digital image processing -...

Introduction

Impulse noise removal with adaptive median filter based on homogeneity level information

1

Chapter 1

DIGITAL IMAGE PROCESSING

1. Introduction

The aim of digital image processing is to improve the potential

information for human interpretation and processing image for storage

transmission and representation for autonomous machine perception.

Digital images are often corrupted by impulse noise in transmission error,

malfunctioning of pixel elements in the camera, sensor’s faulty memory

locations, and timing error in the Analog to Digital conversion. The

different types of noise occur during image processing and they affect the

image and degrade the quality of the image. The different type of noise

are Additive White Gaussian Noise, Rayleigh noise impulse noise.

Different types of noise corrupt an image during the process of

acquisition, transmission, and reception, and storage and retrieval. Then

the two type of impulse noise are salt and pepper noise and the random

valued noise [119-122][150] [151]. For image corrupted by salt and

pepper noise (Random valued noise) the noisy pixels can take only the

maximum and minimum values (Random value) in the dynamic range. A

lot of research works have been done on the restoration of images

corrupted by impulse noise. Image deploring and image de noising are the

two sub areas of image restoration. For instance the nonlinear digital

filters reviewed in [1 ]. The median filter was once the most popular non-

linear filtering technique for removing impulse noise, because of its good

de noising power [2] and computational efficiency [6]. However the noise

level over 60% some details and edges of the original image are smeared

by the filter [2].The median filter is a nonlinear operator that arranges the

Introduction


2

pixels in a local window according to the size of their intensity values and

replaces the value of the pixel in the result image by the middle value in

this order.

1.1 Fundamentals of Digital Image Processing.

The area image processing the two principal applications are the

improvement of pictorial information for human interpretations and

processing of image data for storage, transmission and representation for

autonomous machine perception. The process of receiving and analyzing

visual information by digital computer’s is called digital image

processing [1 ].An image may be described as a two dimensional function

f(p, q) where p and q are spatial coordinates. Amplitude of f at any pair of

co-ordinates (p, q) is called the intensity or gray level of the image at that

point. When special co-ordinates and amplitude values are all finite,

discrete quantities the image is called digital image [2].The image

composed of a finite number of elements each of which has a particular

location and values. These elements are related to as picture elements.

That means the elements of image are pixels. Pixel is the term most

widely used to denote the elements of digital image. To emulate human

vision, including some analysis. Performing some mechanical operation

(robot motion) is the goal of the Image processing. In the figure [1.1]

typical blocks diagram of image processing system. This consists of the

center part is the computer system, one image acquisition, image

processing software, storage devices, transmitters and display devices.

Digital image processing has many advantages over analog image

processing. It allows a much wider range of algorithms to be applied to

the input data, and can avoid problems such as the build-up of noise and

signal distortion during processing.

Introduction

Figure 1.1 Typical Image Processing System.

The different functions in the image processing are image

acquisition, image enhancement, image restoration, Colour image

processing [4], multi resolution processing, compression, morphological

processing, segmentation, restoration and description and object

recognition.

The image processing system starts with image acquisition. Two

factors are required to acquire a digital image. First is a sensor that is a

physical device that is sensitive to the energy radiated by the object has to

be imaged. The second part is called Digitizer is used to converting the

output of the sensing image to digital form. For example, in a digital

camera the sensor produces an electrical output proportional to light

intensity. During the process of image acquisition noise are formed and

the digitizer converts the output into digital data. Image enhancement is

among the simplest and most appealing area of Digital Image Processing

[114-120]. Basically the idea behind enhancement techniques is to bring

out detail that is obscured or simply to highlight certain time of intent in

an image. A familiar example of enhancement is when we increase the


3

Introduction


4

contrast of an image it looks better. One of the major areas of the Image

Processing is image enhancement on the other hand image restoration is

very much objective[107][109]. The restoration techniques are based on

mathematical and statistical models of image degradation. Denoising [2]

and deploring tasks come under this category.

Image restoration and image filtering are another major parts of the

image processing. Image restoration is different from image

enhancement, that is the latter is designed to emphasize features of the

image that make the image more pleasing to the observer, but not

necessary to produce realistic data from a scientific point of view. In the

image filtering, the image contains many types of noise, and removing

this noise from the image.

The colour image processing is divided into two major areas called

full colour and pseudo colour processing. In the full colour processing,

the image is acquired with full colour sensor such as a colour TV, camera

or colour scanner. But in the pseudo colour processing, the problem is of

assigning a colour to a particular monochrome intensity or range of

intensities. The basic colours in the colour processing are Blue, Green

and Red.

