Report on image enhancement

8/12/2019 Report on image enhancement

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Colored Satellite Image Enhancement Using Wavelets And Threshold decomposition

CHAPTER 1

INTRODUCTION

Digital images have been widely used in a growing number of applications in the modern

information system The effort on edge enhancement has been focused mostly on improving the

visual perception of images that are unclear because of blur In general! the popular edge

enhancement filtering is carried out with the help of traditional filters "ut these filters do have

some problems! especially while enhancing a noisy image #oise removal and preservation of

useful us information are important aspects of image enhancement A wide variety of methods

have been proposed to solve the edge preserving and noise removal problem

$ainly focusing on the clarity of the image and the number of computations done for

enhancing the image! we developed a novel approach The edge enhancement done by smoothing

filters decreases the comple%ity and also increases the &uality of the image The basic aim of

edge enhancement is to modify the appearance of an image to ma'e it visually more attractive or

to improve the visibility of certain features specially the satellite images The edge enhancement

techni&ue enhances all high spatial fre&uency detail in an image! including edges! lines and

points of high gradients

In spite of all these efforts! none of the proposed operators are fully satisfactory in real

world applications They do not lead to satisfactory results when used as a means of identifying

locations at which to apply image sharpening The previous methods stated can wor' under

certain circumstances meanwhile( it is in accurate to use the method in case of low contrast

image or low resolution image

In this paper! the enhancement is applied through a framewor' of threshold

decomposition This has two advantages) it reduces the edge detection to a simple binary

process( and it ma'es the estimation of edge direction straightforward Edge detection and

direction estimation may be carried out by identifying simple patterns! which are closely related

to the *rewitt operators

Dept. Of ECE, MITSPage 1


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These detected edges were then sharpened by using some morphological filters"inary

morphological operations of dilation and erosion are used to increase the contrast in the region

and direction of the detected edges with the aid of a flat structuring element A summation is

applied over all levels in order to reconstruct the sharpened image

Another method was proposed lately on satellite image enhancement which proposed an

additional step by enhancing the brightness of the image before wor'ing on edge detection The

processes were composed of image brightness! edge detection and the standard deviation of the

image intensity performed by the *ea' Signal to #oise +atio ,*S#+-

Thesis is e%plained as follows)

Chapter . deals with the introduction and chapter / includes image enhancement

techni&ues The proposed method is e%plained with many details in chapter 0 Chapter 1 includes

results and analysis! conclusion and future scope are given in chapter 2



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CHAPTER 2

IMAGE ENHANCEMENT

2.1 INTRODUCTION:

Image enhancement is a process principally focuses on processing an image in such a

way that the processed image is more suitable than the original one for the specific application

The word specific has significance It gives a clue that the results of such an operation are highly

application dependentThe techni&ue falls in two categories on the basis of the domain they are

applied on These are the fre&uencyand spatialdomains The fre&uency domain methods wor's

with the 3ourier Transforms of the image The term spatial domain refers to the whole of pi%els

of which an image is composed of Spatial domain methods are procedures that operate directly

on the pi%els The process can be e%pressed as

g (x , y )=T[ f(x , y )] 44444444444 /.

Where f(x , y ) is the input image! g (x , y ) is the processed image! and T is an

operator on f defined over some neighborhood of (x , y ) A number of enhancement

techni&ues e%ist in the spatial domain Among these are histogram processing! enhancement

using arithmetic! and logical operations and filters

3or the study of each and every filter! we have considered the following algorithms for

implementation)

Mean Filter:

$ean filtering is simply the process of replacing each pi%el value in an image with the

mean ,average- value of its neighbors! including itself This is simply done using 050 'ernel

Median Filter:

The median is calculated by first sorting all the pi%el values from the surrounding

neighborhood in numerical order and then replacing the pi%el being considered with the middle

pi%el value This is also implemented using 050 'ernels



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Mode Filter:

$ode filtering simply involves the replacing of each pi%el value in an image by the mode

value of its neighbors! including itself This is also implemented by 050 'ernels

Circular Filter:

Circular filter is implemented using the product of original matri% and convolution mas'

provided A 252 'ernel is used here

Pra!idal Filter:

*yramidal filter is implemented using the product of the original matri% and convolution

mas' provided A 252 'ernel is used here

Cone Filter:

Cone filter is implemented using the product of original matri% and convolution mas'

provided A 252 'ernel is used here

2.2 HI"TOGRAM E#UA$I%ATION:

6istogram e&uali7ation is one of the well8'nown image enhancement techni&ue Itbecame a popular techni&ue for contrast enhancement because of its simplicity and

comparatively better performance on almost all types of images The operation of 6E is

performed by remapping the gray levels of the image based on the probability distribution of the

input gray levels It flattens and stretches the dynamic range of the image9s histogram and

resulting in overall contrast enhancement

3or a given image &! the probability density function p (Xk) is defined as

p (Xk)=n

k

n 444444444444 //.

