Local Enhancement Histogram processing methods are global processing, in the sense that pixels are modified by a transformation function based on the gray-level

Local EnhancementLocal Enhancement

Histogram processing methods are Histogram processing methods are global processing, in the sense that global processing, in the sense that pixels are modified by a pixels are modified by a transformation function based on the transformation function based on the gray-level content of an entire gray-level content of an entire image.image.

Sometimes, we may need to enhance Sometimes, we may need to enhance details over small areas in an image, details over small areas in an image, which is called a local enhancement.which is called a local enhancement.

Local EnhancementLocal Enhancement

define a square or rectangular neighborhood and move the define a square or rectangular neighborhood and move the center of this area from pixel to pixel.center of this area from pixel to pixel.

at each location, the histogram of the points in the at each location, the histogram of the points in the neighborhood is computed and either histogram equalization neighborhood is computed and either histogram equalization or histogram specification transformation function is obtained.or histogram specification transformation function is obtained.

another approach used to reduce computation is to utilize another approach used to reduce computation is to utilize nonoverlapping regions, but it usually produces an nonoverlapping regions, but it usually produces an undesirable checkerboard effect.undesirable checkerboard effect.

a) Original image (slightly blurred to reduce noise)

b) global histogram equalization (enhance noise & slightly increase contrast but the construction is not changed)

c) local histogram equalization using 7x7 neighborhood (reveals the small squares inside larger ones of the original image. (a) (b) (c)

Explain the result in c)Explain the result in c)

Basically, the original image consists of Basically, the original image consists of many small squares inside the larger dark many small squares inside the larger dark ones.ones.

However, the small squares were too close However, the small squares were too close in gray level to the larger ones, and their in gray level to the larger ones, and their sizes were too small to influence global sizes were too small to influence global histogram equalization significantly.histogram equalization significantly.

So, when we use the local enhancement So, when we use the local enhancement technique, it reveals the small areas.technique, it reveals the small areas.

Note also the finer noise texture is resulted Note also the finer noise texture is resulted by the local processing using relatively by the local processing using relatively small neighborhoods.small neighborhoods.

Enhancement using Enhancement using Arithmetic/Logic OperationsArithmetic/Logic Operations

Arithmetic/Logic operations perform Arithmetic/Logic operations perform on pixel by pixel basis between two on pixel by pixel basis between two or more imagesor more images

except NOT operation which perform except NOT operation which perform only on a single imageonly on a single image

Logic OperationsLogic Operations

Logic operation performs on gray-Logic operation performs on gray-level images, the pixel values are level images, the pixel values are processed as binary numbersprocessed as binary numbers

light represents a binary 1, and dark light represents a binary 1, and dark represents a binary 0 represents a binary 0

NOT operation = negative NOT operation = negative transformationtransformation

Example of AND OperationExample of AND Operation

original image AND image mask

result of AND

operation

Example of OR OperationExample of OR Operation

original image OR image mask

result of OR operation

Image SubtractionImage Subtraction

g(x,y) = f(x,y) – h(x,y)g(x,y) = f(x,y) – h(x,y)

enhancement of the differences enhancement of the differences between imagesbetween images

Image SubtractionImage Subtraction

a). original fractal imagea). original fractal image b). result of setting the four b). result of setting the four

lower-order bit planes to zerolower-order bit planes to zero• refer to the bit-plane slicingrefer to the bit-plane slicing• the higher planes contribute the higher planes contribute

significant detailsignificant detail• the lower planes contribute the lower planes contribute

more to fine detailmore to fine detail• image b). is nearly identical image b). is nearly identical

visually to image a), with a visually to image a), with a very slightly drop in overall very slightly drop in overall contrast due to less variability contrast due to less variability of the gray-level values in the of the gray-level values in the image.image.

c). difference between a). and c). difference between a). and b). (nearly black)b). (nearly black)

d). histogram equalization of d). histogram equalization of c). (perform contrast c). (perform contrast stretching transformation)stretching transformation)

aa bb

cc dd

Spatial FilteringSpatial Filtering

use filter (can also be called as use filter (can also be called as mask/kernel/template or window)mask/kernel/template or window)

the values in a filter subimage are the values in a filter subimage are referred to as coefficients, rather than referred to as coefficients, rather than pixel.pixel.