Wavelets are the foundation for representing images in various

degrees of resolution. Compression is the process of reducing the size of

the digital image. But the morphological processing deals with tools for

extracting image components that are useful in the representation and

description of shape. The process segmentation means regions should be

uniform and homogeneous with respect to some characteristics such as

intensity value, colour or texture. At that time the region interiors should

Introduction


5

be simple and without holes. Another property is boundaries of each

segment should be simple, not ragged and must be spatially accurate.

Then the representation and description almost always follow the output

of a segmentation stage, which usually is raw pixel date, constituting

either the boundary of a region or all the points in the region itself. The

last reorganization is the process that assigns a label to an object based on

its descriptors.

1.2 Image Noise.

In digital images, noise arise during the time of image acquisition

or transmission. Then the performance of imaging sensors is affected by a

variety of factors, such as environmental conditions during image

acquisition and the quality of the sensing elements themselves. At the

time of image acquisition with a charge coupled device [CCD], the light

level and sensor temperature are the major factors affecting the amount of

noise in the resulting image. Then the noise in an image is the result of

errors in the image acquisition process that result is the pixel value of the

image does not reflect the true intensities of real picture, over to noise,

the image is represented as grainy rough, molted or snowy appearance.

The magnitude of image noise can vary from almost gradual speaks on a

digital photograph to optical radio astronomical images that are complex

noise. The second fact in the form of noise is the transmission of data in

the image is corrupted due to interference in the channel used for

transmission. For example an image transmitted using a wireless network

might be corrupted as a result of lightning or other atmosphere

disturbance.

Introduction

In digital image the noise may come from various sources. In the

acquisition process the optical signal is converted in to Electrical signal

and converts into digital signals and at the processing time by which the

noise is introduced in digital image. Each step in the conversion process

in experiences fluctuations caused by natural phenomena, and each of this

steps adds a random value to the resulting intensity to a given pixel.

f(x,y)


6

Degradation Restoration Noise η

Restored image f̂ (x, y)G (x,y)

Degradation function H

+ Restoration Filter

Figure 1.2 Model of the Image Degradation / Restoration Process

The above figure shows the image Degradation / Restoration

process. An input image f(x,y) is degraded by the degradation function H

on it. At that time the additive noise ƞ is added to the image f(x,y) and

produce a degraded image G(x,y) .After the restoration process we get the

original image . f̂ (x, y)

1.2.1 Noise Models

There are different types of noise in the images.

∗ Gaussian Noise

∗ Rayleigh Noise

∗ Erlang (Gama) Noise

∗ Exponential Noise

∗ Impulse Noise ∗ Speckle Noise

Introduction

1.2.1.1 Gaussian Noise.

Gaussian noise is one type of statistical noise. It is evenly

distributed over the signal[17][135]. The Gaussian moves is also called

the normal noise and it is a major part of read noise of an image sensor,

that is of the constant noise level, in dark area of the image. The

probability density function (PDF) of Gaussian noise is equal to that of

the normal distribution and also known as Gaussian distribution. It is

usually used as additive white noise to give additive white Gaussian noise

(AWGN).

Then PDF of Gaussian noise is

2 2(z ) / 21P(z) e2

− −μ σ=πσ

1.1

Where z represents gray level,μ is the mean of average value of z and σ is

its standard deviation.

(a) σ= 10 (b) σ= 25

Figure 1.3 Images of Barbara with AGWN


7

Introduction

1.2.1.2 Rayleigh Noise

A Rayleigh noise distribution is often observed when the overall

magnitude of a vector is related to its directional components that is

where Rayleigh distribution naturally arises is when wind velocity is

analyzed into its orthogonal two dimensional vector components.

The PDF of Rayleigh noise is

2(z a ) / b2 (z a)e for z aP(z) b

0 fo

− −⎧

r z a

− ≥⎪= ⎨⎪ <⎩

1.2

Figure1.4 Rayleigh Noise

1.2.1.3 Salt and Pepper Noise.

When an analog image signal is transmitted in a linear dispersive

channel the image edges (step like or pulse like signal) get blurred [123]

and the image signal gets contaminate with additive white Gaussian noise

since no practical channel is noise free. If the channel is so poor that the

noise variance is high enough to make the signal excurse to very high

negative or positive value when the thresholding operation at the front

end of the receiver will contribute saturated min and max value. As a

result, the image contains some black and white spot. This type of noise


8

Introduction

is called salt and pepper noise. At the same time the image contain the

dark is called pepper and the image contain the bright pixel is known as

salt. There for the analog image signal is transmitted and the signal gets

corrupted with Additive White Gaussian Noise and Salt and Pepper as

well. Then there is an effect of mixed noise.