3or k : ;! .4L< .! where represents the number of times that the level , Xk appears

in the input image & and n is the total number of samples in the input image #ote that p (Xk)



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is associated with the histogram of the input image which represents the number of pi%els that

have a specific intensity In fact! a plot of vs is 'nown histogram of & "ased on the probability

density function! the cumulative density function is defined as

c (X)=j=0

k

p (Xj ) 4444444444 ///

Where : x! for k : ;! .4L< . #ote that c (XL1 )=1 by definition 6E is a scheme

that maps the input image into the entire dynamic range! (X0 , XL1 ) ! by using the cumulative

density function as a transform function =et9s define a transform function f(x ) based on the

cumulative density function as

f(x )=X0+ (XL1X0 ) c (x ) 44444444 //0

Then the output image of the 6E! Y= {Y(i , j )} ,can be e%pressed as

Y=f(X)

{f(X(i , j ) )X (i , j )X} 444 //1

The high performance of the 6E in enhancing the contrast of an image as a conse&uence

of the dynamic range e%pansion! "esides! 6E also flattens a histogram "ase on information

theory! entropy of message source will get the ma%imum value when the message has uniform

distribution property As addressed previously! 6E can introduce a significant change in

brightness of an image! which hesitates the direct application of 6E scheme in consumer

electronics

Suppose we have an image which is predominantly dar' Then its histogram would be

s'ewed towards the lower end of the grey scale and all the image detail is compressed into the

dar' end of the histogram If we could >stretch out? the grey levels at the dar' end to produce a

more uniformly distributed histogram then the image would become much clearer 6istogram

e&uali7ation involves finding a grey scale transformation function that creates an output image

with a uniform histogram 6ow do we determine this grey scale transformation function@



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Assume our grey levels are continuous and have been normali7ed to lie between ; and .

We must find a transformation T that maps grey values r in the input image 3 to grey8

values s : T,r- in the transformed image FIt is assumed that

T is single valued and monotonically increasing! and

0T(r )1 for 0 r 1

a) original b) histogram

c)e&uili7ed image d) histogram e&uali7ation

3ig //) The histogram and histogram e&uali7ation of an image

The inverse transformation from s to r is given by

r : T1 (s ) 44444444 //2

If one ta'es the histogram for the input image and normali7es it so that the area under the

histogram is .! we have a probability distribution for grey levels in the input image Pr(r ) .

If we transform the input image to get s : T,r- what is the probability distribution

Ps(s ) @3rom probability theory it turns out that

Ps(s )=Pr(r ) r

' 4444444444 //

Where r=T1 ( s )

Consider the transformation

s=T(r )=Pr(w ) dw 44444444 //BThis is the cumulative distribution function of r Using this definition of T we see that

the derivative of s with respect to r is

s=Pr(r ) 44444444444 //

Substituting this bac' into the e%pression for Ps ! we get

Ps(s )=Pr(r ) =1 44444444 //

3or all s( where 0 s 1

Thus Ps(s ) is now a uniform distribution function! which is what we want



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2.' THRE"HO$D DECOMPO"ITION:

Threshold decomposition is a powerful theoretical tool! which is used in nonlinear image

analysis $any filter techni&ues have been shown to commute with thresholding9 This means

that the image may be decomposed into a series of binary levels! each of which may be

processed separately These binary levels can then be recombined to produce the final gray scale

image with identical pi%el values to those produced by gray scale processing 6ence a gray scale

operation may be replaced by a series of e&uivalent binary operations The first threshold

decomposition framewor' for image processing was introduced by 3itch This was capable of

modeling linear 3I+ filters with positive weights The framewor' was limited to modeling low

pass filters

$ore recently the framewor' was modified to model both linear and nonlinear filters

with negative as well as positive filter weights It opened up the possibility to model high pass

and band pass filters as well as low pass filters $otivated by this success an image sharpening

techni&ue is developed and implemented through a framewor' of threshold decomposition

Consider the signal F ( ,%. ! %/ !4 ! %n- where %i G8m 4! 8.! ;! .! 4 ! mH The threshold

decomposition of F amounts to decomposing this signal into /m binary signals F 8m.! 4! F ;!

4! F m! where the ith element of % J is defined by E&uation

x i= i 44444444 /0.

