dip2 image enhancement1

7/23/2019 DIP2 Image Enhancement1

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Image Enhancement Spatial domain techniques

Point operations Linear transformation Logarthmatic transformation Power-law transformation

Piece wise linear transformation Contrast Stretching

1

Arithmetic operation Filtering

Filter mask, convolution Smoothing Spatial Filters

Averaging filters or low pass filters Weight average

Sharpening Spatial Filters

Point Operations Overview

Point operations are zero-memory operations where

a given gray level x[0,L] is mapped to anothergray level y[0,L] according to a transformation

)(xfy =y

2

L

L

x

L=255: for grayscale images

Pointoperationsxy =

L

y

3

Lx

No influence on visual quality at all

Digital Negative

xLy =

Lx

0

L

4

Load a imagehh=255-a(1:1536,1:2048,1); digitanegative.figureimshow(hh)hh=255-a(1:1536,1:2048,1:3);g=a(:,:,2);imshow(g)

Matlabfunction for same purpose:

5

Imadjust (f,[low_in,high_in],[low_out,hight_out],gamma

Maps the intensity values in in imagef to new values in g.Values between low_in and high_in map to value between low_out andhigh_out.

A=imread(test.jpg)g1=imadjust(a,[0 1],[1 0]);imshow(g1)

Contrast Stretching

Contraststretch(alsoknown as normalization)operates bystretchingthe pixel range in the input image over a larger dynamic range in theoutputimage.By applyingonly this linearscalingof the dynamic range itis less sophisticated than histogramequalizationandprovides a visuallyless harsh enhancement.

U erandlowerlimit(a,b) shouldbe known 0 ,255

6

In its simplest form this transform then scans the present image to determinethe maximum and minimum pixel values currently present, denoted c and drespectfully.

In reality this method of choosing c and d is very naive as a single outlier inthe image will effect the overall enhancement result


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Contrast Stretching


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Gamma tranform can make pixel brighter or darker depends on its value.% powelawof intesitytransformation. when f(x,y) is in the range of of% [0,1] and gamma is larger than one it makes the image darker.% when gamma is smaller than one it makes the image brighter.

MatLab code

clear allclose allf=imread('winter.jpg');

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f=im2double(f);figure ,imshow(f),title ('org img')[m,n]=size(f)c=1;y=input('Gmmavalue');for i=1:mfor j=1:n

s(i,j)=c*(f(i,j) y);endendfigure, imshow(s),title ('gamma=0.25');

%muliply image , image gets darker bymultiplying it short numberclose allf=imread('test.jpg');

f=im2double(f);figure,imshow(f), title('gray scale');m=0.75; %contrastE=0.55 % slope of function

Contrast Stretching Matlab code with exponential function

EE465: Introduction to Digital ImageProcessing

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g=1./(1+(m./(f+eps)). E);figure,imshow(g), title('emhance image');

SummaryofPointOperation

Sofar,wehavediscussedvariousformsofmappingfunctionf(x)thatleadstodifferentenhancementresults

MATLABfunction>imadjust

Thenaturalquestionis:Howtoselectanappropriatef(x)foranarbitraryimage?

Onesystematicsolutionisbasedonthehistograminformationofanimage

Histogramequalizationandspecification

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HistogramProcessing

Histogramofadigitalimagewithgraylevelsintherange[0,L1]isadiscretefunction

h(rh(rkk) = n) = nkk W ere

rk :thekth graylevel

nk :thenumberofpixelsintheimagehavinggraylevelrk h(rk) :histogramofadigitalimagewithgraylevelsrk

Whatishistogram

Histogramisagraphshowingthenumberofpixelsinanimageateachdifferentintensity

valuefoundinthatimage.

different possible intensities, and so the

histogram will graphically display 256 numbers

showing the distribution of pixels amongst

those grayscale values.

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Example

2 3 3 2

4 2 4 3 4

5

6

No. of pixels

3 2 3 5

2 4 2 4

4x4 image

Gray scale = [0,9]histogram

0 1

1

2

2

3

3

4 5 6 7 8 9

Gray level


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NormalizedHistogram

dividingeachofhistogramatgraylevelrrkk bythetotal

number

of

pixels

in

the

image,

nnp(rp(rkk) = n) = nkk/ n/ n

For =0,1,,L1

p(rp(rkk)) givesanestimateoftheprobabilityofoccurrenceofgraylevelrrkk

Thesumofallcomponentsofanormalizedhistogramisequalto1

Histogram based Enhancement

Histogram of an image represents the relative frequency

of occurrence of various gray levels in the image

2000

2500

3000

20

0 50 100 150 200

0

500

1000

1500

MATLAB function >imhist(x)

Examplerk

h(rk) or p(rk)

Dark image

Components ofhistogram are

Bright image

concentrated on thelow side of the grayscale.