Then the PDF of salt and pepper noise is

x

y

P for z = xP(z) P for z = y

0 otherwise

⎧⎪= ⎨⎪⎩

1.3

Figure 1.5.Salt and Pepper Noise

1.2.1.4 Speckle Noise.

Speckle noise is granular noise that inherently exists in and

degrades the quality of the active radar and Synthetic Aperture Radar

(SAR) images. In some Biomedical applications like Ultrasonic Imaging

and a few emergency applications like Synthetic Aperture Radar (SAR)

imaging such noise is encountered. In the speckle noise, if the image

pixel magnitude is high then the noise is also high. So speckle noise is

dependant to the signal. The noise is multiplicative because initially a

transmitting system transmits a signal to the object and the reflected

Impulse noise removal with adaptive median filter based on homogeneity level information 9

Introduction

signal is recorded. When the signal is transmitted, the signal may get

contaminated with additive noise in the channel. Due to varying

reflectance of the surface of the object, the reflected signal magnitude

varies. So also the noise varies since the noise is also reflected by surface

of the object. Noise magnitude is there for higher when the signal

magnitude is higher so we say that the speckle noise is multiplicative in

next area. But at the same time speckle is random, deterministic,

interference pattern is an image formed with coherent radiation of a

medium containing many sub resolution strategies. Speckle noise is

eliminated using adaptive and non-adaptive filters.

Let a digital image f(x,y), after being corrupted with multiplicative

noise, be represented as P(x,y). Then, the noisy image P(x,y) is

mathematically represented as

P(x,y) = f (x,y) + η (x,y)f (x,y) 1.5

P(x,y) = [1 + η (x,y)] f (x,y) 1.6

Where η (t) is a random variable

Figure1.6SpeckleNoise


10

Introduction


11

1.3 Literature Review.

One of the major problems facing in the image processing is noise

removal. There are many filtering methods available. Efficient

suppression of noise in an image is a very important issue. De-noising

finds extensive applications in many fields of image processing.

Conventional technique of image de noising using nonlinear [7] and

linear filters have already been reported and sufficient literature is

available in the area. Recently various nonlinear and adaptive filters have

been suggested for the purpose. The main objectives of these methods are

to reduce noise and to retain, as far as possible, and the edges and fine

details of the original image in the restored image as well. However both

the objectives conflict each other and the reported schemes are not able to

perform satisfactory in both aspects. Hence, still various research workers

are actively engaged in modifying the existing filtering schemes using

latest signal processing techniques.

1.3.1 Filters for Removal of Additive Noise.

Traditionally, AWGN is suppressed using linear spatial domain

filters such as Wiener filters [29][30], Mean filter [142], Average

filters[118] etc. The traditional linear techniques are very simple in

implementation but they suffer from disadvantages of blurring effect [18].

They also don’t perform well in the presence of signal dependent noise.

To overcome this problem the nonlinear filters are proposed. Some major

types of nonlinear mean filters are Harmonic mean, Geometric mean.

Contra harmonic mean, LP mean proposed by Pitaset al[6] are found to

be good in both suppressing the impulse noise [149-168] and preserving

Introduction


12

edges. J.S Lee proposed one good edge preserving [23] filter that is Lee

filter [31]. For image corrupted by Gaussian noise least square’s methods

based on edge preserving regulations functional [24-27] have been used

successfully to preserve the edge and the details in the images. These

methods fail in the presence of impulse noise because the noise is heavy

tailed. More over the restoration will alter basically all pixels in the

image, including those that are not corrupted by the impulse noise.

Recently, non-smooth data-fidelity terms have been used along with

edge-preserving regularization to deal with impulse noise. Anisotropic

diffusion [43] [44] is also a powerful filter where local image variation is

measured at every pixel and every point, values are averaged from

neighbor hoods whose size and shape depend on local variation. The

basic principle of these methods is numbers of iterations. If more iteration

are used it may lead to instability, in addition to edges noise becomes

prominent. Rudin et al[42] proposed Total Variation (TV) filter which is

also iterative in nature. In the later age of research simple and non-

iterative scheme of edge preserving and smoothing filters are proposed.

One of them is Bilateral filters [41]. Bilatral filter works on the principle

of geometric closeness and photometric similarity of gray levels or

colours. Many variants of Bilateral filters are proposed in literature that

exhibit better performance under high noise conditions [39][40].

A filter named Non-Local means (NL – means)[38] averages

similar image pixels defined according to their local intensity. Similarity.

based on robust statistics [63][79][133] a number of filters are proposed.

Rabei [37] proposed a simple blind denoising[137] filter based on the

theory of robust statistics. Robust statistics addresses the problem of

estimation when the idealized assumptions about a system are

Introduction


13

occasionally violated. Another denoising method based on the Bi-Weight

Mid-Regression is proposed by Hou et al[36] is found to be effective in

suppressing Additive White Gaussian Noise (AWGN). Kernel regression

is a non parametric class of regression method used for image denoising.