The above threshold decomposition is reversible! such that if a set of threshold signals is

given! each of the samples inx can be e%actly reconstructed as shown in E&uation

x i= xi

j

4444444444 /0/Thus! an integer8valued discrete8time signal has a uni&ue threshold signal representation!

and vice versa

2.) IMAGE "HARPENING:

The principle for image filtering method and edge detection can be done by several

techni&ues 3irstly! signal reduction is re&uired to emphasi7e the edge and brighten the image In

this case! high pass filter is used to filter the signal as well as to detect the edges from the

original image 6ence! the solution for this process is the total of the original image and the edge

as the E&/1.

fs (Xi ,Yi )=f(Xi , Yi )+F( f(Xi+Yi)) 44444444444 /1.Where

f(Xi , Yi ) : The original pi%el value at the coordinate (Xi , Yi )3 ( ) : The high pass filter

K : A tuning parameter which is greater or e&ual to 7ero

fs (Xi ,Yi ) : The sharpened pi%el at the coordinate (Xi , Yi )



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The value represents K as the perspective degree of sharpness! the higher the K the more

sharpened is the image Another well8'nown techni&ue which enhances blur images is called

Unsharp $as'ing ,U$- techni&ue The solution of this techni&ue begins by subtracting the

original image with the blur image In the other words! subtract low pass filter from the input

image These results for the output image which emphasi7es on the detail and sharpness

Lenerally! blurred images occur by several low pass filtering in the image 6ereby was the E&

/1/ for Unsharp $as'ing techni&ue

fs (Xi ,Yi )=f(Xi , Yi )fb(Xi , Yi ) 4444444444 /1/Where

fs (Xi ,Yi ) : The sharpened image obtained by unsharp mas'ingfb (Xi , Yi ) : The blurred version of f(Xi , Yi )

According to this e&uation! increase in sharpness is eligible by using high boost filter

The relations between the above two e&uations were as shown in E& /10

fs h (Xi ,Yi )=Af(Xi , Yi )fb(Xi , Yi ) 44444444 /10Mr

fs h (Xi ,Yi )=(A1 )+ fh(Xi ,Y i ) 4444444444 /11A : A variable which is greater or e&ual to .

fs h (Xi ,Yi ) : The high boost sharpened imagefb (Xi , Yi ) : The low pass filter of f(Xi , Yi ) fh (Xi , Yi ) : The high pass filter of f(Xi , Yi )

2.* +A,E$ET":

2.*.1 +a-elet Deinition:

A wavelet is a small wave which has its energy concentrated in time It has an oscillating

wave li'e characteristic but also has the ability to allow simultaneous time and fre&uency

analysis and it is a suitable tool for transient! non8stationary or time8varying phenomena

2.*.2 +a-elet C/aracteri0tic0:

Waves are smooth! predictable and everlasting! whereas wavelets are of limited duration!

irregular and may be asymmetric Waves are used as deterministic basis functions in 3ourier

analysis for the e%pansion of functions ,signals-! which are time8invariant! or stationary The

important characteristic of wavelets is that they can serve as deterministic or non8deterministic

basis for generation and analysis of the most natural signals to provide better time8fre&uency

representation! which is not possible with waves using conventional 3ourier analysis



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3igure /2) +epresentation of a wave ,a-! and a wavelet ,b-

2. E,O$UTION OF +A,E$ET TRAN"FORM:

The need of simultaneous representation and localisation of both time and fre&uency for

non8stationary signals ,eg music! speech! images- led toward the evolution of wavelet transformfrom the popular 3ourier transform Different time8fre&uency representations are very

informative in understanding and modelling of WT

2..1 Fourier Tran0or!:

3ourier transform is a well8'nown mathematical tool to transform time8domain signal to

fre&uency8domain for efficient e%traction of information and it is reversible also 3or a signal

x ( t) ! the 3T is given byXFT(f)= x (t) !j 2 "ftdt 4444444444 2..1

Though 3T has a great ability to capture signal9s fre&uency content as long as %,t- is

composed of few stationary components ,eg sine waves- 6owever! any abrupt change in time

for non8stationary signal %,t- is spread out over the whole fre&uency a%is in F,f- 6ence the

time8domain signal sampled with Dirac8delta function is highly localised in time but spills over

entire fre&uency band and vice versa The limitation of 3T is that it cannot offer both time and

fre&uency localisation of a signal at the same time

2..2 "/ort Ti!e Fourier Tran0or! "TFT3:

To overcome the limitations of the standard 3T! Labor introduced the initial concept ofShort Time 3ourier Transform ,ST3T- The advantage of ST3T is that it uses an arbitrary but

fi%ed8length window g (t) for analysis! over which the actual non stationary signal is assumed

to be appro%imately stationaryThe ST3T decomposes such a pseudo8stationary signal x (t)

into a two dimensional time8fre&uency representation #($ , f) using that sliding windowg (t) at different times N Thus the 3T of windowed signal x (t) g

(t$) yields ST3T as#TFTx($ , f)= x (t) g (t$) !j2"ftdt 44444444444 //

Mnce a window has been chosen for ST3T! the time8fre&uency resolution is fi%ed over the

entire time8fre&uency plane because the same window is used at all fre&uencies There is always

a trade off between time resolution and fre&uency resolution in ST3T

2..' +a-elet Tran0or! +T3:

3i%ed resolution limitation of ST3T can be resolved by letting the resolution O t and Of

vary in time8fre&uency plane in order to obtain $ultiresolution analysis The Wavelet Transform