Components ofhistogram areconcentrated on the

high side of the grayscale.

Example

Low-contrast image

histogram is narrowand centered toward

High-contrast image

e m e o egray scale

histogram covers broadrange of the gray scaleand the distribution ofpixels is not too far fromuniform, with very fewvertical lines being muchhigher than the others

WhyHistogram?

1

1.5

2

2.5

3

3.5

4

x 104

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Histogram information reveals that image is under-exposed

0 50 100 150 200 250

0

0.5

It is a baby in the cradle!

AnotherExample

4000

5000

6000

7000

24

0 50 100 150 200 250

0

1000

2000

Over-exposed image


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HistogramEqualization OfaImage

Oneoftheseveraltechniquestoenhanceanimageinsuchamannerishistogramequalization,whichiscommonlyusedto

compareimages

made

in

entirely

different

circumstances.

Theconceptofhistogramequalizationistospreadotherwisecluttered fre uencies more evenl over the len th of the

histogram.Frequenciesthatlieclosetogetherwill

dramaticallybestretchedout

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HistogramEqualization OfaImage

Histogramequalizationassignstheintensity

values

of

pixels

in

the

input

image

such

that

theoutputimagecontainsauniformdistributionofintensities.

Histogramequalizationredistributesintensitydistributions.Ifthehistogramofanyimagehasmanypeaksandvalleys,itwillstillhavepeaksandvalleyafterequalization,butpeaksandvalleywillbeshifted.

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HistogramEqualization

Asthelowcontrastimageshistogramisnarrowandcenteredtowardthemiddleofthegrayscale,ifwe

distributethehistogramtoawiderrangethequality

oftheimagewillbeimproved.

Wecandoitbyadjustingtheprobabilitydensityfunctionoftheoriginalhistogramoftheimageso

thattheprobabilityspreadequally

Example

before after Histogramequalization

Example

before after Histogramequalization

The quality isnot improvedmuch becausethe originalimage alreadyhas a broadengray-level scale

GeneralworkingThe histogram equalization is operated on an image in three step:1). Histogram Formation2). New Intensity Values calculation for each Intensity Levels3). Replace the previous Intensity values with the new intensity values

New intensity values are calculated for each intensity level by applying thefollowing equation:

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if the image is in the grayscale domain, then the count is 255. And if theimage is of size 256x256 then, the No. of pixels is 65536.

The next step is to replace the previous intensity level with the new intensitylevel. This is accomplished by putting the value ofOi in the image for allthe pixels, where Oi represents the new intensity value, whereas i

represents the previous intensity level.


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Example

2 3 3 2

4 2 4 3 4

5

6

No. of pixels

3 2 3 5

2 4 2 4

4x4 image

Gray scale = [0,9]histogram

0 1

1

2

2

3

3

4 5 6 7 8 9

Gray level

Gray

Level(j)0 1 2 3 4 5 6 7 8 9

No. ofpixels 0 0 6 5 4 1 0 0 0 0

k

0 0

6

/

16

11

/

16

15

/

16

16

/

16

16

/

16

16

/

16

16

/

16

16

/

16

s x9 0 03.3

3

6.1

6

8.4

89 9 9 9 9

=jj

0

=

=k

j

j

n

ns

0

Example

3 6 6 3

8 3 8 6 4

5

6

No. of pixels

6 3 6 9

3 8 3 8

Output image

Gray scale = [0,9]Histogram equalization

0 1

1

2

2

3

3

4 5 6 7 8 9

Gray level

Histogramequalizationclear allclose alla=imread('humd.jpg');h=imhist(a(:,:,1));h1=h(1:10:256);horz=1:10:256;figure,title('histogram')bar(horz,h1);

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g= s eq a :,:, , ;gg=g(1:10:256);bar(horz,gg);

figure ,title('histogrameq')bar(horz,gg);figure,title('orgpic'),imshow(a(:,:,1))figure,title('histogrameqpic'),imshow(g)

Histogramequalizationimplemenationclear all, close allx0=imread('histest1.jpg');imshow(x0);x0=rgb2gray(x0);figure,imshow(x0),title('gray')[m,n]=size(x0);len=m*n;x=reshape(x0,len,1);

