Salt & Pepper Noise Reduction from Gray-Scale Images using Adaptive Median Filter A Project Report submitted By Puspani Das Under the supervision of Bishwa Ranjan Roy Assistant Professor Department Of Computer Science
Salt & Pepper Noise Reduction
from Gray-Scale Images using
Adaptive Median Filter
A Project Report submitted
By
Puspani Das
Under the supervision of
Bishwa Ranjan Roy
Assistant Professor
Department Of Computer Science
Abstract
The existence of impulse noise is one of the most frequent problems in
many digital image processing applications. So for the removal of such impulse
noise median based filter becomes widely used. However, there are many
variations of median filter in literature. In addition to standard median filter, there
are weighted median filter, recursive median filter, iterative median filter,
directional median filter, adaptive median filter and switching median filter.
In this project a simple, yet efficient way to remove impulse noise from
digital images is presented. Linear and nonlinear filters are available for the
removal of impulse noise; however the removal of impulse noise often brings
about blurring which results in edges being distorted and poor quality. Therefore
the necessity to preserve the edges and fine details during filtering is the challenge
faced by researchers today. In this project, we present a new median filter based
technique, which is a combination of adaptive median filter and hybrid median
filter.
This method consists of noise detection followed by the removal of
detected noise by Adaptive median filter using selective pixels that are not noise
themselves in gray level images. Noise detection is based on only the two intensity
values i.e. 0 & 255; the pixels are roughly divided into two classes, which are
“noise-free pixel” and “noise pixel”. In impulse noise elimination, only the “noise
pixels” are processed. The “noise-free pixels” are copied directly to the output
image. The method adaptively changes the size of the median filter based on the
number of the “noise- pixels” in the neighborhood. For the filtering, only “noise-
free pixels” are considered for the finding of the median value. Computer
simulations were carried out to analyze the performance of this method.
Contents
Chapter 1: Introduction
1.1 Overview
1.2 Objective
Chapter 2: Digital Image Processing
Chapter 3: Noise in digital images
Chapter 4: Image filtering techniques
Chapter 5: Noise Reduction by Proposed Filtering Approach
5.1 Adaptive median Filter
5.2 Purpose of the Algorithm
5.3Hybrid median filter
5.4Literature Survey
Chapter 6: Implementation
Chapter 7: Comparative Analysis
7.1 Image quality assessment matrices
7.2 Results based on noise density
Chapter 8: Conclusion
Chapter 9: Scope of future work
Appendix
Appendix A: References
Appendix B: Screenshots
Appendix C: Hardware and Software
Appendix D: Application Setup
Chapter 1 Introduction
1.1 Overview
Digital images which are related to digital signals are normally corrupted
by many types of noise, including impulse noise. Impulse noise is a set of random
pixels which has a very high contrast compared to the surroundings. So, even a
small percentage of impulse noise distorts the image greatly compared to other
noises.
Image noise removal plays a vital role in image processing as a pre-
processing stage. The non-ideal imaging systems introduce potential degradations
in digital images. Noise disturbances may also be caused by electronic imaging
sensors, film granularity, and channel noise. High levels of noise are always
undesirable; hence noise removal has to be employed before the image could be
used for further analysis.
Salt and pepper noise is an impulse type of noise, which is also referred to
as intensity spikes. This is caused generally due to dead pixels, analog-to-digital
converter errors, errors in data transmission, malfunctioning of pixel elements in
the camera sensors, faulty memory locations, or timing errors in the digitization
process. It has only two possible values, ‘a’ and ‘b’. The probability of each is
typically less than 1. The corrupted pixels are set alternatively to the minimum or
to the maximum intensity values, giving the image a “salt and pepper” like
appearance. Unaffected pixels remain unchanged. For an 8-bit image, the typical
intensity value for pepper noise is 0 and for salt noise 255.
1.2 Objectives
The objective of this project is analysis of Adaptive Median filter and
improving its performance by using hybrid median technique on grayscale
images.
CHAPTER 2
DIGITAL IMAGE PROCESSING
Pictures are the most common and convenient means of conveying or
transmitting information. A picture is worth a thousand words. Pictures concisely
convey information about positions, sizes and inter-relationships between objects.
They portray spatial information that we can recognize as objects. Human beings
are good at deriving information from such images, because of our innate visual
and mental abilities. About 75% of the information received by human is in
pictorial form.
In the present context, the analysis of pictures that employ an overhead
perspective, including the radiation not visible to human eye are considered.
Thus our discussion will be focusing on analysis of remotely sensed images.
These images are represented in digital form. When represented as numbers,
brightness can be added, subtracted, multiplied, divided and, in general, subjected
to statistical manipulations that are not possible if an image is presented only as a
photograph. Although digital analysis of remotely sensed data dates from the early
days of remote sensing, the launch of the first Landsat earth observation satellite
in 1972 began an era of increasing interest in machine processing (Cambell, 1996
and Jensen, 1996). Previously, digital remote sensing data could be analyzed only
at specialized remote sensing laboratories. Specialized equipment and trained
personnel necessary to conduct routine machine analysis of data were not widely
available, in part because of limited availability of digital remote sensing data and
a lack of appreciation of their qualities.
DIGITAL IMAGE
A digital remotely sensed image is typically composed of picture elements
(pixels) located at the intersection of each row i and column j in each K bands of
imagery. Associated with each pixel is a number known as Digital Number (DN)
or Brightness Value (BV) that depicts the average radiance of a relatively small
area within a scene (Fig. 1). A smaller number indicates low average radiance
from the area and the high number is an indicator of high radiant properties of the
area. The size of this area effects the reproduction of details within the scene. As
pixel size is reduced more scene detail is presented in digital representation
Scan Lines Pixels
Pixels
Figure 1: Structure of a Digital Image and Multispectral Image
A very large portion of digital image processing is devoted to image
denoising. This includes research in algorithm development and routine goal
oriented image processing. Image denoising is the removal or reduction of
degradations that are incurred while the image is being obtained. Image denoising
finds applications in fields such as astronomy where the resolution limitations are
severe, in medical imaging where the physical requirements for 2 high quality
imaging are needed for analyzing images of unique events, and in forensic science
where potentially useful photographic evidence is sometimes of extremely bad
quality.
Let us now consider the representation of a digital image. A 2-
dimensional digital image can be represented as a 2-dimensional array of data
s(x,y), where (x,y) represent the pixel location. The pixel value corresponds to the
brightness of the image at location (x,y). Some of the most frequently used image
types are binary, gray-scale and colour images.
Binary images are the simplest type of images and can take only two
discrete values, black and white. Black is represented with the value ‘0’
10 15 17 20 21
15 16 18 21 23 17 18 20 22 24 18 20 22 24 26 18 20 22 25 25
while white with 1’.It should be note that a binary image is generally
created from a gray-scale image. A binary image finds applications in
computer vision areas where the general shape or outline information of
the image is needed. They are also referred to as 1 bit/pixel images.
Gray-scale images are known as monochrome or one-colour images. They
contain no colour information. They represent the brightness of the image.
This image contains 8 bits/pixel data, which means it can have up to 256(0-
255) different brightness levels. A ‘0’represents black and ‘255’ denotes
white. In between values from 1 to 254 represent the different gray levels.
As they contain the intensity information, they are also referred to as
intensity images.
Colour images are considered as three band monochrome images, where
each band is of a different colour. Each band provides the brightness
information of the corresponding spectral band. Typical colour images are
red, green and blue images and are also referred to as RGB images. This
is a 24 bits/pixel image.
Processing of images, for some specific task as per the application
requirements, is known as Image Processing. For processing using digital
computers, image has to be converted into a discrete form using the process of
sampling and quantization, known collectively as digitization.
The field of digital image processing refers to the use of computer algorithms
to extract useful information from digital images. The entire process of image
processing may be divided into three major stages:-
(i) Image acquisition: converting 3D visual information into 2D digital form
suitable for processing, transmission and storage.
(ii) Processing: improving image quality by enhancement, restoration, etc.
(iii) Analysis: extracting image features; quantifying shapes and recognition.
In the first stage, input is an image scene, and output is a corresponding
digital image.
In the second stage of processing, both input and output are digital images
where the output is an improved version of the input.
In the final stage, input is still a digital image but the output is description
of the contents.
