chapter 3 image enhancement in the spatial domaincsie/ycliaw/dip/03_enhancement.pdf · © 2002 r....

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Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.www.imageprocessingbook.com

© 2002 R. C. Gonzalez & R. E. Woods

The principal objective of enhancementThe principal objective of enhancementto process an image so that the result is more suitablethan the original image for a specific application.

Enhancement methodsEnhancement methodsSpatial Domain (in this chapter)

based on direct manipulation of pixels in an image

Frequency Domain (in chapter 4)based on modifying the Fourier transform of an image

The viewer is the ultimate judge of how well ofThe viewer is the ultimate judge of how well ofa particular method works.a particular method works.

Chapter 3 Chapter 3 Image Enhancement in theImage Enhancement in theSpatial DomainSpatial Domain



Chapter 3 Chapter 3 Image Enhancement in theImage Enhancement in theSpatial DomainSpatial Domain

3.1 Background3.2 Some basic gray level transformations3.3 Histogram processing3.4 Enhancement using arithmetic/logic operations3.5 Basics of spatial filtering3.6 Smoothing spatial filters3.7 Sharpening spatial filters3.8 Combining spatial enhancement methods

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3.1 Background3.1 Background

Spatial domain methods operate directly onSpatial domain methods operate directly onimage pixelsimage pixels

T operates only for one pixel

MappingContrast StretchingThresholdingBinary Image

2)-(3.1 )(rTs =

( ) ( )[ ] 1)-(3.1 ,, yxfTyxg =




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– T operates with neighboring pixels• Mask (filter, kernel, template, window)




( )[ ] ( ) ( ) ( )( ) ( ) ( )( ) ( ) ( ) 222120

121110

020100

1,1,11,11,,1,

1,1,11,1,

myxfmyxfmyxfmyxfmyxfmyxf

myxfmyxfmyxfyxfT

×+++×++×−++×++×+×−

+×+−+×−+×−−=

=

222120

121110

020100

mmmmmmmmm

Mask


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=

91

91

91

91

91

91

91

91

91

Mask

Original Image Processed Image



3.2 3.2 Some basic gray level transformationsSome basic gray level transformations

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3.2 3.2 Some basic gray level transformationsSome basic gray level transformationsImage NegativeImage Negative

( ) 1)-(3.2 1 rLs −−=



3.2 3.2 Some basic gray level transformationsSome basic gray level transformations


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3.2 3.2 Some basic gray level transformationsSome basic gray level transformationsLog TransformationLog Transformation

( ) 2)-(3.2 1log rcs +=



3.2 3.2 Some basic gray level transformationsSome basic gray level transformationsLog TransformationLog Transformation


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3.2 3.2 Some basic gray level transformationsSome basic gray level transformationsPower-Law TransformationPower-Law Transformation

3)-(3.2 γcrs =




8







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3.2 3.2 Some basic gray level transformationsSome basic gray level transformationsPiecewise-Linear Transformation FunctionsPiecewise-Linear Transformation Functions

Contrast StretchingContrast Stretching




Processed ImageOriginal Image

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Gray-level slicingGray-level slicing



Processed ImageOriginal Image


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Bit-plane slicingBit-plane slicing




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3.3 Histogram Processing3.3 Histogram Processing

( ) kk nrh =



3.3 Histogram Processing3.3 Histogram Processing

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3.3 Histogram Processing3.3 Histogram ProcessingHistogram EqualizationHistogram Equalization

Transformation FunctionTransformation Function

Inverse functionInverse function

( ) 1)-(3.3 1r0 ≤≤= rTsConditions:(a) T(r) is single valued and

monotonically increasing(b) 0 ≤ T(r) ≤ 1 for 0 ≤ r ≤ 1

( ) 2)-(3.3 1s0 1 ≤≤= − sTr

*不一定符合條件(a)或(b)




PDFsPDFs((機率密度函式機率密度函式) ) of of rr and and ss

( )rpr

( ) ( ) 3)-(3.3 dsdrrpsp rs =s的機率密度函式：

r的機率密度函式：

s的機率密度函式為所有經3.3-1公式轉換後會對映到s值之所有r值之機率密度函式的總和

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If s is the Cumulative Density Function (CDF) of pr

*符合條件(a)與(b)



( ) ( )dsdrrpsp rs =


ps(s) is a uniform PDFBecause ps(s) is 1 for any pr(r)

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Discrete VersionDiscrete Version

rk = 第k階的灰階值, nk 是灰階值為 rk 之像素個數

1s0 k ≤≤




Histogram EqualizationHistogram Equalizationto produce an output image that has a uniformto produce an output image that has a uniformhistogramhistogram像素值均勻分佈可拉大影像明暗對比像素值均勻分佈可拉大影像明暗對比

proceduresprocedures求影像的求影像的HistogramHistogram求影像的機率密度函數求影像的機率密度函數

產生產生CDF(CDF(累積密度函數累積密度函數))T()T()使用使用T()T()處理每個像素處理每個像素

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3.3 Histogram Processing3.3 Histogram ProcessingHistogram Matching (Specification)Histogram Matching (Specification)

Development of the methodDevelopment of the methodrr是來源影像灰階值是來源影像灰階值

zz是目的影像灰階值是目的影像灰階值

T( ): r -> sT( ): r -> sG( ): z->sG( ): z->s

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Discrete VersionDiscrete Version