L=256

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xpdf=hist(x,[0:L-1]); % pdf, 1 x Ltr=round(xpdf*triu(ones(L))*(L-1)/len); % cdf, range from 0 to L-1y0=zeros(m,n);for i=1:L,

if xpdf(i)>0,y0=y0+[x0==i-1]*tr(i);

endendypdf=hist(reshape(y0,len,1),[0:L-1]); % pdfof y, 1 x L

Histogramequalizationimplemenation

figure,subplot(211),stem([0:L-1],xpdf),title('histogram, original')axis([0 256 0 500])

subplot(212),stem([0:L-1],ypdf),title('histogram, equalized'),axis([0 256 0 500])

figure,subplot(121),imshow(uint8(x0)),title('before')

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subplot(122),imshow(uint8(y0)),title('after')

figurestairs([0:L-1],tr),title('transformation'),axis([0 256 0 256])

AssignmentApply the image histogram on color imageHint apply on single frame then find color value see lecture 1.


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Image Example

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before after

Arithmetic & logic operations on images used extensively inmost image processing applications

May cover the entire image or a subsetArithmetic operation between pixels p and q are definedas:

Arithmetic operation on image

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on: p+q :a ng a vaue o eac mage pxe vaueContrast Adjustment:Adding a +ve constant value to each pixel locationincreases its value and hence its brightness.Blending:Adding images together produces a composite image ofboth input images.

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Image subtraction

Subtraction: subtracting a value from each pixel location .....

Contrast Adjustment: as per addition

Image differencing :

subtracting one image from another shows us the difference between images.If we subtract two images in a video sequence, taken from a static camera, weget a difference image showing the movement that has occurred betweenthese video frames in the sceneA useful variation on subtraction is the absolute difference Ioutput=| IA - IB |

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e ween mages.

Division: dividing each pixel value ....

Contrast Adjustment: to uniformly scale image contrast by a given

factor (e.g. reduce contrast by 25% =division by 4 (=100/25). Oftenreferred to as image colour scaling. Image differencing: dividing image by another gives a result of 1

where the image pixel values are identical and a value !=1 wheredifferences occur. Notably image differencing using subtraction iscomputationally more efficient.

Multiplication

Contrast Adjustment: image colour scaling as per division

Saturation

This is commonly known as saturation in the image space the valueexceedsthe representational capacity of the image.A solution is todetectthis overflowand avoid itby setting all such values tothe max value forthe image representation (e.g. 255). We mustalso be aware of -ve pixelvalues resulting fromsubtraction and dealwiththese accordingly

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.

Image blending

This can be used to produce ghosting or overlay effects between differentimages.

equal weights for each image (1/N) produces and equally weightedcomposite of each input image 1...N. Alternatively different weights can beused between images to enhance/suppress the features of differentimages in the final result.

Alpha Bl end ing

Transparency in a given image can be introduced by giving a weight between 0 and1 to individual in the image. The combined alpha for each pixel location in theimage form an additional image channel, the alpha-channel, indexed as alpha(i,j).

An alpha value of 0 is transparent (no pixel colourvisible, only background)and a value of 1 is opaque (full pixel colourvisible, no background visible).

A value in between gives a level of blending with the background so that the

dis la ed ixel colour, Idis la (i, ), is:

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Adding an image

when we add 128, all grey values of 127 or greater will be mapped to 255. Andwhen we subtract 128, all grey values of 128 or less will be mapped to 0. Bylooking at these graphs, we see that in general adding a constant will lighten animage, and subtracting a constant will darken it.

b=imread('blocks.tif');b1=b+128 ??? E rrorb1=uint8(double(b)+128); orb1=imadd(b 128)

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,b2=imsubtract(b,128);% Adding two images

a1=imread('sence1.jpg');a2=imread('sence2.jpg');ad=a2(:,1:138,1:3); % should have samesizeb=imadd(a1,ad);imshow(a1)imshow(a2)imshow(b)

We can also perform lightening or darkening of an image by multiplication;

b3=immultiply(b,0.5); or b3=imdivide(b,2)b4=immultiply(b,2);

b5=imadd(immultiply(b,0.5),128); orb5=imadd(imdivide(b,2),128);

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Filtering

Filteringisatechniqueformodifyingorenhancinganimagetoemphasizecertainfeaturesorremoveotherfeatures.