A block diagram of different stages is shown in figure below:-
Figure 2: Steps in image processing
Often, the captured image may not be of a good quality, because of factors
such as noise, poor brightness, contrast, blur, or artefacts. Image enhancement is
the process of enhancing the quality of a given image for analysis. The aim of this
process is to improve the quality of the image so that the image analysis is
accurate, leading to improvement in the reliability of the application.
Image applications are frequently affected by the noise present in the
image. A noise is introduced in the transmission medium due to a noisy channel,
error during the measurement process and during quantization of the data for
digital storage. There are various methods to help restore an image from noisy
distortions. Selecting the appropriate method plays a major role in getting the
desired image. The denoising methods tend to be problem specific.
For example, a method that is used to denoise satellite images may not be suitable
for denoising medical images. Noise removal or noise reduction can be done on
an image by filtering, by wavelet analysis, or by multifractal analysis.
Image processing has a broad spectrum of applications and can be
surveyed using domains where images are used.
Object
Image Acquisition
(Image sensing & A/D
Conversion)
Processing
(Enhancement/Restorati
on/De-noising, etc)
Analysis (Feature
Extraction/Object
Description/Pattern
recognition, etc)
Output
The applications of image processing covering different areas are as follows:
(i) Medicine: X-rays, CT-scan, MRI, Ultrasound, etc. for detecting various
diseases.
(ii) Forensics: Identifying physiological characteristics such as face, iris,
fingerprints, palm, etc.
(iii) Remote Sensing: Meteorological applications such as weather forecasting,
locating natural resources- forests, water, etc.
(iv) Communication: Watermarking, Video conferencing, HDTV, etc.
(v) Industry automation: Automated visual inspection in aerospace, food, textile
etc.
(vi) Traffic control: Analyzing pictures taken by cameras for crowd control.
(vii) Defence: Night vision devices, RADAR, etc.
(viii) Robotics: Pilot-less vehicles, surface measurements, etc.
Chapter 3
Noise in digital images
Noise gets introduced into the data via any electrical system used for storage,
transmission, and/or processing. In addition, nature will always plays a "noisy" trick or
two with the data under observation.
When encountering an image corrupted with noise you will want to improve its
appearance for a specific application. The techniques applied are application-oriented.
Also, the different procedures are related to the types of noise introduced to the image.
Some examples of noise are: Gaussian or White, Rayleigh, Shot or Impulse, periodic,
sinusoidal or coherent, uncorrelated, and granular.
Type of Noise
Typical images are corrupted with additive noises modeled with either a
Gaussian, uniform, or salt or pepper distribution. Another typical noise is a speckle
noise, which is multiplicative in nature. Noise is present in an image either in an
additive or multiplicative form.
An additive noise follows the rule
w(x, y) = s(x, y) + n(x, y) ,
While the multiplicative noise satisfies
w(x, y) = s(x, y)× n(x, y),
where, s(x,y) is the original signal, n(x,y) denotes the noise introduced into the
signal to produce the corrupted image w(x,y), and (x,y) represents the pixel location.
i. Gaussian Noise
Gaussian noise is evenly distributed over the signal. This means that each pixel in the
noisy image is the sum of the true pixel value and a random Gaussian distributed noise
value. As the name indicates, this type of noise has a Gaussian distribution, which has
a bell shaped probability distribution function given by,
22 2/)(
2
1)(
zezp
where, Mean:
Standard deviation:
Variance:
Graphically, it is represented as shown in figure below:
Figure 3: Gaussian distribution
Figure 4: Gaussian noise image (a) mean=0, variance=0.05
(b) mean=1.5, variance=10
ii. Salt and Pepper Noise
Salt and pepper noise is an impulse type of noise, which is also referred to as intensity
spikes. This is caused generally due to dead pixels, analog-to-digital converter errors,
errors in data transmission, malfunctioning of pixel elements in the camera sensors,
faulty memory locations, or timing errors in the digitization process.
It has only two possible values, ‘a’ and ‘b’. The probability of each is typically
less than 1. The corrupted pixels are set alternatively to the minimum or to the
2
maximum intensity values, giving the image a “salt and pepper” like
appearance. Unaffected pixels remain unchanged.
Usually, for an 8-bit image, a =1(black) and b=0 (white)
The probability density function for this type of noise is shown in figure below:
(a) (b)
Figure 5: a) Salt and pepper noise image b) PDF for salt and pepper noise
iii. Speckle Noise
Speckle noise is a multiplicative noise. This type of noise occurs in almost all coherent
imaging systems such as laser, acoustics and SAR (Synthetic Aperture Radar) imagery.
The source of this noise is attributed to random interference between the coherent
returns. Fully developed speckle noise has the characteristic of multiplicative noise.
The gamma distribution is given below in figure below:
(a) (b)
Figure 6: a) Gamma distribution b) Speckle noise image
iv. Brownian Noise
Brownian noise comes under the category of fractal or 1/f noises. The mathematical
model for 1/f noise is fractional Brownian motion. Fractal Brownian motion is a non-
stationary stochastic process that follows a normal distribution. Brownian noise is a
special case of 1/f noise. It is obtained by integrating white noise. It can be graphically
represented as shown in figure below:
(a) (b)
Figure 7: a) Brownian noise distribution b) Brownian noise image
Chapter 4
Image filtering techniques
The existence of impulse noise is one of the most frequent problems in many
digital image processing applications. So for the removal of such impulse noise median
based filter becomes widely used. However, there are many variations of median filter
in literature. In addition to standard median filter, there are weighted median filter,
recursive median filter, iterative median filter, directional median filter, adaptive
median filter and switching median filter. Among all these, the standard median
filtering and adaptive median filtering techniques are discussed below.
A. Standard median filter (SMF)
The standard median filter is a simple rank selection filter also called as median
smoother, introduced by tukey in 1971 that attempts to remove impulse noise by
changing the luminance value of the center pixel of the filtering window with the
median of the luminance values of the pixels contained within the window. Although
the median filter is simple and provides a reasonable noise removal performance, it
removes thin lines and blurs image details even at low noise densities. A Median filter
belongs to the class of non-linear filters. The median filter follows the moving window
principle.
e.g.:- A 3x3, 5x5, or 7x7 kernel of pixels is scanned over the pixel matrix of the entire
image. The median of the pixel values in the window is computed, and the centre pixel
of the window is replaced with the computed median.
The median is just the middle value of all the values of the pixels in the neighborhood.
This is not the same as the average (or mean); instead, the median has half the values
in the neighborhood larger and half smaller. The median is a stronger "central
indicator" than the average.
The Standard Median filtering (SMF) is done by first sorting all the pixel
values from the surrounding neighborhood into numerical order and then replacing the
pixel being considered with the middle pixel value.
Figure 8: Calculating the median value of a pixel neighborhood in 3x3 window
Here, neighborhood values are:
115,119,120,123,124,125,126,127,150
arranged in increasing order.
Median value: 124
Central pixel value: 150
Now, the central pixel value 150 in the 3x3 window is replaced with the median value
of 124.
The disadvantage of the SMF:-
Although SMF is a useful non-linear image smoothing and enhancement
technique. It also has some disadvantages.
The SMF removes both the noise and the fine detail since it can't tell the
difference between the two.
Anything relatively small in size compared to the size of the neighborhood will
have minimal affect on the value of the median, and will be filtered out.
In other words, the SMF can't distinguish fine detail from noise.
123 125 126 130 140
120 124 126 127 135
118 120 150 125 134
119 115 119 123 133
111 116 110 120 130
B. Adaptive Median Filter
The Adaptive Median Filter is designed to eliminate the problems faced with
the standard median filter. The basic difference between the two filters is that, in the
Adaptive Median Filter, the size of the window surrounding each pixel is variable. This
variation depends on the median of the pixels in the present window. If the median
value is an impulse, then the size of the window is expanded. Otherwise, further
processing is done on the part of the image within the current window specifications.
Processing the image basically entails the following: The center pixel of the window is
evaluated to verify whether it is an impulse or not. If it is an impulse, then the new
value of that pixel in the filtered image will be the median value of the pixels in that
window. If, however, the center pixel is not an impulse, then the value of the center
pixel is retained in the filtered image. Thus, unless the pixel being considered is an
impulse, the gray-scale value of the pixel in the filtered image is the same as that of the
input image. Thus, the Adaptive Median Filter solves the dual purpose of removing the
impulse noise from the image and reducing distortion in the image. Adaptive Median
Filtering can handle the filtering operation of an image corrupted with impulse noise of
probability greater than 0.2. This filter also smoothens out other types of noise, thus,
giving a much better output image than the standard median filter.
