ch03-enhancementspdom

8/19/2019 ch03-enhancementspdom

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H.R. Pourreza

Digital ImageProcessing

H.R.Pourreza

Image Enhancement in theSpatial Domain

(Chapter 3)


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The principal objective of enhancement is toprocess an images so that the result is moresuitable than the original image for aSPECIFIC application

Category of image enhancement• Spatial domain• Frequency domain

Objective


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Background

g ( x , y) = T [ f ( x , y) ]


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Point Processing,Gray-Level rans!or"ation Function

s = T (r )

Contrast

stretching

Thresholding


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g ( x , y) = T [ f ( x , y) ] 1

0

0

-1

0

0

0

0

0

T

f ( x, y) g ( x, y)

#ask Processing Filtering


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I"age $egative

s = L - 1 - r


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Log rans!or"ations

s = c log(1+r )

Pixel values dynamic range=[ ! "#$%"&'


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Po%er-La% rans!or"ations

s = cr

s = r 2.5

r = [1 10 20 30 40 210 220 230 240 250 255]

s(γ = 2.5) = [0 0 0 1 2 157 176 197 219 243 255]

s(γ =.4) = [28 70 92 108 122 236 240 245 249 253 255]


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&uto"atic

Selection


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Po%er-La% rans!or"ations - Ga""aCorrection


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c=1

γ = 0.4c=1

γ = 0.3

c=1γ = 0.6


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c=1

γ = 3

c=1

γ = 5

c=1

γ = 4


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• A!antage• Ar"itraril# comple$

• Disa!antage• %ore user input

• pe o' &rans'ormations•

Contrast stretching• ra#le!el slicing

• *itplane slicing

Piecewise-Linear Transformation

Functions


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Contrast Stretc'ing

(bjective+ Increase the #namic range o' the gra#le!els in the image

Causes for poorimagePoor illumination,rong lens aperture,rong shutter spee-ac o' #namicrangein the imaging sensor


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)xample "For image *ith intensity range [$ ! "$'+hat should ,r"-s". and ,r/-s/. be to increase

the dynamic range of the image to [ !/$$'0

r

s

Contrast Stretc'ing


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(bjective1 2ighlighting a speci3c range of gray levels inan image#

Gray-Level Slicing


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255 138 30

65 12 201

180 111 85

255

138

30

65

12

201

183

111

85

1 1 1 1 1 1 1 1

0 1 0 1 0 0 0 1

1 1 1 1 1 0 0 0

1 0 0 0 0 0 1 0

0 0 1 1 0 0 0 0

1 0 0 1 0 0 1 1

1 1 1 0 1 1 0 1

1 1 1 1 0 1 1 0

1 0 1 0 1 0 1 0

MSBLSB

1 1 0

0 0 1

1 0 0

MSB plane

1 0 1

1 0 1

1 1 1

LSB plane

Bit-Plane Slicing


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Bit-Plane Slicing


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Bit-Plane Slicing


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2istogram &he histogram o' a igital image /ith gra# le!els inthe range 012 L4 is a iscrete 'unction

h(r k

) 5 nk

2

/here r k is the k th gra# le!el an nk is the num"er o'

pi$els in the image ha!ing gra# le!el r k .

4ormali5ed 2istogram

Di!iing each !alue o' the histogram "# the total numo' pi$els in the image2 enote "# n.

p(r k ) 5 nk 6n.

7ormalize histogram pro!ie use'ul image statistics.