Filteringisaneighborhoodoperation,inwhichthevalueofanygivenpixelintheoutputimageisdeterminedbyapplyingsomealgorithmtothevaluesofthepixelsintheneighborhoodofthecorresponding inputpixel.

includesmoothing,sharpening,andedgeenhancement.

FilterterminDigitalimageprocessing isreferredtothesubimage ,mask,kernel,template,orwindow.

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Spatialfilteringisapixelneighborhoodoperation

Linearfilteringisaccomplishedbyconvolutionandcorrelation

meansthevalueofanygivenpixelinoutputimageisrepresentedbyweightedsumofthepixelvalueofitneighborhood

Commonelementofafilterare neighborhood

anoperationonneighborhoodincludingpixelitself.

AFilterMaskofdifferentsize3X3,5X5etc.

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FilterMask

Thesumofweightsinamaskaffecttheoverallintensityoftheresultingimage.

Typically,amaskisnormalized suchthatthesumofweightsisequaltoone.

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,thatthesumofweightsisequaltozero.

Processoffiltering Theprocessconsistssimplyofmovingthefiltermaskfrompoint

topointinanimage.

Spatialfilteringrequiresthreesteps: 1.positionthemaskoverthecurrentpixel, 2.formallproductsoffilterelementswiththe

correspondingelementsoftheneighbourhood, 3.addupalltheproducts.

Thismustberepeatedforeverypixelintheimage.

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Frequenciesinimage

Fundamentally,thefrequenciesofanimagearetheamountbywhichgreyvalueschangewithdistance

Highfrequencycomponents arecharacterizedbylargechangesingreyvaluesoversmall

distances;

i.e.edges andnoise.

Lowfrequency components,ontheotherhand,arepartsoftheimagecharacterized

bylittlechangeinthegreyvalues.Thesemayincludebackgrounds,skintextures.

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SpatialFiltering

Twotypeoffiltering Linearfiltering

Medianfiltering

averagefiltering Gaussianfiltering

Orderstatistic

erscan ec ass e as:

Lowpass(preservelowfrequencies,reducesoreliminateshigh frequencycomponents) Highpass (i.e.,preservehighfrequencies,reducesoreliminateslow frequencycomponents)

Bandpass (i.e.,preservefrequencieswithinaband) Bandreject (i.e.,preservefrequenciesoutsideaband)

CorrelationinlinearSpatialFiltering

f(x-1,y-1)f(x-1,y)f(x-1,y+1)

f(x,y-1) f(x,y)f(x,y+1)

w(-1,-1) w(-1,0) w(-1,1)

w(0,-1) w(0,0) w(0,1)

The result is the sum of productsof the mask coefficients with thecorresponding pixels directly underthe mask

Pixels of image

Mask coefficientsw(-1,-1) w(-1,0) w(-1,1)

w(0,-1) w(0,0) w(0,1)

f(x+1,y-1)f(x+1,y)f(x+1,y+1)w(1,-1) w(1,0) w(1,1)

w(1,-1) w(1,0) w(1,1)

)1,1()1,1(),1()0,1()1,1()1,1(

)1,()1,0(),()0,0()1,()1,0(

)1,1()1,1(),1()0,1()1,1()1,1(

++++++

++++

++++

yxfwyxfwyxfw

yxfwyxfwyxfw

yxfwyxfwyxfw=),( yxf

Linearfiltering

Thecoefficientw(0,0)coincideswithimagevaluef(x,y),indicatingthatthemaskis

centeredat(x,y)whenthecomputationof

Ingeneral,linearfilteringofanimagefofsizeMxN withafiltermaskofsizemxn isgivenby

theexpression:

= =++=

a

as

b

bt tysxftswyxg ),(),(),(

Eq-A

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IssuesinspatialFilteringWhat happens when center of filter approaches image border

For nxn mask , at least one edge of the mask will coincide with borderof the image at distance (n-1)/2One or more column of the mask will be located outside image plane.

Remedy:Limit the excursions of centre of mask to be at distance no less than

(n-1)/2 pixels from border.

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Problem: resulting image will be shorter than orginal but all the pixels inthe filter image would be processed by mask.

PaddingAdding rows and column of zeros or other constant gray level.Padding by replicating rows and columnPadding is then stripped off at the end of filtering. filtered and originalimage would have same size.Value of the padding will effect at the edges which increase with themask size.


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SmoothingSpatialFilters

Smoothingfiltersareusedforblurringandfornoisereduction.