Chapter 5
NOISE REDUCTION BY PROPOSED FILTERING APPROACH
The proposed filtering approach is the combination of adaptive median filter
and the hybrid median filter. First of all the adaptive median filter is used to remove
salt and pepper noise from a gray-scale image and then hybrid median filter is used to
retain the edges and fine details of the image. These two filtering techniques are
discussed below.
5.1 Adaptive median Filter
The Adaptive Median Filter discussed so far is applied to an entire image
without any regard for how image characteristics vary from one point to another. The
behavior of adaptive filters changes depending on the characteristics of the image inside
the filter region.
This approach often produces better results than linear filtering. The adaptive filter is
more selective than a comparable linear filter, preserving edges and other high-
frequency parts of an image.
The application of median filter has been investigated. As an advanced method
compared with standard median filtering, the Adaptive Median Filter performs spatial
processing to preserve detail and smooth non-impulsive noise. A prime benefit to this
adaptive approach to median filtering is that repeated applications of this Adaptive
Median Filter do not erode away edges or other small structure in the image.
The adaptive median filtering has been introduced as an improvement
to the standard median filtering, as we explained before that the Median filtering can
detect the noise but in the same it can't differentiate between the fine details and the
noise. So the main idea in the Adaptive Median Filter is to perform a spatial processing
to determine which pixels in an image have been affected by impulse noise, and run the
filter only in this pixel. The Adaptive Median Filter classifies pixels as noise by
comparing each pixel in the image to its surrounding neighbor pixels. The size of the
neighborhood is adjustable, as well as the threshold for the comparison. A pixel that is
different from a majority of its neighbors, as well as being not structurally aligned with
those pixels to which it is similar, is labeled as impulse noise. These noise pixels are
then replaced by the median pixel value of the pixels in the neighborhood that have
passed the noise labeling test.
5.2 Purpose of the Algorithm
The purpose of the algorithm is to:-
1). Remove impulse noise (SALT & PEPPER)
2). Smoothing of other noise
3). Reduce distortion.
The standard median filter does not perform well when impulse noise is greater than
0.2, while the adaptive median filter can better handle these noises. The output of the
filter is a single value used to replace the value of the pixel at (x, y), the particular point
on which the window Sxy is centered at given time. Consider the following notation:
zmin = minimum gray level in Sxy
zmax = maximum gray level in Sxy
zmed = median of gray levels in Sxy
zxy = gray level at coordinates (x, y)
Smax =maximum allowed size of Sxy
WORKING OF THE ALGORITHM
The adaptive median filtering algorithm works in two levels,
denoted level A and level B, as follows:
Level
A1 = zmed –zmin
A2 = zmed –zmax
If A1 > 0 and A2 < 0, Go to level B
Else increase the window size
If window size ≤Smax repeat level A
Else output zxy
Level B:
B1 = zxy –zmin
B2 = zxy –zmax
If B1 > 0 and B2 < 0, output zxy
Else output zmed
● Explanation
Level IF Zmin < Zmed < Zmax, then
• Zmed is not an impulse
Go to level B to test if Zxy is an impulse...
ELSE
• Zmed is an impulse
The size of the window is increased and
Level A is repeated until...
(a) Zmed is not an impulse and go to level B or
(b) Smax reached: output is Zxy
Level B: IF Zmin < Zxy < Zmax, then
• Zxy is not an impulse
Output is Zxy (distortion reduced) ELSE
•Either Zxy = Zmin or Zxy = Zmax
Output is Zmed (standard median filter)
• Zmed is not an impulse (from level A)
Example: Apply 3x3 adaptive median filter on pixel (2,2) , with maximum allowed
size of 3x3.
4 0 0
5 7 7
3 6 0
Solution:
Zxy = 7 , Zmed = 4, Zmin = 0, Zmax = 7
Level A
Test if Zmin < Zmed < max True, Go to level B
Level B
Test if Zmin < Zxy < Zmax False, then output = Zmed =4
5.3 Hybrid Median Filter
Hybrid median filter is windowed filter of nonlinear class that easily removes
impulse noise while preserving edges. In comparison with basic version of the median
filter hybrid one has better corner preserving characteristics. The basic idea behind filter
is for any elements of the signal (image) apply median technique several times varying
window shape and then take the median of the got median values.
B = hmf (A, n) performs hybrid median filtering of the matrix A using an NXN
box. Hybrid median filter preserves edges better than a square kernel (neighbor pixels)
median filter because it is a three-step ranking operation: data from different spatial
directions are ranked separately. Three median values are calculated: MR is the median
of horizontal and vertical R pixels, and MD is the median of diagonal D pixels. The
filtered value is the median of the two median values and the central pixel C: median
([MR, MD, C]).
Hybrid median filter algorithm:
1. Find the median MR of the pixels marked as R and the central pixel C in the NxN window
2. Find the median MD of the pixels marked as D and the central pixel C in the NxN window 3. Finally compute M median ( MR , MD , C)
4. Filter value yi , j M
The time complexity of hybrid median filter is O(N)
For all window filters there is some problem and that is edge treating. If you
place window over an element at the edge, some part of the window will be empty. To
fill the gap, signal should be extended. For hybrid median filter there is good idea to
extend image symmetrically. In other words we are adding lines at the top and at the
bottom of the image and add columns to the left and to the right of it. A hybrid median
filter has the advantage of preserving corners and other features that are eliminated by
the 3 x 3 and 5 x 5 median filters. With repeated application, the hybrid median filter
does not excessively smooth image details (as do the conventional median filters), and
typically provides superior visual quality in the filtered image. One advantage of the
hybrid median filter is due to its adaptive nature, which allows the filter to perform
better than the standard median filter on fast-moving picture information of small spatial
extent.
5.4 Literature Survey
D * R * D
* D R D *
R R C R R
* D R D *
D * R * D
1. An Enhancement in Adaptive Median filter for Edge Preservation has been done by
Kesari Verma Department of Computer Applications,National Institute of Technology
Raipur Chhattisgarh, Bikesh Kumar Singh Department of Bio-medical
Engineering,National Institute of Technology Raipur Chhattisgarh, A.S. Thoke
Department of Electrical Engineering, National Institute of Technology Raipur
Chhattisgarh.
In this paper an enhancement in existing median filtering has been proposed that
preserve more edges without much lose in Peak signal to noise ratio(PSNR) and signal
to noise ratio SNR). In this paper we also proposed a new parameter for performance
evaluation Edge Retrieval Index (ERI) that evaluates the edge preservation index in
images. The algorithm cleans up the image noise in the homogeneous areas, but
preserves the edges in other region.
2. Image denoising using new adaptive based median filter has been done by Suman
Shrestha , University of Massachusetts Medical School, Worcester, MA 01655,
Department of Electrical and Computer Engineering. In this paper, the comparison of
known image denoising techniques is discussed and a new technique using the decision
based approach has been used for the removal of impulse noise. All these methods can
primarily preserve image details while suppressing impulsive noise. The principle of
these techniques is at first introduced and then analysed with various simulation results
using MATLAB. Most of the previously known techniques are applicable for the
denoising of images corrupted with less noise density. Here a new decision based
technique has been presented which shows better performances than those already
being used. The comparisons are made based on visual appreciation and further
quantitatively by Mean Square error (MSE) and Peak Signal to Noise Ratio (PSNR) of
different filtered images.
3. Digital Image Segmentation Using Median Filtering and Morphological Approach
has been done by Pinaki Pratim Acharjya, Soumya Mukherjee Department of CSE,
B.I.T.M. India And Dibyendu Ghoshal Department of ECE, NITA India. This paper
advocates an effective image segmentation approach for noisy images. The approach
can broadly be divided into application of two strategies namely noise removal from
noisy images using median filtering on initial digital color image and secondly applying
watershed algorithm using distance transform over noise free images obtained after
median filtering of noisy images. Comparative analysis is also shown in this paper
between application of only watershed algorithm on noisy image and application of
proposed approach over watershed algorithm. Statistical results are included in the
paper to .support our approach of median filtering and morphological segmentation of
noisy digital color image.