Many filters based on fuzzy logic are developed for suppression of

additive noise. S.Meher et al[20] proposed fuzzy filters for suppression of

AWGN. The first stage compute a fuzzy derivatives and second stage

uses these fuzzy derivatives to perform fuzzy smoothing by weighting the

contributions of neighbouring pixel values[69][70]71]. By applying

iteratively the filter effectively reduces high noise[53][54].

Various fuzzy logic filters are applicable. One of the new efficient

Fuzzy Based Decision Algorithms (FBDA) for the restoration of image

that are corrupted with high density of impulse noises. FBDA is a Fuzzy

based [34] filter in which the filtering is applied only to corrupted pixel in

the image while the uncorrupted pixels are left unchanged.

Now a day’s Wavelet transforms [9][11][33] is employed as a

powerful tool for image denoising. Image denoise using wavelet

technique is effective because of its ability to capture most of the energy

of a signal in a few significant transform coefficients, when natural image

is corrupted with Gaussian noise. The wavelet transformation is mainly

Discrete Wavelet transformation and Stationery or Continuous Wavelet

transformation. In discrete wavelet transformation different types of

wavelets are used for image filtering. The different types of wavelets are ,

Mexican hat function, Mexican hat Wavelet, Biorthogonal, Symlets,

Morlet[13][14][8] etc.

Introduction


14

1.3.2 Impulsive Noise Removal Filters.

An impulsive noise of low and moderate noise densities can be

removed easily by simple denoising schemes available in the literature. A

simple median filter [58][31] works very nicely for denoising impulsive

noise of low density and is easy to implement. But the cost paid for it is

distorts edges and fine details of an image. The distortion increases as the

filtering window size is increased to suppress high density noise. Median

Filter is a non linear filtering technique widely used for removal of

impulse noise[3][53][72][88]. Despite its effectiveness in smoothing

noise the median filter tends to remove fine details when it is applied to

an image uniformly. But some specialized median filters such as

Weighted Median Filter[58] and Recursive Weighted Median Filter

RWMF [47-49][51], Center Weighted Median Filter[21][50][101] are

proposed in literature to improve the performance of the median filter by

giving more weight to some selected pixels in the filtering window. But

they are still implemented uniformly across an image without considering

whether the current pixel is noisy or not. Additionally they prove to edge

preserving.[24-27] in cases where the noise density is high. As a result

their effectiveness in noise suppression is often at the expense of blurred

and distorted image features.

In the Adaptive Median Filter [19][110][111][112]the noise

candidates are first identified and then noise candidates are selectively

restored using an objective function data fidelity term and an edge

preserving regularization term. Since the edges are preserved for the

noise candidates and no changes are made to the other pixels.The

performance of combined approach much better than the other methods.

Introduction


15

Conventional median filtering approach applies the median

operation everywhere without considering whether it is uncorrupted or

not[65]. As a result, image quality degrades severely. An initiative

solution to overcome this problem is to implement an impulse noise

detection mechanism prior to filtering ,hence only those pixels identified

as corrupted would undergo the filtering process.While those identified as

uncorrupted would remain intact[124]. By incorporating such noise

detection mechanism or intelligence into the median filtering frame work,

so called Switching Median Filters[78][92] have shown significant

performance improvement.

The most popular approaches for dealing with such noise have

been based on median filtering on the rich class of order statistics filters

[56][93] that have emerged from the study of median filters. Recently

variations on the median filtering scheme have been shown under various

specific signal, noise models, to deliver improved performance relative to

the corresponding traditional methods. Examples of some type of

modified median filters have been proposed are Minimum – Maximum

Exclusive Mean Filter [77] (MMEM), Florencio’s [58] Conditional

Median Filter (CMF)[64], Signal Dependent Rank Order Means

(SDROM) filter [99]. The filters have all demonstrated excellent

performance but at the price of significant computational complexity. The

latest Pre Scanned Min- Max Center Weighted (PMCW) filter proposed

by Z Wang [154]and Decision Based Filter [58] proposal by D.A

Florencio et al.[58] in these methods the filtering operations adapts to the

local properties and structures in the image. In the decision based filtering

[140][150] for example image pixel are first classified as corrupted and

uncorrupted and then passed through the median and identify filters

Introduction


16

respectively. The main issue of the decision based filter in building a

decision rule or a noise measure [106 – 109] that can discriminate the

uncorrupted pixel from the corrupted ones as precisely as possible.

