Image Processing Reference

In-Depth Information

hyperbolization algorithm

In this phase, fuzzy image processing techniques have been applied to enhance the contrast

of the whole image and to enhance the edges surrounding the region of interest (Aboul Ella

and Dominik, 2006). The gray level modification is one of the most popular methods to per-

form image enhancement because it is simple in implementation and fast in computing. But

the selection of suitable mathematical function for the gray level transformation depends

on the specific grayness properties of the image, it is necessary to develop some techniques

for automatic selection of an appropriate function. In recent years, many researchers have

applied the fuzzy set theory to develop new techniques for contrast improvement. It is

based on gray level mapping into a fuzzy plane, using a membership transformation func-

tion. The aim is to generate image of higher contrast than the original image by giving a

larger weight to the gray levels that are closer to the mean gray level of the image than to

those that are farther from the mean. We present a fuzzy-based histogram hyperbolization

algorithm to enhance the edges surrounding the region of interest. It starts by initializa-

tion the parameters of the image phase. Then by fuzzification of the gray levels phase

(i.e. membership values such as dark, gray and bright) sets of gray levels. It followed

by the grey level modification phase. Finally, generation of a new gray levels phase. The

main steps of the fuzzy-based histogram hyperbolization algorithm are given in Algorithm 1.

tering algorithm and Gray level co-occurrence matrix

The standard fuzzy c-means objective function for partitioning data set y ={y
1
, . . . , y
N
}

into c clusters is given by:

c

N

X

X

(u
ik
)
p
ky
k
−v
i
k
2

J =

(5.5)

i

=1

k=1

where v
i
are the prototypes of the clusters and the array u
ik
= U represents a partition

matrix. The parameter p is a weight exponent determining the amount of fuzziness in the

resulting classification. It has the effect of reducing the square distance error by an amount

that depends on the observation's membership in the cluster. With p decreasing, partitions

that minimize J become increasingly crisp. Conversely, higher values of p tend to soften

memberships and partitions become more blurred. Generally p should be selected experi-

mentally.

The FCM objective function is minimized when high membership values are assigned to

pixel whose intensities are close to the centroid of its particular class, and low membership

values are assigned when the pixel data is far from the centroid. The FCM algorithm is

computationally expensive and sensitive to the noise. To solve these problems, we present

a modified version of the fuzzy c-mean clustering algorithm, (refer to (Aboul Ella, 2007) for

more details and algorithm steps).

To reduce the computational complexity, only some of these features were selected. As

for feature extraction and to reduce the computational complexity, only some features were

selected; energy, entropy, contrast and inverse difference moment features. Energy, also

called Angular Second Moment, is a measure of textural uniformity of an image. Energy

reaches its highest value when gray level distribution has either a constant or a periodic form.

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