Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.

1 중앙대학교 첨단영상대학원

CH 3 Image Enhancement in the Spatial DomainCH 3 Image Enhancement in the Spatial Domain

3.1 Background3.1 Background

),( of odneighborho someover defined ,on operator an :

image processed the:),(

imageinput the:),(

,),(

yxfT

yxg

yxf

yxfTyxg

Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.

2 중앙대학교 첨단영상대학원

Point ProcessingPoint Processing

)( odneighborho 11 rTs

Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.

3 중앙대학교 첨단영상대학원

3.2 Gray Level Transformations3.2 Gray Level Transformations

Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.

4 중앙대학교 첨단영상대학원

3.2.1 Image Negatives3.2.1 Image Negatives

rLs 1

Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.

5 중앙대학교 첨단영상대학원

3.2.2 Log Transformations3.2.2 Log Transformations

rcs 1log

Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.

6 중앙대학교 첨단영상대학원

3.2.3 Power-Law Transformation3.2.3 Power-Law Transformation

crs

Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.

7 중앙대학교 첨단영상대학원

Gamma CorrectionGamma Correction

Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.

8 중앙대학교 첨단영상대학원

Gamma Correction: Example 3.1Gamma Correction: Example 3.1

Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.

9 중앙대학교 첨단영상대학원

Gamma Correction: Example 3.2Gamma Correction: Example 3.2

Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.

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3.2.4 Piecewise-Linear Transformation

Contrast Stretching

3.2.4 Piecewise-Linear Transformation

Contrast Stretching

Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.

11 중앙대학교 첨단영상대학원

Gray-Level SlicingGray-Level Slicing

Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.

12 중앙대학교 첨단영상대학원

Bit-Plane SlicingBit-Plane Slicing

Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.

13 중앙대학교 첨단영상대학원

3.3 Histogram Processing

What is Histogram?

3.3 Histogram Processing

What is Histogram?

1,,1,0for

levelgray having image in the pixels ofnumber :

levelgray th - :

Histogram

Lk

rn

kr

nrh

kk

k

kk

1,,1,0for

levelgray having image in the pixels ofnumber :

levelgray th - :

image in the pixels ofnumber total:

Histogram Normalized

Lk

rn

kr

n

nnrp

kk

k

kk

Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.

14 중앙대학교 첨단영상대학원

3.3.1 Histogram Equalization

Fundamental Assumptions on the Transformation

3.3.1 Histogram Equalization

Fundamental Assumptions on the Transformation

10 ,

:ation transforminverse The

10for ,10 ii

increasinglly monotonica valued,-single i

:on sassumption Two

10 ,

1

ssTr

rrT

rT

rrTs

Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.

15 중앙대학교 첨단영상대학원

Histogram Equalization

The Continuous Case

Histogram Equalization

The Continuous Case

10 ,11

)(

functionation transformaConsider

,

y theory,probabilit elementaryan From

0

0

srp

rpds

drrpsp

rpdwwpdr

d

dr

rdT

dr

ds

dwwprTs

ds

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rrrs

r

r

r

r

r

rs

Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.

16 중앙대학교 첨단영상대학원

Histogram Equalization

The Discrete Case

Histogram Equalization

The Discrete Case

1,...,1,0 ,

1,...,1,0 ,

00

Lkn

nrprTs

Lkn

rrp

m

j

jk

jjrkk

kkr

Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.

17 중앙대학교 첨단영상대학원

3.3.2 Histogram Matching (Specification)

Development of Method

3.3.2 Histogram Matching (Specification)

Development of Method

Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.

18 중앙대학교 첨단영상대학원

Histogram Matching (Specification)

Implementation

Histogram Matching (Specification)

Implementation

Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.

19 중앙대학교 첨단영상대학원

Chapter 3Chapter 3

Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.

20 중앙대학교 첨단영상대학원

Chapter 3Chapter 3

Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.

21 중앙대학교 첨단영상대학원

Chapter 3Chapter 3

Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.

22 중앙대학교 첨단영상대학원

3.3.3 Local Enhancement3.3.3 Local Enhancement

Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.