our focus will be on masks of odd our focus will be on masks of odd sizes, e.g. 3x3, 5x5,…sizes, e.g. 3x3, 5x5,…

Spatial Filtering ProcessSpatial Filtering Process

simply move the filter mask from simply move the filter mask from point to point in an image.point to point in an image.

at each point (x,y), the response of at each point (x,y), the response of the filter at that point is calculated the filter at that point is calculated using a predefined relationship.using a predefined relationship.

mn

iiii

mnmn

zw

zwzwzwR ...2211

Smoothing Spatial FiltersSmoothing Spatial Filters

used for blurring and for noise used for blurring and for noise reductionreduction

blurring is used in preprocessing steps, blurring is used in preprocessing steps, such as such as • removal of small details from an image removal of small details from an image

prior to object extractionprior to object extraction• bridging of small gaps in lines or curvesbridging of small gaps in lines or curves

noise reduction can be accomplished noise reduction can be accomplished by blurring with a linear filter and also by blurring with a linear filter and also by a nonlinear filterby a nonlinear filter

Smoothing Linear FiltersSmoothing Linear Filters

output is simply the average of the output is simply the average of the pixels contained in the neighborhood of pixels contained in the neighborhood of the filter mask.the filter mask.

called averaging filters or lowpass filters.called averaging filters or lowpass filters.

Smoothing Linear FiltersSmoothing Linear Filters

replacing the value of every pixel in an replacing the value of every pixel in an image by the average of the gray levels in image by the average of the gray levels in the neighborhood will reduce the “sharp” the neighborhood will reduce the “sharp” transitions in gray levels.transitions in gray levels.

sharp transitionssharp transitions• random noise in the imagerandom noise in the image• edges of objects in the imageedges of objects in the image

thus, smoothing can reduce noises thus, smoothing can reduce noises (desirable) and blur edges (undesirable)(desirable) and blur edges (undesirable)

3x3 Smoothing Linear Filters3x3 Smoothing Linear Filters

box filter weighted average

the center is the most important and other pixels are inversely weighted as a function of their distance from the center of the mask

Weighted average filterWeighted average filter

the basic strategy behind weighting the basic strategy behind weighting the center point the highest and then the center point the highest and then reducing the value of the coefficients reducing the value of the coefficients as a function of increasing distance as a function of increasing distance from the origin is simply from the origin is simply an attempt an attempt to reduce blurring in the to reduce blurring in the smoothing processsmoothing process..

ExampleExample

a). original image 500x500 a). original image 500x500 pixelpixel

b). - f). results of smoothing b). - f). results of smoothing with square averaging filter with square averaging filter masks of size n = 3, 5, 9, 15 masks of size n = 3, 5, 9, 15 and 35, respectively.and 35, respectively.

Note:Note:• big mask is used to eliminate big mask is used to eliminate

small objects from an image.small objects from an image.• the size of the mask establishes the size of the mask establishes

the relative size of the objects the relative size of the objects that will be blended with the that will be blended with the background.background.

aa bb

cc dd

ee ff

Order-Statistics Filters (Nonlinear Order-Statistics Filters (Nonlinear Filters)Filters)

the response is based on ordering the response is based on ordering (ranking) the pixels contained in the (ranking) the pixels contained in the image area encompassed by the filterimage area encompassed by the filter

exampleexample• median filter : R = median{zmedian filter : R = median{zk k |k = 1,2,|k = 1,2,

…,n x n}…,n x n}• max filter : R = max{zmax filter : R = max{zk k |k = 1,2,…,n x n}|k = 1,2,…,n x n}• min filter : R = min{zmin filter : R = min{zk k |k = 1,2,…,n x n}|k = 1,2,…,n x n}

note: n x n is the size of the masknote: n x n is the size of the mask

Median FiltersMedian Filters

replaces the value of a pixel by the median replaces the value of a pixel by the median of the gray levels in the neighborhood of of the gray levels in the neighborhood of that pixel (the original value of the pixel is that pixel (the original value of the pixel is included in the computation of the median)included in the computation of the median)

quite popular because for certain types of quite popular because for certain types of random noise (random noise (impulse noise impulse noise salt and salt and pepper noisepepper noise) , they ) , they provide excellent provide excellent noise-reduction capabilitiesnoise-reduction capabilities, with , with considering considering less blurring than linear less blurring than linear smoothing filters of similar size.smoothing filters of similar size.

