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)
forall chromosomes of X do
calculate their rough entropy measure values RECA
Fuzzy Rough Entropy Measure
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
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
d(x i , C l ) −2/(µ−1)
P j=1
µ C l (x i ) =
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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