,WT- in its continuous ,CoWT- form provides a fle%ible time8fre&uency window! which narrows

when observing high fre&uency phenomena and widens when analy7ing low fre&uency



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behaviour Thus time resolution becomes arbitrarily good at high fre&uencies! while the

fre&uency resolution becomes arbitrarily good at low fre&uencies This 'ind of analysis is

suitable for signals composed of high fre&uency components with short duration and low

fre&uency components with long duration! which is often the case in practical situations

2..) Di0crete +a-elet Tran0or! D+T3:The CWT has the drawbac's of redundancy and impracticability with digital computers

As parameters ,a! b- ta'e continuous values! the resulting CWT is a very redundant

representation! and impracticability is the result of redundancy Therefore! the scale and shift

parameters are evaluated on a discrete grid of time8scale plane leading to a discrete set of

continuous basis functions The discreti7ation is performed by setting

%=%0jb=k %0

jb0 for j,k & 444444444444 /1

Where, %0>1 is a dilated step and b0 ( 0 is a translation step

The family of wavelets then becomes

( t=%2 %

jtk b 4444444444444 /2

and the wavelet decomposition of a function f ,t- isf t= * f j , k ) j , k t 444444444444........ /

where /8dimensional set of coefficients *f(j , k) is called DWT of a given function f ,t-

CHAPTER '

PROPO"ED METHOD

The following figure shows the proposed scheme)

Dept. Of ECE, MITSPage 10Threshold

Decomposition

Wavelet

Transform

Color

inputimage

Decompose

+L" image


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3ig 0) "loc' Diagram

'.1 Color In4ut I!a5e:

When images are captured from long distances they are affected due to some

environmental effects li'e irregular weather conditions! far distances In these images

preservation of useful us information problem occurs due to presence of noise This low contrast

color satellite images are ta'en as input images

'.2 Deco!4o0e RG6 i!a5e:

Color images also 'nown as an +L" images A color image is an image in which eachpi%el is specified by three values one each for the red! blue! and green components of the pi%el

scalar The array of class uint! uint.! single! or double whose pi%el values specify intensity

values 3or single or double arrays! values range from P;! .Q 3or uint! values range from P;!

/22Q 3or uint.! values range from P;! 2202Q

The +L" encoding of pure red is ,/22!;!;-! pure green ,;!/22!;-! and pure blue

,;!;!/22- In all +L" encodings! the first value is the amount of red! the second value is the

amount of green! and the last value represents the amount of blue The range of the three

numbers is ; to /22

When converting an +L" color image to gray scale all the color is replaced with shades

of gray +L" uses additive color mi%ing and is the basic color model used in any other medium

that proJects color with light

Lray Scale Image P Q : ;/5+ed ;2B5Lreen ;..15 "lue

The captured images are subJected to +L" to grey conversion The ac&uired image in

+L" is first converted to grey and then the output image is given to wavelet transform

'.' +a-elet Tran0or!0:

+a-elet0:

The Wavelet analysis is performed using a prototype function called a wavelet! which has

the effect of a band pass filter Wavelets are functions defined over a finite interval and having an

average value of 7ero The basic idea of the wavelet transform is to represent any arbitrary

function f ,t- as a superposition of a set of such wavelets or basis function These basis functions

are derived from a single prototype called mother wavelets

The term wavelet means a small wave The smallness refers to the condition that this


Mutput

image

+econstruct

+L" image

Inverse

WaveletTransform


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window function is of finite length ,compactly supported- The wave9 refers to the condition that

this function is oscillatory The term mother implies that the functions with different region of

support that are used in the transformation process are derived from one main function! or the

mother wavelet by dilations or contractions ,scaling- and translations ,shifts-

+a-elet0 O-er-ie7:

The fundamental idea behind wavelets is to analy7e according to scale Indeed! some

researchers in the wavelet field feel that! by using wavelets! one is adopting a whole new mindset

or perspective in processing data Wavelets are functions that satisfy certain mathematical

re&uirements and are used in representing data or other functions 6owever! in wavelet analysis!

the scale that we use to loo' at data plays a special role Wavelet algorithms process data at

different scales or resolutions They are more appropriate functions than the sines and cosines

which comprise the bases of 3ourier analysis! to appro%imate choppy signals ,.- "y their

definition! these functions are non8local ,and stretch out to infinity- They therefore do a verypoor Job in appro%imating sharp spi'es "ut with wavelet analysis! we can use appro%imating

functions that are contained neatly in finite domains Wavelets are well8suited for appro%imating

data with sharp discontinuities The wavelet analysis procedure is to adopt a wavelet prototype

function! called an analy7ing wavelet . Temporal analysis is performed with a contracted! high8

fre&uency version of the prototype wavelet! while fre&uency analysis is performed with a dilated!

low8fre&uency version of the same wavelet "ecause the original signal or function can be

represented in terms of a wavelet e%pansion ,using coefficients in a linear combination of the

wavelet functions-! data operations can be performed using Just the corresponding wavelet

coefficients

+a-elet A44lication0:

. Image Enhancement

/ 3"I finger print recognition

0 De8noising #oisy Data

1 Detecting self8similar behavior in a time8series

+a-elet Tran0or!ation0:

Wavelet transforms have been one of the important signal processing developments in the

last decade! especially for the applications such as time8fre&uency analysis! data compression!

segmentation and vision During the past decade! several efficient implementations of wavelet

transforms have been derived The theory of wavelets has roots in &uantum mechanics and the

theory of functions though a unifying framewor' is a recent occurrence Wavelet analysis is



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performed using a prototype function called a wavelet Wavelets are functions defined over a

finite interval and having an average value of 7ero The basic idea of the wavelet transform is to

represent any arbitrary function f ,t- as a superposition of a set of such wavelets or basis

functions These basis functions or baby wavelets are obtained from a single prototype wavelet

called the mother wavelet! by dilations or contractions ,scaling- and translations ,shifts-

Efficient implementation of the wavelet transforms has been derived based on the 3ast 3ourier

transform and short8length fast8running 3I+ algorithms9 in order to reduce the computational

comple%ity per computed coefficient

$athematical transformations are applied to signals to obtain further information from

that signal that is not readily available in the raw signal #ow! a time8domain signal is assumed

as a raw signal! and a signal that has been transformed by any available transformations as a

processed signal

There are a number of transformations that can be applied such as the 6ilbert

transform! short8time 3ourier transform! Wigner transform! the +adon transform! among

which the 3ourier transform is probably the most popular transform These mentioned

transforms constitute only a small portion of a huge list of transforms that are available at

engineers and mathematicians disposal Each transformation techni&ue has its own area of

application! with advantages and disadvantages

The development of wavelets is an e%ample where ideas from many different fields

combined to merge into a whole that is more than the sum of its parts Wavelet transforms

have been widely employed in signal processing application! particularly in image

compression research It has been used e%tensively in multi8resolution analysis ,$+A- for

image processing In signal processing applications! different implementations of the

wavelet theory have been used for effective evaluation of biological signals emanating from

bio8medical devices

The techni&ue based on the interpolation of the high8fre&uency sub bands obtained

bywavelettransformand the input image The proposed resolution enhancement techni&ue

uses WT to decompose the input image into different sub bands

'.'.1 Dau8ec/ie0 +a-elet Tran0or!)

In this wor' Daubechies ,db.- wavelet has been used to decompose the images as well as

to reconstruct the images also Daubechies ,db.- wavelet is the same as 6aar wavelet So the



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discussion of the 6aar wavelet is essential to understand the concept of Daubechies ,db.-

wavelet In mathematics! the 6aar wavelet is a certain se&uence of functions This se&uence was

proposed in .; by AlfrRd 6aar 6aar used these functions to give an e%ample of a countable

ortho normal system for the space of s&uare integrable functions on the real line P.Q The 6aar

wavelet9s mother wavelet function

and characteri7ed Daubechies wavelet transform has been used in this wor' Daubechies

wavelets are a family of orthogonal wavelets defining a discrete wavelet transform by a ma%imal

number of vanishing moments for some given support This 'ind of /8dimensional Discrete

Wavelet Transform ,DWT- aims to decompose the image into appro%imation coefficients ,cA-

and detailed coefficients c6! c and cD ,hori7ontal! vertical and diagonal- obtained by wavelet

decomposition of the input image ,F- The /8dimensional Discrete Wavelet Transform ,DWT-

'.'.2 "u898and Codin5 :

Sub8band coding is a coding strategy that tries to isolate different characteristics of a

signal in a way that collects the signal energy into few components This is referred to as energy

compaction Energy compaction is desirable because it is easier to efficiently code these

components than the signal itself

The sub8band coding scheme tries to achieve energy compaction by filtering a signal with

filters of different characteristics "y choosing two filters that are orthogonal to each other and

decimating the output of these filters a new two component representation is achieved

3ig0/) $ultilevel decomposition hierarchy of an image with /8D DWT

In two dimensions! usually apply filtering both hori7ontally and vertically 3iltering in

one8dimension results in decomposing the image into two components The total numbers of

produced components after the vertical and hori7ontal decompositions is four These 18

components are referred to as image sub bands! ==! =6! 6=! 66 The first sub band ,the == sub

band- will contain low pass information! which is essentially a low8resolution version of the

image Sub band 6= will contain low pass information vertically and high pass information

hori7ontally! and sub band =6 will contain low pass information hori7ontally and high pass

information vertically 3inally! sub band 66 will contain high pass information in both

directions Sub band == is more important than the other 0 sub bands! as it represents the coarse

version of the original image

Each decomposition divides an image into four &uadrants Two8dimensional fre&uency

partition produces four sub bands) ==! =6! 6= and 66 Leneral space8fre&uency segmentation

applies the general time8fre&uency8pruning algorithm to choose between the four8way splits in

space or fre&uency in a space8fre&uency tree This algorithm should generate a better optimal