2626

Example : Median FiltersExample : Median Filters

2727

Sharpening Spatial FiltersSharpening Spatial Filters

to highlight fine detail in an image to highlight fine detail in an image or to enhance detail that has been or to enhance detail that has been

blurred, either in error or as a natural blurred, either in error or as a natural effect of a particular method of effect of a particular method of image acquisition.image acquisition.

2828

Blurring vs. SharpeningBlurring vs. Sharpening

as we know that blurring can be done as we know that blurring can be done in spatial domain by pixel averaging in in spatial domain by pixel averaging in a neighbors a neighbors

since averaging is analogous to since averaging is analogous to integrationintegration

thus, we can guess that the sharpening thus, we can guess that the sharpening must be accomplished by must be accomplished by spatial spatial differentiation.differentiation.

2929

Derivative operatorDerivative operator

the strength of the response of a derivative the strength of the response of a derivative operator is proportional to the degree of operator is proportional to the degree of discontinuity of the image at the point at discontinuity of the image at the point at which the operator is applied.which the operator is applied.

thus, image differentiation thus, image differentiation • enhances edges and other discontinuities enhances edges and other discontinuities

(noise)(noise)• deemphasizes area with slowly varying gray-deemphasizes area with slowly varying gray-

level values.level values.

3030

First-order derivativeFirst-order derivative

a basic definition of the first-order a basic definition of the first-order derivative of a one-dimensional derivative of a one-dimensional function f(x) is the differencefunction f(x) is the difference

)()1( xfxfx

f

3131

Second-order derivativeSecond-order derivative

similarly, we define the second-order similarly, we define the second-order derivative of a one-dimensional derivative of a one-dimensional function f(x) is the differencefunction f(x) is the difference

)(2)1()1(2

2

xfxfxfx

f

Response of First and Second Response of First and Second order derivativesorder derivatives

Response of first order derivative is:Response of first order derivative is: zero in flat segments (area of constant grey zero in flat segments (area of constant grey

values)values) Non zero at the onset of a grey level step or rampNon zero at the onset of a grey level step or ramp Non zero along ramps Non zero along ramps

Response of second order derivative is:Response of second order derivative is: Zero in flat areasZero in flat areas Non zero at the onset of a grey level step or rampNon zero at the onset of a grey level step or ramp Zero along ramps of constant slopeZero along ramps of constant slope

First and Second-order derivative First and Second-order derivative of f(x,y)of f(x,y)

when we consider an image function when we consider an image function of two variables, f(x,y), at which time of two variables, f(x,y), at which time we will dealing with partial we will dealing with partial derivatives along the two spatial derivatives along the two spatial axes.axes.

y

yxf

x

yxf

yx

yxf

),(),(),(f

2

2

2

22 ),(),(

y

yxf

x

yxff

(linear operator)

Laplacian operator

Gradient operator

Discrete Form of LaplacianDiscrete Form of Laplacian

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

2

yxfyxfyxfx

f

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

2

yxfyxfyxfy

f

from

yield,

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

),1(),1([2

yxfyxfyxf

yxfyxff

Result Laplacian maskResult Laplacian mask

Laplacian mask implemented an Laplacian mask implemented an extension of diagonal neighborsextension of diagonal neighbors

Other implementation of Laplacian Other implementation of Laplacian masksmasks

give the same result, but we have to keep in mind that when combining (add / subtract) a Laplacian-filtered image with another image.