4. Modified Adaptive Median Filter for Salt & Pepper Noise has been proposed by
Sukhwinder Singh, Dr. Neelam Rup Prakash (2014) PhD Scholar, Electronics and
Electrical Comm. .Deptt. PEC University of Technology, Chandigarh (India), PhD
Supervisor, Electronics and Electrical Comm. Deptt.,PEC University of Technology,
Chandigarh (India)
In this paper, an image denoising filter for salt & pepper noise is proposed. They
introduced a ROAD (Rank Order Absolute Difference) statistics in this filter to identify
the noisy pixels in image corrupted with salt & pepper noise. ROAD statistics values
quantify how different in intensity the particular pixels are from their most similar
neighbors. After identify the presence of impulse noise, adaptive window filtering
concept is used to filter the salt & pepper noise. To evaluate the performance of
proposed filter, both quantitative and qualitative techniques are used and a comparison
is carried out between proposed filter and other standard filters, it is observed from
experimental results that proposed filter performs remarkably well in filtering and
preserving the image detail as compared to well known standard filters. In this paper,
we proposed a modified adaptive median filter to remove the salt & pepper noise. In
the proposed filter, they introduce a ROAD statistic in some neighborhood of a pixel to
process impulse pixels and edge pixels differently. In other words, Rank-Ordered
Absolute Differences (ROAD) statistic is used to detect the presence of impulse noise
in corrupted image because it works in both domains i.e. geometric domain and
intensity domain. At the end, to check the filtering performance of the proposed filter;
various tests were conducted by taking various salt & pepper noise corrupted gray scale
images as test images.
5. An Experimental Analysis on Salt and Pepper Noise Detection and Removal in
Gray Scale Images has been done by E.Jebamalar Leavline, D.Asir Antony Gnana
Singh Bharathidasan Institute of Technology, Anna University Chennai. Impulse
noise removal is a mechanism for detection and removal of impulse noise from images.
Median filters are preferred for removing impulse noise because of their simplicity and
less computational complexity. In this paper, impulse noise removal using the standard
median filter and its variants are analyzed. Extensive simulations have been carried out
on a set of standard gray scale images and the state of the art median filter variants are
compared in terms of the well known image quality assessment metrics namely mean
square error, peak signal to noise ratio and multiscale structural similarity index.
Experimental results show that, among the methods compared, tristate median filter and
switching median filter exhibit visually appealing results. The other methods such as
standard median filter, adaptive median filter, weighted median filter lack in preserving
edges while retaining some noise components. However, these methods are suitable for
impulse noise removal provided the noise density is low.
6. A Survey on Various Median Filtering Techniques for Removal of Impulse Noise
from Digital Images has been done by Ms. Rohini R. Varade, Prof. M. R. Dhotre, Ms.
Archana B. Pahurkar Department of Electronics and Telecommunication, Government
College of Engineering, Jalgaon (Maharashtra), India. This paper surveys seven
common median filtering techniques. Each technique has its own advantages, and
disadvantages. From literature, they found that most of the recent median filtering based
methods employ two or more than two of this framework in order to obtain an improved
impulse noise cancellation.
7. Adaptive median filter (AMF) In 2008, S.Saudia, Justin Varghese, Krishnan
Nallaperumal, Santhosh.P.Mathew, Angelin J Robin, S.Kavitha, Proposes a new
adaptive 2D spatial filter operator for the restoration of salt & pepper impulse corrupted
digital images name as -“Salt & Pepper Impulse Detection and Median based
Regularization using Adaptive Median Filter”, The Adaptive Impulse Filter effectively
identifies the impulsive positions with a valid impulse noise detector and replaces them
by a reliable signal determined from an appropriate neighborhood. Experimental results
in terms of objective metrics and visual analysis show that the proposed algorithm
performs better than many of the prominent median filtering techniques reported in
terms of retaining the fidelity of even highly impulse corrupted images. High
objectiveness and visual reliability is provided by the new restoration algorithm at
lower quantum of impulse noise also. The Adaptive Median Filter (AMF) for salt &
pepper impulse noise removal that can give much acceptable and recognizable image
restoration with better visual quality at all impulse noise levels than most other median
filters which develop impulse patches in the output at higher impulse noise levels.
Images restored by the proposed filter for Noise ratio at 95% restoration of the Proposed
Filter with better objective metrics and fidelity at higher noise ratios is an improvement
in the field of impulse restoration. The computational efficiency of the proposed filter
is also significant at all impulse noise ratios.
CHAPTER 6
IMPLEMENTATION
This project is implemented using MATLAB R2009b.
Flowchart
User Defined ADPMEDIAN Function
ADPMEDIAN Perform adaptive median filtering.
Function = ADPMEDIAN (G, SMAX) performs adaptive median filtering
of % image G.
The median filter starts at size 3-by-3 and iterates up % to size SMAX-
by-SMAX. SMAX must be an odd integer greater than 1.
Adaptive Median Filter function. adpmedian.m
START
P1=Zmed-Zin
P2=Zmed-Zmax
hhhhh
P1>0
&&
P2<0
Sxy=Sxy+2
Sxy<=Sm
ax
Zxy
Level 1 Level 2
Q1=Zxy-Zmin Q2=Zxy-Zmax
Q1>0
&&
Q2<0
Zmed
Yes
No
No
No
No
Yes
function f = adpmedian(g, Smax) %ADPMEDIAN Perform adaptive median filtering. % F = ADPMEDIAN(G, SMAX) performs adaptive median filtering of % image G. The median filter starts at size 3-by-3 and iterates up % to size SMAX-by-SMAX. SMAX must be an odd integer greater than 1.
% SMAX must be an odd, positive integer greater than 1. if (Smax <= 1) | (Smax/2 == round(Smax/2)) | (Smax ~= round(Smax)) error('SMAX
must be an odd integer > 1.') end [M, N] = size(g);
% Initial setup. f = g; f(:) = 0; alreadyProcessed = false(size(g));
% Begin filtering. for k = 3:2:Smax
zmin = ordfilt2(g, 1, ones(k, k)); %order-statistic filtering. zmax = ordfilt2(g, k * k, ones(k, k)); zmed = medfilt2(g, [k k]);%median filtering.
processUsingLevelB = (zmed > zmin) & (zmax > zmed) & ...
~alreadyProcessed;
zB = (g > zmin) & (zmax > g); outputZxy =
processUsingLevelB & zB; outputZmed =
processUsingLevelB & ~zB; f(outputZxy) =
g(outputZxy); f(outputZmed) =
zmed(outputZmed);
alreadyProcessed = alreadyProcessed | processUsingLevelB; if all(alreadyProcessed(:))
break; end
end
% Output zmed for any remaining unprocessed pixels. Note that this % zmed was computed using a window of size Smax-by-Smax, which is % the final value of k in the loop. f(~alreadyProcessed) = zmed(~alreadyProcessed);
CHAPTER 7
COMPARATIVE ANALYSIS
7.1 Image Quality Assessment Metrics
The image quality assessment measures are helpful in detecting the quality of
the processed image in comparison with the original image. In our work, we concentrate
on objective quality measurement like Mean Square Error (MSE), Peak Signal to Noise
Ratio (PSNR) to evaluate the quality of the processed image.
7.1.1. Mean Square Error:
The most frequently used image quality measures are deviations between the
original and processed images of which the mean square error (MSE) or signal to noise
ratio (SNR) are the most common measures. The effectiveness of the algorithm stands
in minimizing the mean square error. If F(X, Y) is the original clean image, G(X, Y) is
the corrupted image and I(X, Y) is the denoised image then MSE is given by
7.1.2. Peak Signal to Noise Ratio:
Larger PSNR indicate a smaller difference between the original uncorrupted
image and the denoised image. This is the most widely used objective image
quality/distortion measure. The main advantage of this measure is ease of computation.
