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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for the Removal of Impulse Noise”, Electronics & Communication Technology,Vol.

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fine details in a gray scale image”

[16.] Motwani m. et al., “Survey of image denoising techniques”,University of Nevada,

Reno,Dept. of Comp. Science & Engg.,Reno,2003

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