Effect of Laplacian OperatorEffect of Laplacian Operator

as it is a derivative operator,as it is a derivative operator,• it highlights gray-level discontinuities in it highlights gray-level discontinuities in

an imagean image• it deemphasizes regions with slowly it deemphasizes regions with slowly

varying gray levelsvarying gray levels tends to produce images that have tends to produce images that have

• grayish edge lines and other grayish edge lines and other discontinuities, all superimposed on a discontinuities, all superimposed on a dark, dark,

• featureless background.featureless background.

Correct the effect of featureless Correct the effect of featureless backgroundbackground

easily by adding the original and easily by adding the original and Laplacian image.Laplacian image.

be careful with the Laplacian filter usedbe careful with the Laplacian filter used

),(),(

),(),(),(

2

2

yxfyxf

yxfyxfyxg

if the center coefficient of the Laplacian mask is negative

if the center coefficient of the Laplacian mask is positive

ExampleExample

a). image of the North a). image of the North pole of the moonpole of the moon

b). Laplacian-filtered b). Laplacian-filtered image with image with

c). Laplacian image c). Laplacian image scaled for display scaled for display purposespurposes

d). image enhanced by d). image enhanced by addition with original addition with original image image

11 11 11

11 -8-8 11

11 11 11

Mask of Laplacian + additionMask of Laplacian + addition

to simply the computation, we can to simply the computation, we can create a mask which do both create a mask which do both operations, Laplacian Filter and operations, Laplacian Filter and Addition the original image.Addition the original image.

Mask of Laplacian + additionMask of Laplacian + addition

00 -1-1 00

-1-1 55 -1-1

00 -1-1 00

)]1,()1,(

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

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

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

yxfyxf

yxfyxfyxf

yxfyxfyxf

yxfyxfyxfyxg

ExampleExample

NoteNote

00--11

00

--11

55--11

00--11

00

00 00 00

00 11 00

00 00 00

),(),(

),(),(),(

2

2

yxfyxf

yxfyxfyxg

= +00

--11

00

--11

44--11

00--11

00

00--11

00

--11

99--11

00--11

00

00 00 00

00 11 00

00 00 00= +

00--11

00

--11

88--11

00--11

00

Unsharp maskingUnsharp masking

to subtract a blurred version of an image to subtract a blurred version of an image produces sharpening output image.produces sharpening output image.

),(),(),( yxfyxfyxf s

sharpened image = original image – blurred imagesharpened image = original image – blurred image

High-boost filteringHigh-boost filtering

generalized form of Unsharp maskinggeneralized form of Unsharp masking A A 1 1

),(),(),( yxfyxAfyxfhb

),(),()1(

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

yxfyxfA

yxfyxfyxfAyxf

s

hb


if we use Laplacian filter to create if we use Laplacian filter to create sharpen image fsharpen image fss(x,y) with addition of (x,y) with addition of original imageoriginal image

),(),()1(),( yxfyxfAyxf shb

),(),(

),(),(),(

2

2

yxfyxf

yxfyxfyxf s


yieldsyields

),(),(

),(),(),(

2

2

yxfyxAf

yxfyxAfyxfhb

if the center coefficient of the Laplacian mask is negative

if the center coefficient of the Laplacian mask is positive

High-boost MasksHigh-boost Masks

A A 1 1 if A = 1, it becomes “standard” if A = 1, it becomes “standard”

Laplacian sharpeningLaplacian sharpening

ExampleExample

Gradient OperatorGradient Operator

first derivatives are implemented first derivatives are implemented using the using the magnitude of the magnitude of the gradientgradient..

y

fx

f

G

G

y

xf

21

22

2122 ][)f(

y

f

x

f

GGmagf yx

the magnitude becomes nonlinearyx GGf

commonly approx.