PSNR is calculated using,
7.2 Results based on noise density
PSNR
Filter 10% 20% 30% 40% 50%
MF(3X3) 34.3998562 34.2442217 34.0981522 33.9541612 33.7844514
MF(5X5) 33.5965313 33.4969483 33.3655143 33.2639888 33.1541360
MF(7X7) 33.3076611 33.1992265 33.0966836 32.9993293 32.9143468
AMF(3X3) 41.5590665 41.4724943 41.3997296 41.3570081 41.2793782
AMF(5X5) 42.6972876 42.6878704 42.6592092 42.5859100 42.4198768
AMF(7X7) 43.4951050 43.4065394 43.3400422 43.3259104 43.2427435
HMF(3X3) 49.7115664 49.5670763 49.5718381 49.4796871 49.2353513
HMF(5X5) 48.9179644 48.8600667 49.0062441 48.6769562 48.8428934
HMF(7X7) 49.1511468
49.2792620
49.2864201
48.8889387
48.9536373
MSE
10% 20% 30% 40% 50%
MF(3X3) 23.80 24.66 25.51 26.37 27.42
MF(5X5) 28.63 29.29 30.19 30.91 31.70
MF(7X7) 30.60 31.37 32.12 32.85 33.50
AMF(3X3) 4.58 4.67
4.75
4.79
4.88
AMF(5X5) 3.52
3.53
3.55
3.61
3.75
AMF(7X7) 2.93 2.99 3.04
3.05
3.11
HMF(3X3) 0.70
0.72
0.72
0.74
0.78
HMF(5X5) 0.84 0.85 0.82
0.89
0.86
HMF(7X7) 0.80
0.77
0.77
0.85
0.83
PSNR
Filter 10% 20% 30% 40% 50%
MF(3X3) 36.8572421 36.4520558 36.0871152 35.7609416 35.4480445
MF(5X5) 34.0717118 33.8957024 33.7249284 33.5743003 33.3773725
MF(7X7) 33.1521579 33.0157377 32.8928393 32.7484905 32.6410077
AMF(3X3) 48.4867430 48.3588111 48.3094425 48.1251537 48.0223169
AMF(5X5) 51.8938398 51.8671403 51.3380567 51.6908180 51.1874759
AMF(7X7) 55.5903999 55.5091989 55.5163056 55.5713015 55.2818263
HMF(3X3) 53.4288628 53.0652158 52.6950772 52.4768435 52.4961583
HMF(5X5) 50.0282195 49.9005039 49.8097476 49.7670111 49.8018669
HMF(7X7) 49.5265835 49.4660741 49.3643092 49.2970288 49.2674364
MSE
10% 20% 30% 40% 50%
MF(3X3) 13.51 14.83 16.13 17.39 18.69
MF(5X5) 25.66 26.72 27.80 28.78 30.11
MF(7X7) 31.71 32.73 33.67 34.80 35.68
AMF(3X3) 0.93 0.96 0.97 1.01 1.03
AMF(5X5) 0.42 0.43 0.48 0.44 0.50
AMF(7X7) 0.18 0.18 0.18 0.18 0.19
HMF(3X3) 0.30 0.32 0.35 0.37 0.37
HMF(5X5) 0.65 0.67
0.68 0.69 0.69
HMF(7X7) 0.73 0.74 0.76 0.77 0.78
PSNR
Filter 10% 20% 30% 40% 50%
MF(3X3) 32.7352501 32.6124146 32.4842563
32.3439908
32.2250294
MF(5X5) 30.8364347
30.7733551
30.7053952
30.6416678 30.5872004
MF(7X7) 30.2014293 30.1565069
30.1014436 30.0521608 30.0100123
AMF(3X3) 41.2183752
41.1422159 41.0301614 40.9904774 40.9164215
AMF(5X5) 43.3468823
43.3769962
43.1808292 43.1966646 43.1324133
AMF(7X7) 45.1154366
45.0900374 45.2118587 44.9433038
45.0687799
HMF(3X3) 46.5050771
46.2424155 46.1722194 46.0789989 45.9074280
HMF(5X5) 43.2748435
43.1824649 43.1935836 43.1728124 43.1058601
HMF(7X7) 42.9553904
42.9005824 42.8592175 42.8223903 42.8676586
MSE
10% 20% 30% 40% 50%
MF(3X3) 34.91 35.91 36.99 38.20 39.26
MF(5X5) 54.06 54.85 55.71 56.53 57.25
MF(7X7) 62.57 63.22 64.02 64.75 65.39
AMF(3X3) 4.95 5.04 5.17 5.22 5.31
AMF(5X5) 3.03 3.01 3.15 3.14 3.19
AMF(7X7) 2.02 2.03 1.97 2.10 2.04
HMF(3X3) 1.47 1.56 1.58 1.62 1.68
HMF(5X5) 3.08 3.15 3.14 3.16 3.21
HMF(7X7) 3.32 3.36
3.39 3.42 3.39
.
PSNR
Filter 10% 20% 30% 40% 50%
MF(3X3) 34.7877402 34.5514815 34.3231644 34.1374837 33.9156213
MF(5X5) 32.7809773 32.6672135 32.5120636 32.3989290 32.2902559
MF(7X7) 31.9746512 31.8860551 31.7801345 31.6973581 31.6008294
AMF(3X3) 43.1727442 43.1378924 43.1222020 42.9334398 42.8673602
AMF(5X5) 44.3490653 44.3187901 44.1306178 44.2709873 44.1276283
AMF(7X7) 45.4437376 45.3094916 45.4554938 45.2587884 45.3625923
HMF(3X3) 50.1172384 49.9605592 49.8877000 49.5359557 49.4239390
HMF(5X5) 46.7677342 46.7253428 46.6275715 46.6313408 46.5554037
HMF(7X7) 46.3086727 46.2477928 46.1913395 46.3114397 46.2772464
MSE
MF(3X3) 21.76 22.98 24.22 25.28 26.60
MF(5X5) 34.54 35.46 36.75 37.72 38.68
MF(7X7) 41.59 42.45 43.50 44.33 45.33
AMF(3X3) 3.16 3.18 3.19 3.34 3.39
AMF(5X5) 2.41 2.42 2.53 2.45 2.53
AMF(7X7) 1.87 1.93 1.87 1.95 1.91
HMF(3X3) 0.64 0.66 0.67 0.73 0.75
HMF(5X5) 1.38 1.39 1.42 1.42 1.45
HMF(7X7) 1.53 1.55 1.58 1.53 1.54
PSNR
Filter 10% 20% 30% 40% 50%
MF(3X3) 33.1885216 33.0528508 32.9051991 32.7689498 32.6405912
MF(5X5) 31.4083609 31.3309442 31.2585474 31.1855680 31.1211928
MF(7X7) 30.8817489 30.8211751 30.7620734 30.6946813 30.6372437
AMF(3X3) 42.2305842 42.1346590 42.0463591 41.9416603 41.8722531
AMF(5X5) 44.9875326 44.9583926 44.7565423 44.8166894 44.7177310
AMF(7X7) 46.9965863 47.0357159 46.9237739 46.9844121 46.7137386
HMF(3X3) 48.5036900 48.4625279 48.2507659 48.1792366 47.8977693
HMF(5X5) 46.9616723 46.9390510 46.8759469 46.7824712 46.7618893
HMF(7X7) 47.1007229 47.0535086 46.9805508 47.0038464 46.8008391
MSE
10% 20% 30% 40% 50%
MF(3X3) 31.45 32.45 33.57 34.64 35.68
MF(5X5) 47.39 48.24 49.05 49.88 50.62
MF(7X7) 53.49 54.25 54.99 55.85 56.59
AMF(3X3) 3.92 4.01 4.09 4.19 4.26
AMF(5X5) 2.08 2.09 2.19 2.16 2.21
AMF(7X7) 1.31 1.30 1.33 1.31 1.40
HMF(3X3) 0.92 0.93 0.98 1.00 1.06
HMF(5X5) 1.32 1.33 1.35 1.37 1.38
HMF(7X7) 1.28 1.29 1.31 1.31 1.37
PSNR
Filter 10% 20% 30% 40% 50%
MF(3X3) 36.7201687 36.3653247 36.0584979 35.7248886 35.4569323
MF(5X5) 34.5649650 34.3633116 34.1653109 33.9829645 33.8147969
MF(7X7) 33.7352493 33.5961714 33.4444493 33.3095098 33.1337457
AMF(3X3) 45.9574658 45.9216178 45.8215105 45.7036754 45.6564253
AMF(5X5) 48.2892782 48.3114298 48.2264500 48.2455981 48.0975634
AMF(7X7) 49.9137422 49.9153533 49.8202127 49.8075221 49.7912290
HMF(3X3) 53.8843535 53.8129731 53.5002070 53.3782177 53.3689279
HMF(5X5) 51.2221384 51.1134784 51.1646746 51.0381836 50.9266481
HMF(7X7) 50.8100084 50.7994508 50.7253610 50.6337822 50.5110688
MSE
10% 20% 30% 40% 50%
MF(3X3) 13.95 15.13 16.24 17.54 18.65