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ImplementationImplementation1.1.取得影像的取得影像的HistogramHistogram2.2.使用公式使用公式(3.3-13)(3.3-13)計算每個計算每個 sskk

3.3.使用公式使用公式(3.3-14)(3.3-14)取得取得pz(z)pz(z)的轉換函式的轉換函式GG4.4.使用公式使用公式(3.3-17)(3.3-17)計算每個計算每個 zzkk

5.5.使用步驟使用步驟2-42-4的結果處理每個像素的結果處理每個像素取得取得 rrkk 的對映像素的對映像素sskk

取得取得 sskk的對映像素的對映像素zzkk



Comparison between histogramComparison between histogramequalization and histogram matchingequalization and histogram matching

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3.3 Histogram Processing3.3 Histogram ProcessingLocal EnhancementLocal Enhancement

步驟:1.定義方型或矩型的大小 2.針對每個像素 2.1.找出以目前像素為中心點之區塊內像素的histogram 2.2.使用histogram equalization/matching 方法取得像素對應值



3.3 Histogram Processing3.3 Histogram ProcessingUse of histogram statistice for image enhancementUse of histogram statistice for image enhancement

使用像素統計資訊使用像素統計資訊

子影像 Sx,y 的區域統資訊

mean value

N-Norm

2-NormStandard Deviation

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Block Size = 3x3


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© 2002 R. C. Gonzalez & R. E. Woods E=4.0, k0=0.4, k1=0.02, k2=0.4




3.4 Enhancement using Arithmetic/Logic3.4 Enhancement using Arithmetic/LogicOperationsOperations

performed on a pixel by pixel basis between two orperformed on a pixel by pixel basis between two ormore imagesmore imagesLogic OperationsLogic Operations

ANDANDORORNOTNOT

Arithmetic OperationsArithmetic OperationsSubstractionSubstractionAveragingAveraging

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Image SubstractionImage Substraction

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取得影像 = 原始影像 + 雜訊

平均結果


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3.4 Enhancement using Arithmetic/Logic3.4 Enhancement using Arithmetic/LogicOperations - Operations - Image averagingImage averaging



3.4 Enhancement using Arithmetic/Logic3.4 Enhancement using Arithmetic/LogicOperations - Operations - Image averagingImage averaging

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3.5 Basics of spatial filtering3.5 Basics of spatial filtering

MaskMaskfilter, kernel, templete, windowfilter, kernel, templete, window



3.5 Basics of spatial filtering3.5 Basics of spatial filtering

MaskMaskfilter, kernel, templete, windowfilter, kernel, templete, windowconverlution mask/kernelconverlution mask/kernel

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3.6 Smoothing Spatial Filter3.6 Smoothing Spatial Filter

Smoothing filters are used forSmoothing filters are used forblurringblurringnoise reductionnoise reduction



3.6 Smoothing Spatial Filter3.6 Smoothing Spatial FilterSmoothing Linear FiltersSmoothing Linear Filters

Smoothing linear filtersSmoothing linear filtersalso called

averaging filterlowpass filter

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Mask大小與影像平滑效果的關係




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3.6 Smoothing Spatial Filter3.6 Smoothing Spatial FilterOrder-Statistics FiltersOrder-Statistics Filters

Non-linear filtersNon-linear filtersMedian filterMedian filter

exampleexampleunsorted (60,20,15,23,35,47,78,53,65)unsorted (60,20,15,23,35,47,78,53,65)sorted (15,20,23,35,sorted (15,20,23,35,4747,53,60,65,78),53,60,65,78)the median is the median is 4747

Max filterMax filterMin filterMin filter



3.6 Smoothing Spatial Filter3.6 Smoothing Spatial FilterOrder-Statistics FiltersOrder-Statistics Filters

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3.7 Sharpening Spatial Filters3.7 Sharpening Spatial Filters

Sharpening Spatial filters are used toSharpening Spatial filters are used tohighlight fine detailhighlight fine detailenhance detail that has been blurredenhance detail that has been blurred



3.7 Sharpening Spatial Filters3.7 Sharpening Spatial FiltersFoundationFoundation

First-order derivativeFirst-order derivative

Second-order derivativeSecond-order derivative

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3.7 Sharpening Spatial Filters3.7 Sharpening Spatial FiltersFoundationFoundation



3.7 Sharpening Spatial Filters3.7 Sharpening Spatial FiltersUse of second Derivatives for enhancementUse of second Derivatives for enhancement

The LaplacianThe LaplacianDevelopment of the methodDevelopment of the method

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FiltersFilters




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SimplificationSimplification




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Unsharp masking and high-boost filteringUnsharp masking and high-boost filtering




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3.7 Sharpening Spatial Filters3.7 Sharpening Spatial FiltersUse of First Derivatives for enhancementUse of First Derivatives for enhancement

The Gradient (The Gradient (坡度坡度))

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(d) and (e) are calledSobel Operators

(b) and (c) are refered asRoberts cross-gradient Operators

for 3 x 3 masks




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水平強度




垂直強度


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3.8 Combining Spatial Enhancement3.8 Combining Spatial EnhancementMethodsMethods



3.8 Combining Spatial Enhancement3.8 Combining Spatial EnhancementMethodsMethods

chapter 3 image enhancement in the spatial domaincsie/ycliaw/dip/03_enhancement.pdf · © 2002 r....

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