Blurringisusedinpreprocessingsteps,suchas

removalof

small

details

from

an

image

prior

to

objectextraction,andbridgingofsmallgapsinlinesorcurves

Noisereductioncanbeaccomplished byblurringduetoreducedsharptransitioningraylevels

Imageblurringcanbeobtainedinspatialdomainbypixelaveragingorintegrationinaneighborhood.

Theimagecanbefurtherblurredbyusinganaveragingfilteroflargersize

LinearFilters Averaging,GaussianandHighpassfilter. Averagingfilter: IsaLowPassFiltermeansitpassesonlylow

frequencyrangespixelsandblockthehigher

frequencypixels.

That

swhy

edges

which

are

attributesofsharpnessinanimageduetotheirhighchangeinfrequenciesareblurredafter

. Theideaisreplacingthevalueofeverypixelinan

imagebytheaverageofthegraylevelsintheneighborhoodi.e.outputpixelvalueisthemeanofitsneighborhood.

Sizeofthemaskcontrolsthedegreeofsmoothingandlossofthedetails.

Two3x3SmoothingAverageFiltersMasks

1 1 1

1 1 1

1 1 1

9

1

1 2 1

2 4 2

1 2 1

16

1

Standard average Weighted average

=

9

19

1

i

zi

Pixels aremultiplied bydifferentcoefficients givingmore weights toSomepixels.Forexamplepixel atcentre is givenmore weightTheother pixels are inverselyrelatedtotheirdistancefromcentre

A averaging filter in which all cofficientare equal to one is called as box filter

SmoothingLinearFilters

ThegeneralimplementationforfilteringanMxNimagewithaweightedaveragingfilterof

sizemxnisgivenbytheexpression

= =

= =

++

=a

as

b

bt

a

as

b

bt

tsw

tysxftsw

yxg

),(

),(),(

),(

ExampleofAverageFilter Theeffectofcomputingtheaverageofaneighborhoodofpixelsis

toeliminateanysuddenjumpsinthegreylevelwhichcouldbecausedbysomenoiseprocesses i.e.largedeviationsfromthenorm

Supposewehavethe3 3neighborhood:2 2 3

3 30 2

1

3

2 Compared to the numbers 1,2 and 3, the number 30 is relatively

large and can be taken to be a digital representation of a noisespike. The average value of this group of numbers is 5.3. By assigningthis value to the central pixel we obtain the neighborhood

2 2 3

3 5.3 2

1 3 2

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Averagefilter:Imfilter examplesa=imread('p.jpg');

h=ones(5,5)/25;

f1=imfilter(a,h);%useofzeropadding

h10=ones(10,10)/100;

f2=imfilter(a,h10);%useofzeropadding

f3=imfilter(a,h10,'replicate');%useofzeropadding

figure

subplot(2,2,1),imshow(a),title('orginal')

, , , ,

title('5X5withzeropadding')

subplot(2,2,3),imshow(f2),



title('10X10withoutzeropadding,replicate'

Effectofimfilter withandwithoutzeropadding,replicatemeanswithout.

Withzeropaddingablacklineisobservedatboundariesespeciallyathigherfilterbutnotwhenusedwithreplicate.

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Gaussianfiltering

61

Gaussianfilter

a=imread('p.jpg');

h=fspecial('gaussian',5,1)

f1=imfilter(a,h,'conv');%useofzeropadding

h10=fspecial('gaussian',10,1)

f2=imfilter(a,h10,'conv');

%

use

of

zero

paddingf3=imfilter(a,h10,'replicate','conv');%useofzeropadding

figure






subplot(2,2,4),imshow(f3)

,title('10X10withoutzeropadding,rep)

Doesnotmuchdifferencethanaveragefilter.Testdifferent valueofsigma

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HighPassfilter

Sumofthecoefficients(thatis,thesumofalleelementsinthematrix),inthe

highpassfilteriszero. Thismeansthatinalowfrequencypartofanimage,wherethegrey

valuesaresimilar,theresultofusingthisfilteristhatcorrespondinggrey

valuesinthenewimagewillbeclosetozero.

Theresultingvaluesareclosetozero,

whichistheexpectedresultofapplying

ahighpassfiltertoalowfrequencycomponent

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a=imread('coins.bmp');

h=fspecial('laplacian',0.9)

f1=imfilter(a,h);%useofzeropadding

h10=fspecial('laplacian',0.9)

f2=imfilter(a,h10);%useofzeropadding

f3=imfilter(a,h10,'replicate');%useofzeropadding

figure


subplot(2,2,2),imshow(f1),title('5X5withzeropadding')

subplot(2,2,3),imshow(f2),title('10X10withzeropadding')

subplot(2,2,4),imshow(f3),title('10X10withoutzeropadding,replicate')

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Medianfilter Themedianfilterisalsoaslidingwindowspatialfilter,butit

replacesthecentervalueinthewindowwiththemedianof

allthepixelvaluesinthewindow.Asforthemeanfilter,the

kernelisusuallysquarebutcanbeanyshape.Anexampleof

medianfilteringofasingle3x3windowofvaluesisshown

below.

