13-04-2013, 03:33 PM
Fuzzy Filters to the Reduction of Impulse and Gaussian Noise in Gray and Color Images
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Abstract
Noise removal from a corrupted image is finding
vital application in image transmission over the
wideband network. Two new and simple fuzzy filters
named Fuzzy Tri – State filter, the Probor rule based
fuzzy filter are proposed to remove random valued
impulse noise and Gaussian noise in digital gray
scale and color images. The Fuzzy Tri – State filter is
a non linear filter proposed for preserving the image
details while effectively reducing both the types of
noises. The Probor filter is sub divided into two sub
filters. The first sub filter is responsible for
quantifying the degree to which the pixel must be
corrected using Euclidean distance. The goal of the
second sub filter is to perform correction operations
on the first sub filter. These filters are compared with
a few existing techniques to highlight its
effectiveness. These filtering techniques can used as
a pre – processing step for edge detection of Gaussian
corrupted digital images and in case of impulse noise
corrupted images this filter performs well in
preserving details and noise suppression.
INTRODUCTION
Image processing has become a common technique
for making images more comprehensible to the
human eye. Communication channels, due to
imperfections inherent to them are responsible for the
corruption of digital color images. Images acquired
are found to be corrupted with noise in many cases.
Thus this leads to the image being corrupted in some
places and others are virtually noise free. There are
three main types of noise, impulse, gaussian and
multiplicative noise. This paper deals with reduction
of impulse noise and Gaussian noise. Multiplicative
noise occurs when the image is corrupted with
varying levels of intensity based on signal levels. It’s
more difficult to remove multiplicative noise in
images. In the literature [3],[4], there are many
methods available to remove impulse noise in gray
scale and color images. But very little has been done
for the removal of gaussian noise in color images
[1].Of the many filters presented unto date, most of
them are only for gray scale images.
PROBOR FILTER
The Probor filter basically performs averaging
operation, but also takes into account important
image structures such as edges which should not be
destroyed by the filter. The first sub filter is to
distinguish between local variations due to noise and
the image structures such as edges. This can be
performed by using the two dimensional distances
between color couples, and the colors are coupled as
(red-green) , (red-blue) and (blue-green). The idea
behind the fuzzy rules is to assign large weights to
neighborhood that have similar colors as the center
and small weights for dissimilar colors. The distances
are calculated for all the pixels in the window and
calculate the maximum of all the values and compute
the weights for the mask. Based on the distances the
mask has different values for different positions. The
distance is calculated using the Euclidean formula for
all the combinations of color couples. Then activation
degree is calculated using the sum of the weights
minus the product of the weights. This rule is
commonly known as the “probor rule”.
CONCLUSION
This paper proposes two simple fuzzy filters for the
removal of impulse and gaussian noise in gray scale
and color images. The fuzzy tri – state filter preserves
edges better because it is capable of distinguishing
between the noise corrupted pixels (local variations)
and the edges. The Fuzzy Tri – State Filter gives us
the best possible visual output so far achieved. In
addition, the proposed filter presents a quite stable
performance over a wide variety of images; provided
that the threshold is chosen based on fuzzy rules for a
given noise percentage. Similar is the case for the
probor filter. Edges are well preserved for the fuzzy
tri – state filter. Hence it can be used as a pre –
processing step for detecting edges of a gaussian
corrupted images and both the methods can be used
to remove impulse and gaussian noise in gray scale
andcolor images.