Gradient MaskGradient Mask simplest approximation, 2x2simplest approximation, 2x2

zz11 zz22 zz33

zz44 zz55 zz66

zz77 zz88 zz99

)( and )( 5658 zzGzzG yx

212

562

582

122 ])()[(][ zzzzGGf yx

5658 zzzzf

Gradient MaskGradient Mask

Sobel operators, 3x3Sobel operators, 3x3

zz11 zz22 zz33

zz44 zz55 zz66

zz77 zz88 zz99

)2()2(

)2()2(

741963

321987

zzzzzzG

zzzzzzG

y

x

yx GGf

the weight value 2 is to achieve smoothing by giving more important to the center point

NoteNote

the summation of coefficients in all the summation of coefficients in all masks equals 0, indicating that they masks equals 0, indicating that they would give a response of 0 in an area would give a response of 0 in an area of constant gray level.of constant gray level.

ExampleExample

Example of Combining Spatial Example of Combining Spatial Enhancement MethodsEnhancement Methods

want to sharpen want to sharpen the original image the original image and bring out more and bring out more skeletal detail.skeletal detail.

problems: narrow problems: narrow dynamic range of dynamic range of gray level and high gray level and high noise content noise content makes the image makes the image difficult to enhancedifficult to enhance

Example of Combining Spatial Example of Combining Spatial Enhancement MethodsEnhancement Methods

solve : solve :

1.1. Laplacian to highlight fine Laplacian to highlight fine detaildetail

2.2. gradient to enhance gradient to enhance prominent edgesprominent edges

3.3. gray-level transformation to gray-level transformation to increase the dynamic range of increase the dynamic range of gray levelsgray levels

Image Enhancement in the Image Enhancement in the Frequency DomainFrequency Domain

Fourier SeriesFourier Series

Any function that periodically repeats itself can be expressedas the sum of sines and/or cosines of different frequencies, each multiplied by a different coefficients. This sum is called a Fourier series.

Fourier SeriesFourier Series

00

0

00

0

00

0

00

00

00

1000

sin)(2

cos)(2

)(1

sincos)(

Tt

tn

Tt

tn

Tt

t

nnn

dttnwtgT

b

dttnwtgT

a

dttgT

a

tnwbtnwaatg

Fourier TransformFourier Transform

A function that is not periodic but the area under its curve is finite can be expressed as the integral of sines and/or cosines multiplied by a weighing function. The formulationin this case is Fourier transform.

The One-Dimensional Fourier The One-Dimensional Fourier Transform and its InverseTransform and its Inverse

The fourier transform F(u) :The fourier transform F(u) :

The inverse Fourier transform f(x) :The inverse Fourier transform f(x) :

Two variables Fourier transform F(u, v) : Two variables Fourier transform F(u, v) :

The inverse transform f(x, y) : The inverse transform f(x, y) :

dxexfuF uxj 2)()(

dueuFxf uxj 2)()(

dxdyeyxfvuF vyuxj )(2),(),(

dudvevuFyxf vyuxj )(2),(),(


The discrete Fourier Transform F(u) :The discrete Fourier Transform F(u) :

The inverse DFT :The inverse DFT :

Apply euler’s formula : Apply euler’s formula :

1,,1,0)(1

)(1

0

/2

MuforexfM

uFM

x

Muxj

1,,1,0)()(1

0

/2

MxforeuFxfM

u

Muxj

1

0

]/2sin/2)[cos(1

)(M

x

MuxjMuxxfM

uF


F(u) in polar coordinates :F(u) in polar coordinates :

spectrum)Fourier theof (square

spectrumpower : )()()()(

ansformFourier tr theof

spectrum phaseor angle phase the: )(

)(tan)(


spectrumor magnitude the: )]()([)( where

)()(

222

1

2/122

)(

uIuRuFuP

uR

uIu

uIuRuF

euFuF uj


The two dimensional DFT and its The two dimensional DFT and its InverseInverse

The discrete fourier transform of a function f(x,y) The discrete fourier transform of a function f(x,y) of size M x N :of size M x N :

The inverse Fourier transform :The inverse Fourier transform :

1

0

1

0

)//(2),(1

),(M

x

N

y

NvyMuxjeyxfMN

vuF

1

0

1

0

)//(2),(),(M

u

N

v

NvyMuxjevuFyxf


In the polar coordinateIn the polar coordinate

spectrum)Fourier theof (square

spectrumpower : ),(),(),(),(


spectrum phaseor angle phase the: ),(

),(tan),(


spectrumor magnitude the: )],(),([),(

222

1

2/122

vuIvuRvuFvuP

vuR

vuIvu

yxIyxRvuF


DFT corresponding (u,v)=(0,0)DFT corresponding (u,v)=(0,0)