MF(5X5) 22.91 24.00 25.12 26.19 27.23
MF(7X7) 27.73 28.63 29.65 30.59 31.85
AMF(3X3) 1.66 1.68 1.72 1.76 1.78
AMF(5X5) 0.97 0.97 0.99 0.98 1.02
AMF(7X7) 0.67 0.67 0.68 0.69 0.69
HMF(3X3) 0.27 0.27 0.29 0.30 0.30
HMF(5X5) 0.49 0.51 0.50 0.52 0.53
HMF(7X7) 0.54 0.55 0.55 0.57 0.58
PSNR
Filter 10% 20% 30% 40% 50%
MF(3X3) 39.2600729 38.5639614 38.0287490 37.4928310 37.0554933
MF(5X5) 37.3335724 36.8911689 36.5334537 36.1591848 35.8753282
MF(7X7) 36.5593145 36.1947800 35.8917960 35.6089433 35.3330485
AMF(3X3) 48.5611345 48.4725107 48.2849670 48.2443324 48.2250723
AMF(5X5) 49.7146663 49.8088524 49.8826284 49.6925187 49.7205883
AMF(7X7) 50.7652468 50.6920594 50.6577169 50.6992101 50.6825830
HMF(3X3) 56.9913104 56.8692539 56.6122027 56.5307019 56.3666714
HMF(5X5) 54.9998015 54.9203564 54.9413632 54.8462718 54.8670776
HMF(7X7) 54.3613452 54.3831372 54.0517596 54.2941026 54.3653495
MSE
10% 20% 30% 40% 50%
MF(3X3) 7.77 9.12 10.32 11.67 12.91
MF(5X5) 12.11 13.41 14.56 15.87 16.94
MF(7X7) 14.47 15.74 16.88 18.01 19.19
AMF(3X3) 0.91 0.93 0.97 0.98 0.99
AMF(5X5) 0.70 0.68 0.67 0.70 0.70
AMF(7X7) 0.55 0.56 0.56 0.56 0.56
HMF(3X3) 0.13 0.13 0.14 0.15 0.15
HMF(5X5) 0.21 0.21 0.21 0.21 0.21
HMF(7X7) 0.24 0.24 0.26 0.24 0.24
PSNR
Filter 10% 20% 30% 40% 50%
MF(3X3) 38.5316845 38.0306746 37.5125616 37.0735361 36.7243058
MF(5X5) 36.6361840 36.2810873 35.9268455 35.6305008 35.3931277
MF(7X7) 35.6284752 35.3608251 35.1132387 34.8977481 34.6431840
AMF(3X3) 47.3056938 47.2335169 47.1756926 47.0627536 46.8640444
AMF(5X5) 48.4169916 48.3573908 48.3079183 48.3766393 48.2729762
AMF(7X7) 49.3558229 49.2999110 49.3021492 49.0395715 49.2584551
HMF(3X3) 55.6207272 55.5946146 55.4616417 55.2566508 55.0195105
HMF(5X5) 51.2490510 51.0739033 51.1253856 51.1867449 51.0966222
HMF(7X7) 49.8955407 49.9156260 49.9276672 49.8237067 49.7671308
MSE
10% 20% 30% 40% 50%
MF(3X3) 9.19 10.31 11.62 12.86 13.93
MF(5X5) 14.22 15.43 16.74 17.92 18.93
MF(7X7) 17.93 19.07 20.19 21.22 22.50
AMF(3X3) 1.22 1.24 1.26 1.29 1.35
AMF(5X5) 0.94 0.96 0.97 0.95 0.98
AMF(7X7) 0.76 0.77 0.77 0.82 0.78
HMF(3X3) 0.18 0.18 0.19 0.20 0.21
HMF(5X5) 0.49 0.51 0.51 0.50 0.51
HMF(7X7) 0.67 0.67 0.67 0.68 0.69
PSNR
Filter 10% 20% 30% 40% 50%
MF(3X3) 35.9837101 35.6947047 35.4115719 35.1736765 34.9087252
MF(5X5) 34.6455601 34.4423009 34.2357576 34.0742580 33.8551979
MF(7X7) 33.9604899 33.7925218 33.6290200 33.4837873 33.3412419
AMF(3X3) 44.0558034 43.9679811 43.9314567 43.9303192 43.7962610
AMF(5X5) 45.4238176 45.3399356 45.4362359 45.2576262 45.3135368
AMF(7X7) 46.1780556 46.0808338 46.2061941 46.0574382 46.1045417
HMF(3X3) 53.7873817 53.6900440 53.3745874 53.1911372 53.2174125
HMF(5X5) 51.2569784 51.3730800 51.2714199 50.8768368 50.9242705
HMF(7X7) 50.8577918 50.7568130 50.8233715 50.7287381 50.5353070
MSE
10% 20% 30% 40% 50%
MF(3X3) 16.52 17.66 18.85 19.91 21.16
MF(5X5) 22.49 23.56 24.71 25.65 26.97
MF(7X7) 26.33 27.37 28.42 29.38 30.36
AMF(3X3) 2.58 2.63 2.65 2.65 2.73
AMF(5X5) 1.88 1.92 1.87 1.95 1.93
AMF(7X7) 1.58 1.62 1.57 1.62 1.61
HMF(3X3) 0.27 0.28 0.30 0.31 0.31
HMF(5X5) 0.49 0.48 0.49 0.54 0.53
HMF(7X7) 0.54 0.55 0.54 0.55 0.58
PSNR
Filter 10% 20% 30% 40% 50%
MF(3X3) 31.5812855 31.5056401 31.4277793 31.3311823 31.2536309
MF(5X5) 30.3310017 30.2828824 30.2319673 30.1920921 30.1311838
MF(7X7) 29.7533681 29.7199168 29.6831013 29.6484586 29.6074023
AMF(3X3) 40.3939802 40.3268441 40.2740002 40.1594169 40.0559477
AMF(5X5) 42.2887698 42.2196511 42.1460097 42.1496948 42.1485794
AMF(7X7) 43.7292785 43.6691524 43.7251698 43.6535699 43.6324208
HMF(3X3) 46.6427499 46.5479761 46.3797879 46.3634860 46.1723974
HMF(5X5) 44.2087751 44.0777016 44.0162792 44.0332281 43.9126275
HMF(7X7) 44.2622841 44.1654850 44.1680716 43.9964830 43.9891674
MSE
10% 20% 30% 40% 50%
MF(3X3) 45.54 46.34 47.17 48.23 49.10
MF(5X5) 60.73 61.40 62.13 62.70 63.59
MF(7X7) 69.37 69.90 70.50 71.06 71.74
AMF(3X3) 5.99 6.08 6.15 6.32 6.47
AMF(5X5) 3.87 3.93 4.00 3.99 4.00
AMF(7X7) 2.78 2.82 2.78 2.83 2.84
HMF(3X3) 1.42 1.45 1.51 1.51 1.58
HMF(5X5) 2.49 2.56 2.60 2.59 2.66
HMF(7X7) 2.46 2.51 2.51 2.61 2.62
PSNR
Filter 10% 20% 30% 40% 50%
MF(3X3) 34.0673210 33.8739414 33.7006995 33.5271781 33.3691470
MF(5X5) 32.1483456 32.0497880 31.9615166 31.8625889 31.7870856
MF(7X7) 31.5832681 31.5019694 31.4240134 31.3496673 31.2686625
AMF(3X3) 42.8010904 42.7215494 42.6172247 42.6373936 42.4979912
AMF(5X5) 44.6864270 44.6380583 44.6208602 44.5194637 44.4925452
AMF(7X7) 46.1163099 46.0468251 46.0125254 45.9962358 45.9165306
HMF(3X3) 49.8945784 49.8178365 49.5345701 49.5367963 49.1987903
HMF(5X5) 47.5592704 47.5303863 47.5593569 47.3892086 47.4070104
HMF(7X7) 47.3247803 47.3627109 47.3328843 47.2707497 47.3330485
MSE
10% 20% 30% 40% 50%
MF(3X3) 25.69 26.86 27.95 29.09 30.17
MF(5X5) 39.96 40.88 41.72 42.68 43.43
MF(7X7) 45.51 46.37 47.21 48.03 48.93
AMF(3X3) 3.44 3.50 3.59 3.57 3.69
AMF(5X5) 2.23 2.25 2.26 2.31 2.33
AMF(7X7) 1.60 1.63 1.64 1.65 1.68
HMF(3X3) 0.67 0.68 0.73 0.73 0.79
HMF(5X5) 1.15 1.16 1.15 1.20 1.19
HMF(7X7) 1.21 1.20 1.21 1.23 1.21
PSNR
Filter 10% 20% 30% 40% 50%
MF(3X3) 30.6822011 30.6266265 30.5702460 30.5203001 30.4635368
MF(5X5) 29.8430149 29.8088447 29.7699777 29.7301235 29.6915909
MF(7X7) 29.5723542 29.5398044 29.5018707 29.4677836 29.4333889
AMF(3X3) 39.3609040 39.2932999 39.2244479 39.1786133 39.1032306
AMF(5X5) 42.8434886 42.7594983 42.6518104 42.6273322 42.6227425
AMF(7X7) 45.4604772 45.2439230 45.2380248 45.1346478 45.1116045
HMF(3X3) 43.7612730 43.6782705 43.6404916 43.5312986 43.5446406