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ProcessofMedianfilter

Corpregionofneighborhood

10 15 20

thepixelinour

region

IntheMxN maskthemedianisMxN

div2+1

20 100 20

20 20 25

10, 15, 20, 20, 20, 20, 20, 25, 100

5th


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SharpeningSpatialFilters

Thehighlightingoffinedetailsinanimage ortoenhancedetailsthathasbeenblurrediscalledas

sharpeningofspatialfilters.

Applicationinvolveselectronicprinting,medicalimaging,industrialinspectionandautonomous

gui anceinmi itarysystem

Blurring isaccomplishedinthespatialdomainbypixelaveragingorintegrationinaneighborhood.

Sharpeningcouldbeaccomplishedbyspatialdifferentiation

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ImageProcessingoperations

VerticalImageFlipping

Thetranspose

image

B

(M

XN)

of

A

(N

XM)

can

beobtainedas

B(j;i)=A(i;j)

fori =1:512

forj=1:512

B(j;i)=A(i;j);OR>>B=A0;

end

end

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Thresholdingis a vital part of image segmentation, produces a binaryimage from a graycale or colour image by setting pixel values to 1 or 0depending on whether they are above or below the threshold value. It isused to separate out a region or object within the image based upon itspixel value.

A pixel becomes white if its grey level is >TA pixel becomes black if its grey level is T will perform thethresholding.

r=imread('rice.tif');imshow(r),figure,imshow(r>110)The command X>T will thus return 1 (for true) for all those pixels for which thegrey values are greater than T, and 0 (for false) for all those pixels for whichthe grey values are less than or equal to T.We thus end up with a matrix of 0's and 1's, which can be viewed as a binary

image.Matlab has the im2bw function, which thresholds an image of any data type,using the general syntax im2bw(image, level)

Noise

Noiseisanydegradationintheimagesignal,causedbyexternaldisturbance.

Cleaninganimagecorruptedby noisethusan.

TypesofNoises

SaltandPeeperNoise

GaussianNoise

PeriodicNoise

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SaltandpeeperNoise

SaltandpeeperNoise presenceofwhiteorblackorbothpixelontheimage also

calledbinarynoise.

Canbecausedbysharp,suddendisturbancesintheimagesignal.

Toadd

noise

we

use

the

Matlab function

imnoise,whichtakesanumberof different parameters.To addsaltandpeppernoise:

t_sp=imnoise(t,'salt &pepper');

weincludeanoptionalparameter,beingavaluebetween0and1indicatingthefractionofpixelstobecorrupted.

Exercise:create40%saltandpeepernoiseinagivenimage

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Cleaningsaltandpeppernoise

Giventhatpixelscorruptedbysaltandpeppernoisearehighfrequencycomponentsofanimage,weshouldexpectalowpassfiltershouldreduce them.

a3=fspecial('average');

t s a3=filter2 a3 t s_ _ _ Exercise:Observetheeffectwithlarger

averagefilter:

a7=fspecial('average',[7,7]);

t_sp_a7=filter2(a7,t_sp);

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Cleaningsaltandpeppernoise

Medianfilter:willingeneralreplaceanoisyvaluewithoneclosertoitssurroundings.Amedianfilterismoreeffective

than

convolution

when

the

goal

is

to

simultaneously

reducenoiseandpreserveedges. I=imread(coins.tif');

J=imnoise(I,'salt &pepper',0.02);

K=medfilt2(J);

imshow(J),figure,imshow(K)

Exercise:observethedifferenceofaverageandmedianfilterwithincreasingorderi.e.5x5etconincreasingsaltandpeppernoisei.e.0.4ormore.

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Guassian noise

Gaussiannoiseisanidealizedformofwhitenoise,whichiscausedbyrandomfluctuationsinthesignal.Gaussiannoiseis

whitenoise

which

is

normally

distributed.

