Introduction
Image noise reduction is main step in many
applications. Low pass filter may be used to eliminate
noise from images. An instance of low pass filters is the
medium filter (MF). Other than reducing noise in images,
this filter distorts edges and corners. Various types of MF
have been introduced to solve this problem including
Multistage filter [1], RMF [2] and methods proposed in
[3] and [4] using a noise recognition algorithm plus a
filtering stage to eliminate impulse noises. The above
methods are effective when there is a low noise
probability (NP) for the image. For instance, MF’ is not
effective for NP>=20% [5]. Recently the fuzzy methods
have been widely used in various applications such as
control applications [11-12] and image classification
[13]. Some of methods by using the fuzzy systems may
perform better for noise reduction like Fuzzy Random
Impulse Noise Reduction method (FRINR) in [6]. In [7]
proposed a comparative study for select those filters that
have the best performance for Gaussian noise reduction.
However generally adaptive methods working based on
neural networks and fuzzy systems may perform better in
this field. Just like [8] and [9] and the adaptive filter
provided in [10]. [10] provides an adaptive method for
reducing accumulating noise which has two stages: the
first stage is devoted to calculation of a fuzzy derivative
for 8 different routs from each point in the image, and the
second stage covers the use of these fuzzy derivatives for
fuzzy smoothing and showing that both stages work
based on fuzzy rules. The main subject in the filter
provided by [10] is differentiating between local
derivative results in noisy points as well as noiseless
ones. Also in [9] an adaptive filter has been presented
based on ANFIS. The general idea in [10] is that the
average of pixels around a given pixel is used instead of
the pixel itself, yet it takes care of important image
structures such as edges. The HAF [5] method is
specially efficient at eliminating impulse noises. The
interesting point of the method is that it proceeds to
eliminate the image noises leaving intact the intense slope
of edges. Making a HAF filter has three stages: (1)
defining the fuzzy sets in the input space, (2) a set of Ifthen
rules, and (3) making a filter based on a set of rules.
In this paper unlike most neuro-fuzzy filters in which
long and frequent training phases are employed for
choosing the primary membership functions, the HAF
method provides nice results without any training at all.
HAF has some problems as well; it only works for
impulse noise. While implementing it we observed that it
can also produce noise in the image and we saw that its
power does not come from its fuzzy base, but from the
definition of noise. Most papers written on impulse noise
are of salt and pepper type, and generally it may be said
about the optimization algorithm provided in HAF that
there is no reason the answers are the best and most
optimized. This implies that despite what offered in [5]
there is no reason to say that the presented algorithm is
the best at optimizing HAF parameters, but the provided
algorithm only serves to provide us with the parameters
of membership functions according to the estimated
image histogram. The overall structure of this paper is
such that it first describes the general structure of the
proposed method and then proceeds to each and every
section. The provided structure includes the estimate of
main image histogram in full details and finally it offers
the results of result analysis and implementation of the
method and its comparison to other methods.