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basis than both the singletree and the double8tree Its basis must be at least as good as the best

double8treesingle8tree basis! because the set of possible double8treesingle8tree bases is a subset

of the possible S3S bases It has ma%imum decomposition depth of five The white lines indicate

that the sub8image is space split! while the blac' lines indicate that fre&uency segmentation is

applied If there is no line inside the sub8image! this will indicate that there is no splitting

performed on the sub8image

'.) T/re0/old Deco!4o0ition:

Threshold decomposition is a powerful theoretical tool which is used in nonlinear image

analysis $any filter techni&ues have been shown to commute with thresholding9

This means that the image may be decomposed into a series of binary levels! each of which

may be processed separately These binary levels can then be recombined to produce the final

grey scale image with identical pi%el values to those produced by grey scale processing 6ence a

grey scale operation may be replaced by a series of e&uivalent binary operations

Mor4/olo5ical ilter0:

A morphological filter is used to sharpen these detected edges E%perimental results

demonstrate that the detected edge deblurring filter improved the visibility and perceptibility of

images In this paper! a new edge detected morphological filter is proposed to sharpen aerial

images This is done by detecting the positions of the edges and then applying a class of

morphological filtering $otivated by the success of threshold decomposition! gradient8based

operators are used to detect the locations of the edges

$athematical morphology is the name given to a geometrical branch of nonlinear filtersIt offers a unified and powerful approach to numerous image processing problems Mne of the

most appealing aspects of morphological image processing lies in addressing the image

sharpening problem

6a0ic 6inar O4eration0:

Dilation:



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The transformation which replaces the grey level value at a pi%el by the ma%imum of the

grey level value in its neighborhood is the grey scale dilation operator The structuring element

acts as a mas' implicitly defining the weighted neighborhood

Dilation ,sometimes called $in'ows'y additionV- is defined as follows

AB: Gc | c: a bfor some aAand bB }

Mne way to thin' of this is to ta'e copies of Aand translate them by movement vectors

defined by each of the pi%els in B ,This means we have to define an origin for B- If we union

these copies together! we get AB This can be written as

A B=_tB

Alternatively! we can ta'e copies of Band translate them by movement vectors defined

by each of the pi%els indilation is commutative An interpretation of this latter way of thin'ing

about it is to put a copy of Bat each pi%el inA If we stampV a copy of Bat each pi%el in Aand

union all of the copies! we get AB This can be written this way)

AB: tA

In this way! dilation wor's much li'e convolution) slide a 'ernel to each position in the

image and at each position applyV ,union- the 'ernel In the case of morphology! we call this

'ernel B the structuring element

Dilation is also associative as well as commutative)

,AB-C: , A,BC--

This follows naturally from the way we are unioning multiple translated sets together

This associativity is useful for decomposing a single large dilation into multiple smaller

ones Suppose! for e%ample! that you have available a board that does 0 0 dilation in hardware!

but you want to perform dilation by a B structuring element Does there e%ist a set of 0 0

element that when dilated by each other in succession gives theB one@ If so! you can write

the larger dilation as the result of successively dilating by the smaller elements

Ero0ion:

Similarly! the transformation which replaces the grey level value at a pi%el by the

minimum of the grey level value in its neighborhood is 'nown as the grey scale erosion operator

defined as

#ote that the dilation operator is e%tensive) ,f g-,7-X f ,7-

and the erosion operator is anti e%tensive ,f g- ,7-Yf ,7-

Erosion ,sometimes called $in'ows'y subtractionV- is defined as follows

A_ B: {x | x bAfor every bB}

Mne way to thin' of this is to ta'e copies ofA and again translate them by movement

vectors defined by each of the pi%els in B 6owever! this time we move them in the opposite



17/25


direction ,b- and intersect the copies together This can be written as

A_ B: tB

An interpretation of this latter way of thin'ing about it is to again put a copy of Bat each

pi%el in A If count only those copies whose translated structuring elements lie entirely in Aand

mar' the pi%els inA that these copies were translated to! we get A_ B

Unli'e dilation! erosion is not commutative ,$uch li'e how addition is commutative

while subtraction is not-

Also unli'e dilation! erosion is not associative)

,A_ B-_ C@:A_ ,B_ C-

O4enin5 and Clo0in5:

O4enin5:

An openingis an erosion followed by a dilation with the same structuring element)

A+": ,A_ "-"

+emember that erosion finds all the places where the structuring element fits inside the

image! but it only mar's these positions at the origin of the element "y following an erosion by

a dilation! we fill bac' inV the full structuring element at places where the element fits inside the

obJect So! an opening can be consider to be the union of all translated copies of the structuring

element that can fit inside the obJect Mpenings can be used to remove small obJects! protrusions

from obJects! and connections between obJects So! for e%ample! opening by a 2 2 s&uare

element will remove allthings that are less than 2 pi%els high or less than 2 pi%els tall

Clo0in5 :

Closing wor's in an opposite fashion from opening)

A+B: ,AB-_ B

Whereas opening removes all pi%els where the structuring element won9t fit inside the

image foreground! closing fill sin all places where the structuring element will not fit in the

image background.