If

the

image

is

representedasI,andtheGaussiannoisebyN

then we can model a nois ima e b sim l addin the two, I+N

t_ga=inoise(t,'gaussian');

Aswithsaltandpeppernoise,thegaussian

parameteralsocantakeoptionalvalues,givingthemeanandvarianceofthenoise.

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CleaningGaussiannoise

TherecouldmanycopiesofcorruptedimagehavingGaussiannoise.E.g satelliteimages

ifasatellitepassesoverthesamespotmanytimes,wewillobtainmanydifferentimagesof

the same lace.

InsuchacaseaverysimpleapproachtocleaningGaussiannoiseistosimplytakethe

averagethemeanofalltheimages.

75

edges

Edgescontainsomeofthemostusefulinformationinanimage.Wemayuseedgestomeasure:

thesizeofobjectsinanimage;

toisolateparticularobjectsfromtheirbackground;

.

Anedgemaybelooselydefinedasalineofpixelsshowinganobservabledifference.

76

OriginofEdges

depth discontinuity

surface colordiscontinuit

surface normal discontinuity

Edgesarecausedbyavarietyoffactors

illumination discontinuity

EdgeTypes

Step Edges

Line Edges

Change is measured by derivative in 1DBiggest change, derivative has maximummagnitude Or 2nd derivative is zero.Edge Detection:Difference operatorsParametric-model matchers


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Graylevelprofile

660 1 2 30 0 2 2 2 2 23 3 3 3 30 0 0 0 0 0 0 0 7 7 5 5

7

6

5

4

3

2

1

0

Edgesbydifference

suppose that the values of the "ramp" edge infigure

are, from left to right:20,20,20,20,20,20,100,180,180,180,180,180If we form the differences, by subtracting eachvalue from its successor, we obtain:

80

0,0,0,0,0,80,0,0,0,0and it is these values which are plotted nextfigure:

It appears that the difference tends toenhance edges, and reduce othercomponents.

We can define the difference in three separate ways:

81

Edgesdetectors

Threesteps:

Noisereduction

E.g.,medianfilter

E.g.,meanfilter

82

Largefilter=>removenoise

Largefilter=>removeedges

Smallfilter=>keepedges

Smallfilter=>keepnoise

Edgeenhancement

Edge

localisation

Edgesdetectors

Threesteps:

Noisereduction

Edgeenhancement

Calculatecandidatesfortheedges

83

Decidewhichedgecandidatestokeep

Edgesdetectors

Welllookatfourmethods(butothersexist!)

Withrespecttocomplexity(simplestfirst): Sobel

84

Laplacian

Canny

rew


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Gradientoperators

(a): Roberts cross operator (b): 3x3 Prewitt operator(c): Sobel operator (d) 4x4 Prewitt operator

clear

ic=imread('ic.jpg')

figure,imshow(ic),title('orginal')

ic=ic(:,:,1)

px=[101;101;101];%highlightsverticaledges

icx=filter2(px,ic);

%divide255converttheics matrixintodoubletobeshowninimshow

figure,imshow(icx/255),

title('px')

py=px';

icy=filter2(py,ic);%highlightshorizontaledges

figure,imshow(icy/255),title('py')

%wecancreateafigurecontainingalltheedgeswith:

edge_p=sqrt(icx.^2+icy.^2);

figure,imshow(edge_p/255),title('alledges')

%binaryimagecontainingedgesonlycanbeproducedbythresholding.

edge_t=im2bw(edge_p/255,0.3);

figure,imshow(edge_t);title('bwl')

%WecanobtainedgesbythePrewittlters directlybyusingthecommand

edge_p=edge(ic,'prewitt');

figure,imshow(edge_p);title('directperwettl')

Exercise:useRobertandsobel filtertodosamejob

86

TheCannyEdgeDetector

originalimage

(Lena)

The Canny Edge Detector

magnitude of the gradient

TheCannyEdgeDetector

After non-maximum suppression

Seconddifferences Abasicdefinitionofthefirstorderderivativeofaone

dimensionalfunctionf(x)is

Wedefineasecondorderderivativeasthedifference.