(istogra" Processing


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!n"#$on %o&'al$e*$# = 'g*$#($'g)

[,/]=$e($'g)

$#=e&o(256,1)

o& & = 1o& "=1/

$#($'g(&,")+1,1)=$#($'g(&,")+1,1)+1 8

en

en

%o&'al$e*$# = $#(/) plo#(%o&'al$e*$#)

(istogra" E)traction using #atlab


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(istogra" Processing


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2istogram equali5ation is used to enhance imagecontrast and gray!level detail by spreading thehistogram of the original image# s = , r . r "-*here r and s are normali5ed pixel intensities

Conditions for the transformation*a+ , r . is single!valued and monotonically increasing

in the interval r "

,b. , r . " for r "

1

(istogra" Eualiation


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9":ecti!e o' histogram e;ualization &rans'orm the histogram 'unction o' theoriginal image pr (r ) to a uni'orm histogram

'unction. ps(s) 5 1≤ s ≤

!al$e&

&ano&'a#$on pr (r ) p s( s)

∫ ==r

r dww pr T s

0

)()( ∑=

==k

j

jr k k r pr T s0

)()(

Continuous case Discrete case



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0

1

2

3

128

129

130

253

254

255

0

0

0

0.004

0.15

0.05

0.005

0.006

0.004

pr (r k )k

T (r k )

00

0

0

00.004

0.154

0.204

0.989

0.994

1

sk

0

0

0

0

10

39

52

252

253

255

0

0.004

0.008

0.011

0.5

0.505

0.51

0.992

0.996

1

r k

255 255

np!# $'age !#p!# $'age


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255


(i E li il$


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15

1

8

0.5

4

0.25

12

0.75

0.4

0.2

0.3

0.1

0

1

23

4

5

67

8

9

10

11

12

13

14

15

0

0

00

0.09

0.06

0.10.15

0.3

0.18

0.05

0.07

0

0

0

0

0

0

00

0.09

0.15

0.250.4

0.7

0.88

0.93

1

1

1

1

1

r k pr (r k ) %o&'al$e sk

0

0

00

1

2

46

11

13

14

15

15

15

15

15

sk

plo#( sk )

np!# $'age $e 100 × 100


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6s histogram equali5ation a good approachto enhance the belo* image0

(istogra" #atc'ing


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2istogram 7atching method generates aprocessed image that has a speci3edhistogram#

np!# $'age

pr (r )

T (r )

∫ r

r dt t p

0

)( s

e$&e!#p!# $'age

p z ( z )

G ( z )

∫ z

z dt t p

0

)( v

s ≈ v, $n"e :o#; $'a#el? !n$o&' pdf

z = G-1[T ( s )] s = G[T ( r )]

(istogra" #atc'ing


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(istogra" #atc'ing


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(istogra" #atc'ing


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0.6

0.12

0.08

0.0

0.01

0.005

0

0.6

0.72

0.8

0.8

0.9

0.95

1

153

184

204

204

230

242

255



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) %oi'# the histogram o' the image to o"tain p z ( z ).

e histogram in

step .3) =in the in!erse G ( z )?) Enhance image is

o"taine "# appl#ing G to thepi$els o' the histograme;ualizeimage sho/n in =ig. 3.


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125128

0.98

0.002

250255

0.70.3

178

255

Lo"al $#og&a'

@lo:al $#og&a'

125 128

Local (istogra" En'ance"ent


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Local (istogra" En'ance"ent


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Contrast manipulation using local statistics2 such as the mean an!ariance2 is use'ul 'or images /here part o' the image is accepta"ut other parts ma# contain hien 'eatures o' interest.

(istogra" Statistics !or I"age En'anc.


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-et ( x 2 y ) "e the coorinates o' a pi$el in an image2 an let S xy enote a neigh"orhoo (su"image) o' speci>e size2 centere at( x 2 y ).

.)(][

)(

),(

,2

,2

),(

,,

∑

∑

∈

∈

−=

=

xy

xy xy

xy xy

S t s

t sS t sS

S t s

t st sS

r pmr

r pr m

σ

&he local mean an !ariance are the ecision 'actors to /hetherlocal enhancement or not.



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≤≤≤=

o#;e&e

parameters

E = 4,

k 0 = 0.4,

k 1= 0.02,

k = 0.4

S$e o lo"al a&ea = 3 × 3



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125 135 145 135 ..

168 175 158 149 ..

