower(C
i
) by fuzzy membership value of x
i
Increment Upper(C
i
) by fuzzy membership value of x
i
foreach Cluster C
k
distanced to D and to center(C
i
) by less than
do
Increment Upper(C
k
) by 1.0
end
for l = 1 to number of data clusters do
roughness(l) = 1 - [ Lower(l) / Upper(l)]
Rough entropy = 0
for l = 1 to number of data clusters do
Rough entropy = Rough entropy−
e
2
·roughness(l)·log(roughness(l))
d(x
i
, C
l
)
−2/(µ−1)
P
j=1
µ
C
l
(x
i
) =
(11.1)
d(x
i
, C
j
)
−2/(µ−1)
where a real number µ represents fuzzifier value that should be greater than 1.0 and
d(x
i
, C
l
) denotes distance between data object x
i
and cluster (center) C
l
.
First, distances between the analyzed data point and all clusters centers are computed.
After distance calculations, data object is assigned to lower and upper approximation of the
closest cluster (center) d(x
i
, C
l
). Additionally, if difference between the distance to other
cluster center(s) and the distance d(x
i
, C
l
) is less than predefined distance threshold
dist
- this data object is additionally assigned to this cluster approximations. Approximations
are increased by fuzzy membership value of the given data object to the cluster center.
Fuzzy-Crisp RECA algorithm flow is the same as presented in Algorithm 1 and 2 with the
exception of the lower and upper approximation calculation that follows steps presented
in Algorithm 3.
For each data point x
i
, distance to the closest cluster C
l
is denoted as
d
min
dist
= d(x
i
, C
l
) and approximations are increased by this data point fuzzy membership
value µ
C
m
(x
i
) to clusters C
m
that satisfy the condition:
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