One of the highly efficient and high performance non linear and

non-iterative multi dimensional filters proposed by P.S Windyga[55] is

the Peak and Valley filter. In this filter identifies noisy pixels by

inspecting their neighborhood and then replaces this value with the most

conservative once out of the values of their neighbors. In this method no

new values are introduced into the neighborhood and the histogram

distribution range is conserved. The main benefit of the Peak and Valley

filter is its speed and the simplicity. Which makes it very attractive for

real time application. A modified Peak and Valley filter, detail preserving

impulsive noise [94][38] removal scheme has also been proposed by N

Alajlan et al [54]. This filter provides better detail preservation

performance, but it is slower than the original Peak and Valley filter.

In MMEM filter [80]; where the pixels that have values close to the

minimum and maximum in a filter window are discarded, and the average

of remaining pixels in the window is computed to estimated pixel. To

find the difference between central pixel and average exceeds a threshold,

the central pixel is replaced by average; otherwise, no change. The

efficiency of this filter depends on the selection of threshold value.

Another one type of simple switching filter is Adaptive Centre Weighted

Median(ACWM), [66] proposed by T Chen et al, [52][81] Centre

Weighted Median (CWM)[64] has been used to detect noisy pixels in the

first stage. The main importance is to utilize the centre weighted

median[45-48] filters that have varied centre weights to define a more

general operator which realize the impulse detection by using the

Introduction


17

differences defined between the output of CWM filters and the current

pixels of concern. The ultimate output is switched between the current

pixels and the median itself. While still using a simple thresholding

operation, the proposed filter yields superior results to other switching

schemes in denoising both types of impulses with different noise ratios.

But its estimation efficiency is poor. Florencio et al[58] proposed

decision measure, based on a second order statistic called normalized

deviation.

One of another type of adaptive median filter proposed by H.

Hwang et al[80][62][59]. These have variable window size for removal

of impulses while preserving sharpness. One type of this is called Rank

Order Based Adaptive Median Filter (RAMF) is based on a test for the

presence of impulse in the central pixel, itself followed by the test for the

presence of residual impulses in the median filter output. The second one

called the impulse size based adaptive media filter is based on the

detection of the size of the impulse noise.

The Signal Dependent Rank Ordered Mean Filter [85] is a

switching mean filter that exploits rank order information for impulse

noise detection and removal. The structure of this filter is similar to that

of the Switching Median Filter[74][96][138]except that the median filter

is replaced with a rank ordered mean of its surrounding pixels. This filter

has been shown to exhibit better noise suppression [132] and detail

preservation performance than some conventional and state of the art

impulse noise cancellation filters for both gray scale [85] and colour

images[132- 137]. T. Chen et al[73] propose a new type of filter, named

on the Tri State Median Filter, it is an improved Switching Median Filter

that are constructed by including as appropriate number of Center-

Introduction


18

Weighted Median[50] filters into the basic Switching Median Filters

structure. These filters exhibit better performance than the standard and

the switching median filters at the expense of increased computational

complexity.

S. Zhang et al[60] proposed a new switching median filter for a

new impulse noised detection technique is based on the minimum

absolute value of four convolutions obtained using one dimensional

Laplacin operator. It provides better performance than many of the

existing switching median filters with comparable computational

complexity. Z Wang et al[89] has proposed a Progressive Switching

Median filter PSM [72] for the removal of impulse noise from highly

corrupted images where both the impulse detector and the noise filter are

applied progressively in iterative manner [97]. The noise pixels processed

in the current iteration are used to help the process of the other pixels in

the subsequent iterations. A main advantage of such a method is that

same impulse pixels located in the middle of large noise blotches can also

be properly detected and filtered. Therefore, better restoration results are

expected, especially for the cases where the images are highly corrupted.

Raymond et al [121] Chan et al[67] proposed another type of

median filter for removing noise. It contains two phases that are first

identifying pixels which are likely to be contaminated by noise. Then in

the second phase, the image is restored using specialized regulation

method that applies only to those selected noise candidates. In terms of

edge preservation and noise suppression in restored images show a

significant improvement compared to those restored by using non-linear

filters or regularization method. In this method it removes almost 90%

salt and pepper noise from an image.

Introduction


19

Early developed switching median filters are commonly found

being non adaptive to a given, but unknown, noise density and prone to

yielding pixel misclassifications especially at higher noise density

interference. To address this issue, the Noise Adaptive Soft Switching

Median[60] (NASM) filter is proposed by H L Eng et al[61] which

consist of a three level hierarchical soft switching noise detection process.

The NASM achieves a fairly robust performance in removing impulse

noise, while preserving signal details across a wide range of noise

densities, ranging from 10% to 50%. However, for those corrupted

images with noise density greater than 50%, the quality of the recovered

image become significantly degraded, due to the sharply increased

number of misclassified pixel.