210 231 215 129 ..

187 192 145 200 ..

174

'age Mean

164

187

µ ( x, y)

σ( x, y)

E



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Enhance Image 9riginal Image



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Arithmetic6logic operations in!ol!ing images areper'orme on a pi$el"#pi$el "asis "et/een t/o ormore images.

8rithmetic (perations Aition2 Su"traction2 %ultiplication2 an Di!ision

9ogic (perations

A7D2 9R2 79&

En'ance"ent /sing &rit'"etic0LogicO1.


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A%

-ogic operations are per'orme on the "inar#

representation o' the pi$el intensities

En'ance"ent /sing 84: and (; LogicO1.


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En'ance"ent /sing &rit'"etic O1. 2S


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Pro"lem+ &he pi$el intensities in the i@erence image can range 'rom


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[ ]2

),(

2

),(

1

1),(),(

),(1

),(

),(),(),(

y x y x g

k

k

y x f y x g E

y x g k

y x g

y x y x f y x g

η σ σ

η

==

=

+=

∑=

9riginal image 7oise /ith zero mean

En'ance"ent /sing &rit'"etic O1.8veraging


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@a!$an %o$e

'ean = 0

a&$an"e = 64

! = 8

! = 32

! = 16

! = 128

f ( x, y) g ( x, y)

µ µ+σµ-σ x



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Di@erenceimages"et/eenoriginal imagean imageso"taine 'roma!eraging.

! = 8

! = 16

! = 32

! = 128

7otice themean an

!arianceo' thei@erenceimagesecrease as

K increases.



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Spatial >ltering are>ltering operationsper'orme on the pi$elintensities o' an imagean not on the're;uenc# componentso' the image.

∑ ∑−= −=

++="

" s

#

#t

t y s x f t sw y x g ),(),(),(

" = (m - 1) 2 # = ($ - 1) 2

Basics o! S1atial Filtering - 9inear


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Response2 R2 o' an m × n mas at an# point ( x 2 y )

∑=

=m$

z w %

1

Special consieration is gi!en /hen the center o' theapproach the "oarer o' the image.

Basics o! S1atial Filtering


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7onlinear spatial >lters operate on neigh"orhoos2 anthe mechanics o' sliing a mas past an image are thesame as /as :ust outline. In general ho/e!er2 the>ltering operation is "ase conitionall# on the !alues o'

the pi$el in the neigh"orhoo uner consieration2 anthe# o not e$plicitl# use coeBcients in the sumo'proucts manner escri"e pre!iousl#.

)xampleComputation 'or the meian is a nonlinear operation.

$onlinear o! S1atial Filtering


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Smoothing >lters are use 7oise reuction Smoothing o' 'alse contours Reuction o' irrele!ant etail

nesira"le sie e@ect o' smoothing >lters *lur eges

Ce$g;#e

ae&age

Bo>

$l#e&

,eighte a!erage >lterreuces "lurring in the

smoothing process.

S"oot'ing S1atial Filtering - Linear &veraging *lo%-1ass+ Filters


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$ = $l#e& $e

$ = 3

$ = 5 $ = 9

$ = 15

$ = 35

S"oot'ing S1atial Filtering 2 Linear &veraging *lo%-1ass+ Filters


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$l#e& $e

$ = 15

;&; = 25D o

;$g;e# $n#en$#?