HMF(5X5) 43.2237062 43.1880286 43.2129764 43.0171179 42.9878014
HMF(7X7) 43.3648938 43.3321021 43.2592403 43.2462813 43.2096403
MSE
10% 20% 30% 40% 50%
MF(3X3) 56.01 56.73 57.47 58.14 58.90
MF(5X5) 67.95 68.49 69.10 69.74 70.36
MF(7X7) 72.32 72.86 73.50 74.08 74.67
AMF(3X3) 7.59 7.71 7.83 7.92 8.06
AMF(5X5) 3.41 3.47 3.56 3.58 3.58
AMF(7X7) 1.86 1.96 1.96 2.01 2.02
HMF(3X3) 2.76 2.81 2.83 2.91 2.90
HMF(5X5) 3.12 3.15 3.13 3.27 3.29
HMF(7X7) 3.02 3.04 3.09 3.10 3.13
PSNR
Filter 10% 20% 30% 40% 50%
MF(3X3) 33.3503414 33.1986494 33.0333920 32.8829467 32.7521377
MF(5X5) 31.6575176 31.5696315 31.4937913 31.4023875 31.3219292
MF(7X7) 31.0081108 30.9400961 30.8746422 30.8085602 30.7459736
AMF(3X3) 42.3951102 42.3388132 42.2637753 42.1539019 42.0977094
AMF(5X5) 44.8334744 44.8113664 44.7333703 44.6525863 44.6126704
AMF(7X7) 46.5754758 46.5283486 46.4011595 46.4314865 46.3840187
HMF(3X3) 49.0166126 48.9571353 48.9121949 48.6206553 48.5040483
HMF(5X5) 46.5095562 46.3940130 46.4484033 46.4226035 46.2233982
HMF(7X7) 45.3555503 45.3835424 45.3857172 45.4035500 45.2255620
MSE
10% 20% 30% 40% 50%
MF(3X3) 30.30 31.38 32.59 33.74 34.77
MF(5X5) 44.74 45.66 46.46 47.45 48.34
MF(7X7) 51.96 52.78 53.58 54.40 55.19
AMF(3X3) 3.78 3.82 3.89 3.99 4.04
AMF(5X5) 2.15 2.16 2.20 2.25 2.27
AMF(7X7) 1.44 1.46 1.50 1.49 1.51
HMF(3X3) 0.82 0.83 0.84 0.90 0.92
HMF(5X5) 1.46 1.50 1.48 1.49 1.56
HMF(7X7) 1.91 1.90 1.90 1.89 1.97
PSNR
Filter 10% 20% 30% 40% 50%
MF(3X3) 33.5092729 33.3692409 33.2010487 33.0793835 32.9225069
MF(5X5) 31.7099679 31.6326149 31.5392996 31.4416006 31.3908441
MF(7X7) 30.8000929 30.7440776 30.6769339 30.6082928 30.5618584
AMF(3X3) 42.6465019 42.5740735 42.4862079 42.4069654 42.3199815
AMF(5X5) 44.1955899 44.0785808 44.0485606 44.0473985 44.0385870
AMF(7X7) 45.4944649 45.5382024 45.3897291 45.4765590 45.4192987
HMF(3X3) 49.4449554 49.2901324 49.2711111 49.0335169 49.0483546
HMF(5X5) 45.8484254 45.7327435 45.7745921 45.7034310 45.6575319
HMF(7X7) 45.7266251 45.7164406 45.7134342 45.6070996 45.5791226
MSE
10% 20% 30% 40% 50%
MF(3X3) 29.21 30.17 31.36 32.25 33.44
MF(5X5) 44.21 45.00 45.98 47.02 47.58
MF(7X7) 54.51 55.22 56.08 56.97 57.58
AMF(3X3) 3.56 3.62 3.70 3.77 3.84
AMF(5X5) 2.49 2.56 2.58 2.58 2.59
AMF(7X7) 1.85 1.83 1.89 1.86 1.88
HMF(3X3) 0.74 0.77 0.78 0.82 0.82
HMF(5X5) 1.70 1.75 1.73 1.76 1.78
HMF(7X7) 1.75 1.76 1.76 1.80 1.81
PSNR
Filter 10% 20% 30% 40% 50%
MF(3X3) 36.1420986 35.8032997 35.5238207 35.2391751 34.9678956
MF(5X5) 34.6328080 34.4012698 34.2032341 34.0206047 33.8269402
MF(7X7) 33.7659184 33.6044278 33.4365737 33.2856198 33.1414082
AMF(3X3) 46.4194988 46.2912358 46.1984023 46.0430525 46.0182115
AMF(5X5) 48.1682798 48.0967478 48.0101014 47.9744051 47.9408245
AMF(7X7) 48.5348422 48.5757882 48.4315536 48.3948554 48.4771369
HMF(3X3) 55.9916430 55.8016015 55.2202521 55.4087990 55.3019182
HMF(5X5) 51.2614376 51.0499503 51.1326638 51.0546207 50.9765625
HMF(7X7) 49.4888462 49.3370115 49.3767524 49.2527048 49.4454449
MSE
10% 20% 30% 40% 50%
MF(3X3) 15.93 17.22 18.37 19.61 20.88
MF(5X5) 22.55 23.79 24.90 25.97 27.15
MF(7X7) 27.54 28.58 29.70 30.76 31.79
AMF(3X3) 1.49 1.54 1.57 1.63 1.64
AMF(5X5) 1.00 1.02 1.04 1.04 1.05
AMF(7X7) 0.92 0.91 0.94 0.95 0.93
HMF(3X3) 0.16 0.17 0.20 0.19 0.19
HMF(5X5) 0.49 0.51 0.50 0.51 0.52
HMF(7X7) 0.74 0.76 0.76 0.78 0.74
PSNR
Filter 10% 20% 30% 40% 50%
MF(3X3) 34.0260132 33.8438697 33.6717145 33.4964286 33.3357455
MF(5X5) 32.1729132 32.0835379 31.9863284 31.8874611 31.7942179
MF(7X7) 31.5659225 31.4807689 31.4011175 31.3284591 31.2466944
AMF(3X3) 43.2969737 43.1876283 43.1290294 43.0112175 42.8894014
AMF(5X5) 45.9803877 45.9401896 45.8954551 45.8920670 45.7958558
AMF(7X7) 47.7794980 47.7372847 47.5705255 47.7156586 47.4739229
HMF(3X3) 50.1879059 50.0392763 49.9933993 49.8674980 49.7100054
HMF(5X5) 49.0589464 48.8526845 48.8083648 48.8189257 48.6288144
HMF(7X7) 49.1059334 49.0702170 49.1319988 48.9761650 49.0113951
MSE
10% 20% 30% 40% 50%
MF(3X3) 25.93 27.05 28.14 29.30 30.40
MF(5X5) 39.74 40.56 41.48 42.44 43.36
MF(7X7) 45.70 46.60 47.46 48.27 49.18
AMF(3X3) 3.07 3.15 3.19 3.28 3.37
AMF(5X5) 1.65 1.67 1.69 1.69 1.73
AMF(7X7) 1.09 1.10 1.15 1.11 1.17
HMF(3X3) 0.63 0.65 0.66 0.68 0.70
HMF(5X5) 0.81 0.85 0.86 0.86 0.90
HMF(7X7) 0.81 0.81 0.80 0.83 0.82
PSNR
Filter 10% 20% 30% 40% 50%
MF(3X3) 36.6609534 36.3009938 35.9496507 35.6300498 35.3582104
MF(5X5) 34.1566948 33.9636504 33.7880336 33.6224790 33.4584851
MF(7X7) 33.2875179 33.1468799 33.0040976 32.8758927 32.7568853
AMF(3X3) 46.7239753 46.5364258 46.5110955 46.4298974 46.2666286
AMF(5X5) 49.2425859 49.1916282 49.1736177 49.0016015 48.9408025
AMF(7X7) 51.0424879 51.0906064 51.0636215 51.0194423 50.8967736
HMF(3X3) 54.1934251 53.9980505 53.8500500 53.7193503 53.6086286
HMF(5X5) 51.6831758 51.6609224 51.3865566 51.3797089 51.3481823
HMF(7X7) 51.0312864 50.8931391 50.9370180 50.9947378 50.6995070
MSE
10% 20% 30% 40% 50%
MF(3X3) 14.14 15.36 16.65 17.93 19.08
MF(5X5) 25.17 26.31 27.40 28.46 29.56
MF(7X7) 30.74 31.75 32.81 33.80 34.74
AMF(3X3) 1.39 1.45 1.46 1.49 1.55
AMF(5X5) 0.78 0.79 0.79 0.82 0.84
AMF(7X7) 0.52 0.51 0.51 0.52 0.53
HMF(3X3) 0.25 0.26 0.27 0.28 0.29
HMF(5X5) 0.44 0.45 0.48 0.48 0.48
HMF(7X7) 0.52 0.53 0.53 0.52 0.56
PSNR
Filter 10% 20% 30% 40% 50%
MF(3X3) 37.5018907 37.1007060 36.7023937 36.3148901 36.0039912
MF(5X5) 35.9931429 35.6966517 35.4406354 35.1677749 34.9143233
MF(7X7) 35.2074241 34.9518622 34.7244189 34.5212790 34.3237096