An another type of filter to remove impulse noise from highly

corrupted image named the Adaptive Two Pass Rank Order Filter was

developed by X.Xuet al [74] . Between the passes of filtering, an adaptive

process detects irregularities in the special distribution of the estimated

noise and selectively replaces some pixels changed by the first pass with

their original values. These pixels are kept unchanged during the second

phase filtering. Consequently the reconstructed image maintains a smaller

amount of noise and high degree of fidelity.

Basically all filters use the histogram information of the input

image. In image restoration using parameter adaptive fuzzy filter and an

adaptive fuzzy filter[76][128] for restoring highly corrupted image by

histogram estimation [68][71], the histogram information of the input

image is used to determine the parameters of the membership functions of

an adaptive fuzzy filter [84][86]. An adaptive vector filter exploring

Introduction


20

histogram information is also proposed for the remaking of colour image

[130][131].

Another method for impulse noise reduction from images using

fuzzy cellular automata developed for impulse noise reduction from

corrupted images plays an important role in image processing. This

problem will also affect on image segmentation, object detection, edge

detection [43], and compression. Generally median filters or nonlinear

filters have been used for noise reduction but these methods will destroy

the natural texture and important information in the image like edges. So

he developed a filter named Fuzzy Cellular Automata (FCA) has two

steps [153]. In the first step, based on statistical information, noisy pixels

are detected by Cellular Automata (CA) then using this information the

noisy pixel will change by FCA. Regularly FCA is used for system with

simple components where the behaviour of each component will be

defined and updated based on its neighbours.

Pei-Eng-Ng et al[92] proposed an algorithm named Boundary

Discriminative Noise Detection (BDND) algorithm, which is a highly

accurate noise detection algorithm. With the help of it, an image

corrupted up to 70% noise density may be restored quite efficiently. But

there is no remarkable improvement in the high noise density. A variation

approach noise by M. Nikolva[66] is an edge and details preserving

restoration technique to eliminate impulse noise efficiently. It uses a non

smooth data filtering together with edge preserving regulation functions.

A combination of this variational method with an impulse detector has

also been presented in an interactive procedure for removing Random

Valued Impulse noise[121] [98].

Introduction


21

Now a day’s many researches proposed methods related to random

valued and salt and pepper noise removal. V.Crnojevic et al[100]

proposed a new method advanced impulse detection based on pixel wise

(MAD) [122] is a modification of absolute deviation from median (MAD)

MAD method is used to estimate the presence of image details. An

improved method of the algorithm is impulse noise filter with adaptive

MAD based threshold, proposed by Vladimir et al[130]. In this method,

pixel to pixel based threshold value can be changed on the basis of local

statistics. Since it is a non-iterative algorithm, its execution time quite

reasonable and less than required by PWMAD. The efficiency of MAD

and PWMAD is quite good under low density. But both of them fail in

high density.

Another filter developed for the impulse noise removal is

Adaptive. In this based on high impulse noise detection and reduction. In

this method, a two stage process was executed. The main objective of the

method is to consider a particular digital image as input and make the

preprocessing to remove the impulsive noise content by employing

suitable adaptive nonlinear filter after identifying the impulsive noise of

overall image. In this proposed method, first step is to identify the type

of noise present in the image as additive, multiplicative or impulsive by

the analysis of local histogram. Second section contains denoising the

impulsive noise by employing adaptive nonlinear filter technique which

comprises a process of adaptive noise identification of a corrupt pixel

and filtering it by employing adaptive nonlinear filter[42].

T Chen[81] and H.R have developed a scheme for adaptive

impulse detection using CWM (AID-CWM) filter. It suppressed SPN as

well as RVIN. Its filter performance is compared with standard filters and

Introduction


22

the PSNR values are shown in Table 1.1 The input image is bridge with

20% noise.

Filter RVIN 20% noise SPN20% noise

MED 31.33 31.42

CWM 32.42 30.39

ROM 34.75 36.55

TSM 34.13 31.84

AID-CWM 34.76 36.54

NASM 27.63 28.41

BDND 28.63 29.41

FCA 26.61 27.11

Table 1.1Filter Performances in PSNR.

It may be seen that the performance of ROM filter is comparable to

that of the AID-CWM filter. There for such an adaptive decision directed

filtering scheme may not be appreciated.

At present, a number of algorithms are developed for denoising the

impulse noise. Different types of noise detection and correction methods

are developed on the basis of Wavelet, Fuzzy based, Neural network

based etc[134]. Neural and Fuzzy are very capable for noise removal.

But the problem is the time taken to retain edges and fine details of an

image at high noise densities even though they have high computational

complexities.

Introduction


23

There are several outstanding questions about image filtering

method to remove random valued impulse noise[103][105] and salt and

pepper noise. Hence it may be concluded that there is enough scope to

develop better filtering scheme with very low complexity and very high

noise removal with the preservation of edge and fine details in images.