23 중앙대학교 첨단영상대학원

3.3.4 Use of Histogram Statisticsfor Image Enhancement

3.3.4 Use of Histogram Statisticsfor Image Enhancement

tsSts

StsS

StststsS

i

L

ii

L

iiii

nL

iin

jjr

rpmr

rprm

rrpmr

rprmrpmrn

rn

rrirp

Lr

xy

xyxt

xy

xy

,

2

),(,

2

,,,

21

0

22

10

1

0

1

0

varianceandmean Local

of variance

,0 and ,1 Since

where,

ofmoment th The

of occurrence ofy Probabilit of th value theof histogram normalized :

1,0

Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.

24 중앙대학교 첨단영상대학원

otherwise,

and if,, 2100

yxf

DkDkMkmyxfEyxg GSGS xyxy

Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.

25 중앙대학교 첨단영상대학원

3.4 Enhancement UsingArithmetic/Logic Operations

3.4 Enhancement UsingArithmetic/Logic Operations

Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.

26 중앙대학교 첨단영상대학원

3.4.1 Image Subtraction3.4.1 Image Subtraction

Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.

27 중앙대학교 첨단영상대학원

Image Subtraction: Mask Mode RadiographyImage Subtraction: Mask Mode Radiography

Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.

28 중앙대학교 첨단영상대학원

3.4.2 Image Averaging3.4.2 Image Averaging

yxyx

yxyx

K

ii

K

KyxfyxE

yxgK

yx

yxyxfyxg

,,g

,2

,g2

1

1

1 and,,,g

,1

,g

eduncorrelat mean,-zero is where

,,,

Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.

29 중앙대학교 첨단영상대학원

Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.

30 중앙대학교 첨단영상대학원

3.5 Basics of Spatial Filtering3.5 Basics of Spatial Filtering

a

s

b

bt

tysxftswyxg

yxfwyxfwyxfw

yxfwyxfwR

1

,,,

1,11,1,10,1,0,0

,10,11,11,1

mn

iiimnmn zwzwzwR

111

Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.

31 중앙대학교 첨단영상대학원

mn

iiimnmn zwzwzwR

111

Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.

32 중앙대학교 첨단영상대학원

3.6 Smoothing Spatial Filters

3.6.1 Smoothing Linear Filters

3.6 Smoothing Spatial Filters

3.6.1 Smoothing Linear Filters

a

as

b

bt

a

as

b

bt

ii

tsw

tysxftswyxg

zR

,

,,,

9

1 9

1

Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.

33 중앙대학교 첨단영상대학원

Averaging Filter: Hubble ImageAveraging Filter: Hubble Image

Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.

34 중앙대학교 첨단영상대학원

3.6.2 Order Statistics Filters3.6.2 Order Statistics Filters

Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.

35 중앙대학교 첨단영상대학원

3.7 Sharpening Spatial Filters

3.7.1 Foundation

3.7 Sharpening Spatial Filters

3.7.1 Foundation

121

derivativeorder -second 1D, The

1

derivativeorder -first 1D, The

2

2

xfxfxfx

f

xfxfx

f

Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.

36 중앙대학교 첨단영상대학원

3.7.2 Second Derivatives: Laplacian3.7.2 Second Derivatives: Laplacian

),(4

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

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

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

Laplacian :derivativeorder -second 2D, The

2

2

2

2

2

2

2

2

22

yxf

yxfyxfyxfyxff

yxfyxfyxfy

f

yxfyxfyxfx

f

x

f

x

ff

Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.

37 중앙대학교 첨단영상대학원

LaplacianLaplacian

positive iscenter theif),(),(

negative iscenter theif),(),(),(

2

2

yxfyxf

yxfyxfyxg

Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.

38 중앙대학교 첨단영상대학원

Laplacian Enhancement: SimplificationLaplacian Enhancement: Simplification

)]1,()1,(

),1(),1([),(5

),(),(),( 2

yxfyxf

yxfyxfyxf

yxfyxfyxg

Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.

39 중앙대학교 첨단영상대학원

Unsharp Masking and High-Boost FilteringUnsharp Masking and High-Boost Filtering

),(,,

filteringboost -High

),(,,

masking Unsharp

yxfyxAfyxf

yxfyxfyxf

hb

s

Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.

40 중앙대학교 첨단영상대학원

3.7.3 First Derivatives: The Gradient3.7.3 First Derivatives: The Gradient

Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.

41 중앙대학교 첨단영상대학원

3.8 Combining Spatial Enhancement Methods3.8 Combining Spatial Enhancement Methods

Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.

42 중앙대학교 첨단영상대학원

Homework #2• Problems in Chapter 3

– 3.2(a), 3.8, 3.22, 3.27