)()1( xfxfx

f+=

2

).(2)1()1(2

xfxfxfx

++=


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17/18

Implementation

+=

),(),(

),(),(),(2

2

yxfyxf

yxfyxfyxgIf the center coefficient is negative

If the center coefficient is positive

Laplacian filter image is superimposed on a dark featureless backgroundBackground can be recovered preserving the sharpness effect of thelaplacian operator simply by adding the original image and lapician image

),(2 yxf

Where f(x,y) is the original image

is Laplacian filtered image

g(x,y) is the sharpen image

Implementation closeall

f=imread('moon.jpg');

! fspecial istogenerate2Dfilter

w=fspecial('laplacian',0)

! implementationofequation3Aofslides,

g1=imfilter(f,w,'replicate')

figure,title('Lapician filteredimagewithoutim2double')

imshow(g1)

l l l l l l

!butbecaz ofuint8negativevalueshave beentruncated

!convertimageintodouble

f2=im2double(f);

g2=imfilter(f2,w,'replicate')

figure,title('Lapician filteredimagewithim2double')

imshow(g2)

! Restoregraytonelostbyusinglapician bysubtractingas centrecoefficientisnegative.

g=f2g2;

figure,title('sharpern imageusingLapician implementation')

imshow(g)98

Usingdifferentlaplacian operator,diognal maskaresharper.

closeall

f=imread('moon.jpg');

! fspecial istogenerate2Dfilter

w4=fspecial('laplacian',0)

w8=[111;1 81;111];

f=im2double(f);

g4=fimfilter(f,w4,'replicate');

g8=fimfilter(f,w8,'replicate');

imshow(f)

figure,imshow(g4)

figure,imshow(g8)

99

ZeroCrossing Ingeneralthesearetheplaceswherethefilterschanges

sign.Zerocrossingisdefinedinfilteredimagessatisfying

eitheroffollowing

Theyhavenegativevalueandarenexttoapixelwhosegreyvalueispositive.

Theyhaveavalueofzeroandarebetweennegativeandpositivevaluespixels.

100

OnemoremethodoftheEdge

Detection

TaketheLaplacefilterandapplyzerocrossing

I=imread('coins.bmp');

LP_filter=fspecial('laplacian',0);

= ' ', , , ,

_

verygoodresult????

Toeliminatethem,wemayfirstsmooththeimagewithaGaussianfilter.

Edgedetection;theMarrHildreth method:

101

MarrHildreth method

1. smooththeimagewithaGaussianlter,2. convolvetheresultwithalaplacian,3. fin dthezerocrossings. Methodtobeascloseaspossibletobiologicalvision. Thefirsttwostepscanbecombinedintoone,toproduceaLaplacian of

Gaussianor

LoG filter.

fspecial('log',13,2) h=fspecial('log',hsize,sigma)returnsarotationallysymmetric

Laplacian ofGaussianfilterofsizehsize withstandarddeviationsigma(positive).hsize canbeavectorspecifyingthenumberofrowsandcolumnsinh,oritcanbeascalar,inwhichcasehisasquarematrix.Thedefaultvalueforhsize is[55]and0.5forsigma.

log=fspecial('log',13,2); edge(ic,'zerocross',log);

102


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Edge Enhancement: Unsharp masking

Arelatedoperationistomakeedgesinanimageslightlysharperratherthanisolating,whichgenerallyresultsinanimagemorepleasingtothehumaneye.

Aprocesstosharpenimagesconsistsofsubtracting ablurredversionofanimagefromtheimageitself.Thisprocess,calledunsharpmasking,isexpressedas

),(),(),( yxfyxfyxfs =),( yxfs

),( yxf),( yxf

Where denotes the sharpened image obtained by unsharpmasking, and is a blurred version of

Sharpeningimage closeall

x=imread('butterfly.bmp');

figure,imshow(x(:,:,1)),title('original')

x=x(:,:,1);

f=fspecial('average');

104

xf=filter2(f,x);

xu=double(x)xf/1.5

figure,imshow(xu/70),title('sharpen edges')

Thelastcommandscalestheresultsothatimshow displaysanappropriateimage;

Highboostfiltering

Alliedtounsharp maskinglters arethehighboostfilters,whichareobtainedby

Highboost=A(orginal) lowpass,

g oos ere mage, hb s e ne a any

point(x,y)as1),(),(),( = AwhereyxfyxAfyxfhb

),(),(),()1(),( yxfyxfyxfAyxfhb +=

),(),()1(),( yxfyxfAyxf shb +=

This equation is applicable general and does not state explicityhow the sharp image is obtained

HighboostfilteringandLaplacian

IfwechoosetousetheLaplacian,thenweknowfs(x,y)

+

=

),(),(

),(),(2

2

yxfyxAf

yxfyxAff

hb

If the center coefficient is negative

If the center coefficient is positive

-1

-1

A+4 -1

-1

0 0

0 0

-1

-1

A+8 -1

-1

-1 -1

-1 -1

dip2 image enhancement1

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