1.4 Problem Statement.

In the field of image processing noise suppression is one of the

major factors. It contains the retaining of the fine details and edge

preservation. Many filtering algorithm has low computational complexity

so that they can filter noise in short time, and hence will find themselves

suitable for online and real time applications.

The major challenging factor of our doctoral research work is to

develop an efficient non-linear filter to remove impulse noise. It has very

high efficiency, and yielding extremely low distortion in wide range of

noise densities with low run time overhead and less computational

complexity.It has high performance and keep while retaining edges and

fine details of an image.

This research work mainly focuses on removal of salt and pepper

noise with the help of Adaptive Median Filter Based on Homogeneity

Level Information. Many types of filters are developed by the removal of

salt and pepper noise. The comparison of different types of filters is also

included such as Fuzzy and Discrete Wavelet Transformation and

Stationary Wavelet Transformation [9]. So to develop a new Adaptive

Median Filter Based on Homogeneity Level Information and compare it

with the advantages of the other filters.

Introduction

1.5 Basics of Spatial Domain Filtering.

Let f(x,y), represent an original noise free digital image with P

rows and Q columns with a spatial indices x and y ranging from 0 to P-1

and 0 to Q-1 respectively. It is denoted as

f (0,0) ... f (0,Q 1)f (x,y) ... ... ....

f (P 1,0) ... f (P 1)(Q 1)

−⎡ ⎤⎢ ⎥= ⎢ ⎥⎢ ⎥− −⎣ ⎦−

1.7

A noisy image is represented as g(x,y) with same dimension and

final image f(x,y). Let us define W (k,l) as a window or mask or kernel

that is k, l∈�

k and l are limited in the range of

(Pw 1) Pw 1k2 2− −

− ≤ ≤ and

(Qw 1) Qw 12 2

− −− ≤ ≤l

Where Pw and Qw represent the number of rows and columns in

the window. If it is 3×3, then the range of k and l is given by

and respectively. A noisy sub-image g

1 k 1− ≤ ≤ +

) 1

1 1− ≤ ≤ +l k,l (x, y) for (3×3) with

g(x,y) as a centre pixel is given by gk,l (x+k, y +l) for 1 (k,− ≤ ≤ +l . It is

usually expressed in matrix form

k,

g(x 1,y 1) g(x 1,y) g(x 1,y 1g (x,y) g(x,y 1) g(x,y) g(x,y 1)

g(x 1,y 1) g(x 1,y) g(x 1,y 1)

− − − − +⎡ ⎤⎢ ⎥= − +⎢ ⎥⎢ ⎥+ − + + +⎣ ⎦

l

1.8


24

Introduction

The

help of th

(x,y) pixe

pixel is r

operation

filtering w

en filtering

he pre de

els. The o

eplaced b

the center

window.

g can be

efined rela

one type o

by median

r pixel is r

executed w

ationships

of operatio

n of sub im

replaced b

with the h

s to execu

on such a

mage pixe

by the mea

help of this

ute the op

as median

el and sim

an value o

s mask. W

peration o

filter the

milarly the

of the pixe

With the

on each

center

e mean

el in the

Aft

image

ter the op

Impulse no

f̂ (x

f̂ (x

1.6 Imag

The

as well ob

be observ

complicat

can be ex

The

image. Th

Squared E

Ratio (PS

used like

(IEF) and

The

main vari

noisy ima

ise removal

x, y) that i

perations p

is the nois

performed

se free ima

d in the im

age.

mage we get a noiise free

x, y) = ∑∑l

k,k

g (x, y∑ l y) W(k,× l)l 1.9

ge Metriics.

e quality a

bjective e

ved by hu

ted that is

ecuted wit

and perfor

evaluation

uman exp

s not yet m

th the help

rmance of

. For subj

pert. The h

modeled p

p of objec

f the imag

jective ev

human vi

properly. S

tive evalu

ge is verifi

valuation t

isual syste

So the per

uation.

ied by sub

the image

em (HVS

rformance

bjective

has to

) is so

e check

ere are di

he differe

Error (RM

SNR) etc,

Univers

d Executio

ifferent ty

ent types

MSE),Mea

but now

sal Qualit

n Time (T

ype matric

are Mean

an Absolu

w some a

ty Index

TE)[169][1

ces for ob

n Squared

ute Error (

additional

(UQI) Im

170].