+emember! though! duality doesn9t imply inverse operations) an opening following a

closing will notrestore the original image

Pro4ertie0 o O4enin5 and Clo0in5:

Dualit:

Closing is the dual of opening)

,A+B- c: A c+ZB

[ust as erosion can be implemented using dilation ,and vice versa-! opening can be

implemented using closing ,and vice versa-

Ide!4otence:

An important property of opening and closing operations is that they are idempotent) if



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you apply one more than once !nothing changes after the first application So given as

A+B+B: A+B

A44lication0 o O4enin5 and Clo0in5:

Mpening and closing are the basic wor'horses of morphological noise removal Mpening

removes small obJects! and closing removes small holes

Findin5 T/in50

\ou can also use opening and closing to find specific shapes in an image While these

may not be noiseV! they may Just be other things that you don9t care about ,In this sense!

perhaps noise is Just things you don9t care about@-Mpening can be used to only find things into

which a specific structuring element can fit

"u8di-i0ion into Part0

\ou can also e%tend this idea to part subdivision Suppose that you 'now that a particular

obJect has specific parts with specific shapes Mpenings can be used to separate those parts by

shaping the structuring elements to fitV into those parts They don9t have to e%actly match the

parts]it9s sufficient to only fit into some parts while not fitting into other

'.).1 Ed5e Detection:

Edge detection is a fundamental tool! which detects boundaries between obJects and

bac'ground in the image An edge8detection filter can be used to improve the appearance of low8

contrasted aerial images

Since edge detection has been an active area for researchers! many effective methods

have been proposed such as gradient edge detectors ,.st derivative-! 7ero crossing ,/nd

derivative-! =aplacian of Laussian ,=ML-and much more In spite of all these efforts! none of the

proposed operators are fully satisfactory in real world applications In this paper! the

enhancement is applied through a framewor' of threshold decomposition This has two

advantages) it reduces the edge detection to a simple binary process( and it ma'es the estimation

of edge direction straight forward Edge detection and direction estimation may be carried out by

identifying simple patterns Edge detection is in the forefront of image processing for obJect

detection! it is crucial to have a good understanding of edge detection algorithms This paper

introduces a classification of most important and commonly used edge detection algorithms!

namely Canny! Sobel! =aplacian Different categories are included in our classification! and then

advantages and disadvantages of some available algorithms within this category are discussed

Edge detection is one of the most commonly used operations in image analysis An edge

is defined by a discontinuity in gray level values In other words! an edge is the boundary

between an obJect and the bac'ground

Cla00iication o Ed5e Detector0:

Edge detectors may well be classified into following categories)



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Gradient Ed5e Detector0:

It contains classical operators and uses first directional derivative operation It includes

algorithms such as) Sobel ,.B;-! *rewitt ,.B;-! +obert9s operators

"o8el O4erator:

The operator consists of a pair of 0^0 convolution 'ernels

These 'ernels are designed to respond ma%imally to edges running vertically and

hori7ontally relative to the pi%el grid! one 'ernel for each of the two perpendicular orientations

The gradient magnitude is given by) Typically! an appro%imate magnitude is computed using)

This is much faster to computeThe angle of orientation of the edge ,relative to the pi%el

grid- giving rise to the spatial gradient

Ro8ert0 cro00 o4erator:

The +obert9s Cross operator performs a simple! &uic' to compute! /8D spatial gradient

measurement on an image The operator consists of a pair of /^/ convolution 'ernels as shown

These 'ernels are designed to respond ma%imally to edges running at 12_ to the pi%el grid! one

'ernel for each of the two perpendicular orientations The 'ernels can be applied separately to

the input image! to produce separate measurements of the gradient component in each orientation

,L%and Ly- The angle of orientation of the edge giving rise to the spatial gradient ,relative to

the pi%el grid orientation-

Pre7itt0 o4erator:

*rewitt operator is similar to the Sobel operator and is used for detecting vertical and

hori7ontal edges in images

Edge detection and direction estimation may be carried out by identifying simple

patterns! which are closely related to the *rewitt operators The operators are sometimes called

compass operators because of their ability to determine gradient direction The gradient is

estimated in possible directions ,for a 0^0 mas'- with a difference of 12obetween each

direction The first 1 operators are the four ,0^0 mas'- the other four can be obtained by

applying a cloc'wise rotation "y using the mas's of the *rewitt operators! thic' edges in the

directions can be detected 3our ,0^0 mas'- of *rewitt operators

where g : GD; ! D. ! D/H is the structuring element used in mathematical morphology

and will be e%plained later Mn the other hand! the mas's mentioned in P..Q can be used to

detect thin edges in the directions The first 1 operators are represented by the four ,0^0 mas'-

shown in the outer four can be obtained by negating the elements of these matrices