AMF(3X3) 47.0213431 46.9250066 46.8495546 46.7596590 46.5669358
AMF(5X5) 49.7002740 49.6586430 49.6560966 49.6641848 49.5195393
AMF(7X7) 51.5234217 51.3253469 51.3156850 51.2656646 51.1246323
HMF(3X3) 53.9446213 53.9376678 53.8196078 53.7979154 53.5248962
HMF(5X5) 52.6207222 52.6351207 52.3828496 52.3413479 52.3035462
HMF(7X7) 52.1044389 52.1285552 52.1198974 51.9161041 52.1871791
MSE
10% 20% 30% 40% 50%
MF(3X3) 11.65 12.78 14.00 15.31 16.45
MF(5X5) 16.49 17.65 18.72 19.94 21.14
MF(7X7) 19.76 20.96 22.08 23.14 24.22
AMF(3X3) 1.30 1.33 1.35 1.38 1.44
AMF(5X5) 0.70 0.71 0.71 0.71 0.73
AMF(7X7) 0.46 0.48 0.48 0.49 0.51
HMF(3X3) 0.26
0.26 0.27 0.27 0.29
HMF(5X5) 0.36 0.36 0.38 0.38 0.39
HMF(7X7) 0.40 0.40 0.40 0.42 0.40
PSNR
Filter 10% 20% 30% 40% 50%
MF(3X3) 36.4170188 36.0642272 35.7313403 35.4119111 35.1630149
MF(5X5) 33.9916865 33.8037665 33.6321944 33.4527254 33.2979022
MF(7X7) 32.9695217 32.8471572 32.7100682 32.6009999 32.4682302
AMF(3X3) 48.1294076 47.9271258 47.8820319 47.6196082 47.5326201
AMF(5X5) 50.4428487 50.3663497 50.3654422 50.3592320 50.2910668
AMF(7X7) 52.5917922 52.6446843 52.4792140 52.6076153 52.5330542
HMF(3X3) 54.3756534 54.0961321 53.9315379 53.4357718 53.3958626
HMF(5X5) 50.3243891 50.1197064 50.0303064 49.8576033 49.9390938
HMF(7X7) 49.5009757 49.3812222 49.3131418 49.3457438 49.2632314
MSE
10% 20% 30% 40% 50%
MF(3X3) 14.95 16.22 17.51 18.85 19.96
MF(5X5) 26.14 27.30 28.40 29.59 30.67
MF(7X7) 33.08 34.02 35.11 36.01 37.12
AMF(3X3) 1.01 1.06 1.07 1.13 1.16
AMF(5X5) 0.59 0.60 0.60 0.60 0.61
AMF(7X7) 0.36 0.36 0.37 0.36 0.37
HMF(3X3) 0.24 0.26 0.27 0.30 0.30
HMF(5X5) 0.61 0.64 0.65 0.68 0.66
HMF(7X7) 0.74 0.76 0.77 0.76 0.78
PSNR
Filter 10% 20% 30% 40% 50%
MF(3X3) 36.9913360 36.5900180 36.2373256 35.8868217 35.5897711
MF(5X5) 35.1154491 34.8868072 34.6625909 34.4302155 34.2090733
MF(7X7) 33.9526666 33.7588404 33.6121715 33.4269664 33.2847459
AMF(3X3) 50.5872438 50.3325321 50.0749678 50.2173279 49.9733784
AMF(5X5) 53.5392232 53.3117072 53.4536137 52.7637093 52.5653382
AMF(7X7) 56.0400995 55.8899194 55.2643231 55.4558080 55.5127694
HMF(3X3) 54.6542633 54.3714687 54.2928820 53.5244923 53.5879165
HMF(5X5) 50.4687875 50.2620155 50.4810942 50.0223195 49.9777086
HMF(7X7) 49.3300257 49.1765595 48.9795156 49.1150336 48.8265158
MSE
10% 20% 30% 40% 50%
MF(3X3) 13.10 14.37 15.59 16.90 18.09
MF(5X5) 20.18 21.27 22.40 23.63 24.86
MF(7X7) 26.38 27.58 28.53 29.77 30.76
AMF(3X3) 0.57 0.61 0.64 0.62 0.66
AMF(5X5) 0.29 0.31 0.30 0.35 0.36
AMF(7X7) 0.16 0.17 0.20 0.19 0.18
HMF(3X3) 0.22 0.24 0.24 0.29 0.29
HMF(5X5) 0.59 0.62 0.59 0.65 0.66
HMF(7X7) 0.76 0.79 0.83 0.80 0.86
Chapter 8
Conclusion
In this project, we analyze the images that are corrupted with high density of impulse
noises based on different PSNR and MSE values. Adaptive filtering is an improved filtering
technique as compare to median filter in which the filtering is applied only to corrupted
pixels in the image while the uncorrupted pixels are left unchanged. The Adaptive filtering
approach is used to reduce the number of noisy pixels during filtering. The advantage of
Adaptive filter is that it is retaining the edge information in the case of high density impulse
noises. The Adaptive filter is found to be retaining finer details in the image and the images
restored are with an improved visual quality. The detail preservation ability of the adaptive
filter makes it suitable for medical image denoising, where also detail preservation is an
important issue.
The edges and fine details of the image are preserved by using the hybrid median
filter. The hybrid median filters have some of the advantages in image processing. For
repeated application the hybrid median filter does not excessively smooth image details,
Edge treating is possible, hybrid median filter preserves edges better than a median filter,
preserves brightness difference, simple to understand.
From the simulation result of PSNR and MSE, I have found that after combining
the adaptive median filter and hybrid median filter, image denoising is enhanced. It
produces better result. However for adaptive median filter it is found that for Smax=3 and
Salt-pepper noise density=10%, image denoising is better as compared to standard median
filter. The higher the PSNR value, the higher will be the quality of the image. Also, lower
the value of MSE, higher will be the quality of the image.
Chapter 9
Scope of future work
In Future the adaptive algorithm can be improved for removing the image noise
completely without visible distortion. The main techniques involved for this improvement
are: - (1) adaptive noise detection, (2) non-linear filter. For this adaptive processing, three
parameters with MSE, local background and PSNR can further improve. The PSNR and
MSE can be dynamically modified according to local image features. Furthermore, the
improved adaptive filter can be very appropriate for a VLSI chip implementation in real-
time systems. Therefore, this adaptive approach can be able to provide better performance
in video noise reduction and morphological operations in real-time applications
Appendix
References
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Appendix B: Screenshots
Appendix C: SOFTWARE AND HARDWARE
SOFTWARE
Application Software: MATLAB
Programming Language: MATLAB 7.9.0 (R2009b)
HARDWARE
Processor: Intel Core i5 CPU
Installed Memory (RAM): 4.00GB
System Type: 64-bit Operating System
Hard Disk: 1TB
Appendix D: Application Setup