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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