bjective e

Error (M

(MAE),Pe

objective

mage Enha

evaluation

MSE),Root

eak Signal

evaluatio

ancement

n of an

t Mean

l Noise

ons are

Factor

e perform

iables. Th

age repres

mance calc

ey are ori

sented by

culation ca

iginal nois

g(x,y) an

an be don

se free im

d filtered

ne with th

mage repre

image rep

he help of

sented by

presented b

f three

y f(x,y),

by

with adaptivve median fil

25ter based onn homogeneity level information

Introduction

f̂ (x,y),these are the discrete special co-ordinates of the digital

image. Let P and Q represents the number of rows and columns or the

mask matrices. So the matrix contains P x Q pixels and the values of

x = 1, 2,..…P and y = 1, 2, …. Q

So the MSE and RMSE is defined as

QP2

x 1 y 1

ˆ(f (x, y f (x,y)MSE

P Q= =

−=

×

∑∑

1.10

The RMSE = MSE

Then the PSNR is expressed in logarithmic scale, in dB. That is the

ratio of peak signal power to noise power. Since the MSE represents the

noise power and the peak signal power is unity in case of normalized

image signal, the image matrix PSNR is defined as

PSNR = 10 log 10 1 dB(MSE)

1.11

Recently more objective evaluations in the image filters are

formed. One of the methods is Universal Quality Index. The three major

factors in the Universal quality index are:

∗ Loss of correlation

∗ Luminance distortion

∗ Contrast distortion


Introduction

It is defined as

ˆ fff f2 2

2ˆ ˆf ff f

ˆ 22f fUQIˆf f

σ σ= ⋅ ⋅

σ σ σ + σ+

ˆ2

σ 1.12

Where M N

x 1 y 1

1fM N = =

=× ∑∑f (x,y) 1.13

M N

x 1 y 1

1f̂M N = =

=× ∑∑ f̂ (x, y) 1.14

M N2 2f

x 1 y 1

1 (f (x,y) f (x,y))MN 1 = =

σ = −− ∑∑

1.15

M N2f̂

x 1 y 1

1 ˆ ˆ(f (x,y) f (x,y))MN 1 = =

σ = −− ∑∑ 2 1.16

M N

ˆffx 1 y 1

1 ˆ ˆ(f (x,y) f (x,y))(f (x,y) f (x,y))MN 1 = =

σ = − −− ∑∑

1.17

Then UQI is a combination of three components. That are the correlation

coefficient between the original image f and the noise free image that

measure the degree of linear correlation between original image and noise

free image. The second component with a range of (0,1) measure the

closeness between the average luminance of original image f and noise

image . It has a maximum value of 1if and only if

f̂

f̂


27

f−

= f̂

The standard deviations of these two images σf and σ are also

regard as estimates of their contrast level ranges from 0 to1 and the

f̂

Introduction

optimum value of 1 is achieved only when σf=σ .Then σf̂ x and σy are the

standard deviation of two images are also regarded as estimates of their

contrast levels.

Image Enhancement Factor (IEF).

One of another objective evaluation of image quality is Image

Enhancement Factor. That is widely used. Let we want to calculate the

quality at different noise density indicates qualitatively the relative

quality improvement exhibited by a process (filter). The mathematical

representation of IEF is

2

2

g(x, y) f (x, y)IEF ˆ(f (x, y) f (x, y)

−=

−∑∑

1.18

Execution Time (TE)

Execution Time is like time complexity but in the filtering method

the time taken by a digital computing platform to execute the program

other than the operating system run on it.

Execution time mainly depends on the system performance when

the algorithm complexity is high, the time taken to the execution is also

high. But the algorithm complexity is low, the time taken to the execution

is also low. The low execution time filters are best for online application.

From this situation we concluded that the execution time is depended of

the platform. Some hardware platform contribution Node I, Node II,


28

Introduction


29

Node III presented in the table are taken for the computation for

TE. Then TE parameter value can be varied under different nodes

represented in table 1.2.

Hardware

platform Processor

Clock

GHz

Cache

(MB) RAM(GB) OS

Node I

Node II

Node III

Pentium D

Core i5

Core i7

1.8 GHz

2.3 GHz

2.3Ghz

3 Mb

3 MB

6 MB

4 GB

4 GB

4 GB

Win7

Win 7

Win7

Table1.2 Time Execution Factor of Processing

1.7 Noise Level Classification

For the development of filter, the noise level is one of the major

factors. The factors in the filtering method are the original image, the

noise added image and the noise removed image. So we can specify a

good image by the help of noise ratios in images. So the noise ratio is

variant, normally a good image with signal noise ratio 20 dB is better. If

the signal noise ratio is less than 10 dB the image quality in very much

poor. The Table 1.3 reports the noise ratio.

Introduction

Noise level Signal Noise Ratio( SNR)

Very low ≥ 30 dB

Low ≥ 20 dB

Medium ≥ 15 dB

High ≥ 10 dB

Very high ≥ 5 dB

Extremely High < 5 dB

Table 1. 3The Table Reports the Noise Ratios.


digital image processing -...

Documents