S"oot'ing S1atial Filtering &veraging 4 'res'old


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9rerstatistics >lters are nonlinear spatial >lters/hoseresponse is "ase on orering (raning) the pi$elscontaine in the image area encompasse "# the

>lter2 an then replacing the !alue o' the centerpi$el /ith the !alue etermine "# the raningresult.3 × 3 Me$an $l#e& [10 125 125 135 141 141 144 230 240] = 141

3 × 3 Ma> $l#e& [10 125 125 135 141 141 144 230 240] = 2403 × 3 M$n $l#e& [10 125 125 135 141 141 144 230 240] = 10

%eian >lter eliminates isolate clusters o' pi$elsthat are light or ar /ith respect to their neigh"ors2an /hose area is less than n


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$ = 3

Ae&age

$l#e&

$ = 3

Me$an

$l#e&

Order Statistic Filters


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The principal objective of sharpening is tohighlight 3ne detail in an image or toenhance detail that has been blurred#

∫

∑9

1

9

1

9

1

91

z

z

'age Bl!&&e 'age

The derivatives of a digital function are de3ned interms of di>erences#

S'ar1ening S1atial Filters


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Re;uirements 'or igital eri!ati!e =irst eri!ati!e ) %ust "e zero in at segment


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Comparing the response bet*een 3rst! and second!orderedderivatives1". First!order derivative produce thic?er edge/. Second!order derivative have a stronger responseto 3ne detail- such as thin lines and isolated points#@. First!order derivatives generally have a strongerresponse to a gray!level step A/ B "$B. Second!order derivatives produce a doubleresponse at step changes in gray level#

In general the secon eri!ati!e is "etter than the >rsteri!ati!e 'or image enhancement. &he principle use o' >rsteri!ati!e is 'or ege e$traction.


/se o! First 5erivative !or Edge


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First derivatives in image processing are implementedusing the magnitude of the gradient#

y x

t

GG y

f

x

f m"g f

y

f

x

f

+≈

∂∂

+

∂∂

=∇=∇

∂∂

∂∂

=∇

5.022

)( f

f z 1 z 2

z 6 z 8

z 4 z 7

z 3

z 9 z 5

;oberts operator

G> = ( z 9- z 5) an G? = ( z 8 - z 6)Sobel operator

G> = ( z 3+2 z 6 +9) - ( z 1+2 z 4+7) an

G?

= ( z 7

+2 z 8

+9

) - ( z 1

+2 z 2

+3

)

/se o! First 5erivative !or EdgeE)tractionGradient


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f ( x, y) = [40, 140]

E. 0 0 0 0 0 0

E. 0 200 400 400 400 400 EE

E. 0 400 600 400 400 400 E...

E. 0 400 400 0 0 0

E. 0 400 400 0 0 0

E. 0 400 400 0 0 0

-1 -2

0

2

0

1

-1

1

0

-1 0

2

0

-2

-1

1

1

0

E 0 0 0 0 0

E 0 100 200 200 200

E 0 200 0 0 0

E 0 200 0 0 0

-11

-11




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2

2

2

22

y

f

x

f f

∂

∂+

∂

∂=∇

)],(4)1,()1,(),1(),1([

),(2)1,()1,(

),(2),1(),1(

2

2

2

2

2

y y f y x f y x f y x f y x f f

y x f y x f y x f y

f

y x f y x f y x f x

f

−−+++−++=∇

−−++=∂∂

−−++=∂∂

6nd 5erivative 2 La1lacian


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2

2

2

22

y

f

x

f f

∂

∂+

∂

∂=∇

6sotropic 3lter response is independent of thedirection of the discontinuities in the image to*hich the 3lter is applied#

/se o! 6nd 5erivative !or En'ance"ent La1lacian


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g ( x, y) = f ( x, y) -

0 1

1

1

1

0

0

0

-4

),(2 y x f ∇

=

)],(4)1,()1,(),1(),1([2 y x f y x f y x f y x f y x f f −−+++−++=∇

/se o! 6nd 5erivative !or En'ance"ent La1lacian


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High"oost >ltering is use /hen the original image is"lurre an ar.

),(),( 2 y x f y x &f f '# ∇−= & 1

/n-s'ar1 #asking and (ig'-boostFiltering


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( :)

/n-s'ar1 #asking and (ig'-boostFiltering

Co"bining S1atial


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Co"bining S1atialEn'ance"ent#et'ods

Co"bining S1atial


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Co"bining S1atialEn'ance"ent#et'ods

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