3our ,0^0 mas'- for thin edge detection With the aid of the threshold decomposition

described above! and for each level! the edges are detected by searching for patterns of grey

levels consistent with the mas's of the *rewitt operators for thic' edges! and the mas's

mention for thin edges Thus the sharpening filter is applied only at these detected edges rather



20/25


than all the pi%els of the image

$a4lacian o Gau00ian $oG3:

It was invented by $arr and 6ildrethw ,.;- who combined Laussian filtering with the

=aplacian This algorithm is not used fre&uently in machine vision The =aplacian is a /8D

isotropic measure of the /nd spatial derivative of an image The =aplacian of an image highlights

regions of rapid intensity change and is therefore often used for edge detection The operator

normally ta'es a single gray level image as input and produces another gray level image as

output Since the input image is represented as a set of discrete pi%els! a discrete convolution

'ernel can appro%imate the second derivatives in the definition of the =aplacian "ecause these

'ernels are appro%imating a second derivative measurement on the image! they are very sensitive

to noise To counter this! the image is often Laussian Smoothed before applying the =aplacian

filter choose edge detectors that fit best to the application In this respect! we present some

advantages and disadvantages of algorithms P.! 0! and 1Q within the conte%t of our classification

as follows

Cla00ical "o8el; Pre7itt; Ro8ert03:

Ad-anta5e0:

.- Simple!

/- Detection of edges and their orientations

Di0ad-anta5e0:

.- Sensitive to noise!

/- Inaccurate

$a4lacian o Gau00ian $oG3:

Ad-anta5e0:

.- 3inding the correct places of edges

/- Testing wider area around the pi%el

Di0ad-anta5e0:

.- $alfunctioning at corners! curves and where the gray level intensity function varies

/- #ot finding the orientation of edge because of using the =aplacian filter

Gau00ian o4erator0 Cann3:

Ad-anta5e0:

.- Using probability for finding error rate

/- =ocali7ation and response

0- Improving signal to noise ratio

1- "etter detection specially in noise conditions

Di0ad-anta5e0:

1 Comple% Computations



21/25


2 3alse 7ero crossing

! Time consuming

Since edge detection is the step in obJect recognition! it is necessary to 'now the

differences between edge detection algorithms'.* In-er0e 7a-elet tran0or!0:

The high8fre&uency sub band images and the input low8resolution image have been

interpolated! followed by combining all these images to generate a new resolution8enhanced

image by using inverseWT In order to achieve a sharper image! an intermediate stage for

estimating the high8fre&uency sub bands has been proposed Conse&uently the reconstruction

process is performed using inverse of DWT ,IDWT- We have reconstructed the images based on

the appro%imation co8efficient matri% CA

After applying threshold decomposition on == sub band it is reconstructed by using

inverse wavelet transform Sub band == is more important than the other 0 sub bands

'. Recon0truct RG6 i!a5e:

An +L" image is reconstructed from its three channels after applying the proposed

techni&ues to enhance the original image The reconstructed +L" image is more enhanced than

the original image and preserves useful information

CHAPTER )RE"U$T AND ANA$


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refers to the better &uality is the image

The formula for $SE and *S#+ are E& ,.- and E& ,/-

#-=1 m, n 2 m, n

4444444444 ,.-

P#.0=10log10 4444444444 ,/-

Where $ and # are the number of rows and columns of the input image! respectively

In the *S#+ e&uation! + is the ma%imum fluctuation in the input image data type The

*S#+ ` $SE values are given below for analysis of result

$SE *S#+

3igure. .0.1/. 0;.12

3igure/ B21/.. 01B1

3igure0 2;/.; 0/;2/

3igure1 BB.2/2 012B/0

Table.) $SE and *S#+ values

*ractically! the *S#+ which values higher than 0; d" is invisible for human sight to

analy7e the color distortion between two images

a) Mriginal Color Image b)Enhanced Image

3igure .) The Enhanced Image



23/25



3igure /) The Enhanced Image


3igure 0) The Enhanced Image



24/25



3igure 1) The Enhanced Image

The e%perimental results with the new algorithm procedure shown in figures .! /! 0 and

1 3igure ,a- is the original color image and figure ,b- show the result of the enhanced image

CHAPTER *CONC$U"ION

This proJect introduced a new enhancement filter for digital satellite images In the

proposed system! the edge detected guided smoothing filters succeeded in enhancing low

satellite images This was done by accurately detecting the positions of the edges throughthreshold decomposition The detected edges were then sharpened by applying smoothing filter

"y utili7ing the detected edges! the scheme was capable to effectively sharpening fine details

whilst retaining image integrity The visual e%amples shown above! have demonstrated that the

proposed method was significantly better than many other well8'nown sharpener8type filters in

respect of edge and fine detail restoration



25/25


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Documents

Report on image enhancement