If f(x,y) is real, its Fourier transform is conjugate If f(x,y) is real, its Fourier transform is conjugate symmetricsymmetric

The spectrum of the Fourier transform is The spectrum of the Fourier transform is symmetricsymmetric

),( of average the: ),(1

)0,0(1

0

1

0

yxfyxfMN

FM

x

N

y

),(),( * vuFvuF

),(),( vuFvuF


Basics of filtering in the frequency Basics of filtering in the frequency domaindomain

1.1. Multiply the input image by to Multiply the input image by to center the transformcenter the transform

2.2. Compute F(u,v), by the DFT of the image Compute F(u,v), by the DFT of the image from (1)from (1)

3.3. Multiply F(u,v) by a filter function H(u,v)Multiply F(u,v) by a filter function H(u,v)4.4. Compute the inverse DFT of the result in Compute the inverse DFT of the result in

(3)(3)5.5. Obtain the real part of the result in (4)Obtain the real part of the result in (4)6.6. Multiply the result in (5) by Multiply the result in (5) by

yx )1(

yx )1(

yx )1(

Basics of filtering in the frequency Basics of filtering in the frequency domaindomain

)],([Image Filtered

),(),(),(1 vuG

vuFvuHvuG

Some basic filters and their Some basic filters and their propertiesproperties

otherwise 1

)2/,2/(),( if 0),(

filternotch

NMvuvuH

Some basic filters and their Some basic filters and their propertiesproperties

Lowpass filter : less Lowpass filter : less sharpsharp(Smoothing)(Smoothing)

Highpass filter : less Highpass filter : less gray-level variation gray-level variation and emphasized and emphasized edgesedges(Sharpening)(Sharpening)

Correspondence between Filtering Correspondence between Filtering in the Spatial and Frequency in the Spatial and Frequency

DomainsDomains The convolution theorem :The convolution theorem :

The impulse response :The impulse response :

),(*),(),(),(

),(),(),(*),(

),(),(1

),(*),(1

0

1

0

vuHvuFyxhyxf

vuHvuFyxhyxf

nymxhnmfMN

yxhyxfM

m

N

n

1

0

1

0

1

0

1

00000

)0,0(),(),(

),(),(),(

M

x

N

y

M

x

N

y

syxyxs

yxAsyyxxAyxs


DomainsDomains The Fourier transform of a unit impulse functionThe Fourier transform of a unit impulse function

Let Let

1

0

1

0

)//(2 1),(

1),(

M

x

N

y

NvyMuxj

MNeyx

MNvuF

),(),( yxyxf

),(1

),(),(1

),(*),(1

0

1

0

yxhMN

nymxhnmMN

yxhyxfM

m

N

n

),(),(

),()],([),(*),(

),(),(),(*),(

vuHyxh

vuHyxyxhyx

vuHvuFyxhyxf


DomainsDomains Gaussian functions :Gaussian functions :

222

2221

2

22

22

21

21

222

22

22

21

212/2/

2

2/

22)(

domain spatial in thefilter ingcorrespond the

, with )(

Gaussian of difference a asfilter highpass

2)(

domain spatial in thefilter ingcorrespond the

)(

functionfilter Gaussian

xx

uu

x

u

BeAexh

BABeAeuH

Aexh

AeuH


DomainsDomains

Smoothing Frequency-Domain Smoothing Frequency-Domain FiltersFilters

IdealIdeal ButterworthButterworth GaussianGaussian

Ideal lowpass filterIdeal lowpass filter

0

0

),( 0

),( 1 {),(

DvuDif

DvuDifvuH

2/122 ])2/()2/[(),( NvMuvuD



1

0

1

0

),(M

u

N

vT vuPP

u v

TPvuP ]/),([100



Butterworth Lowpass FiltersButterworth Lowpass Filters

When D(u,v)= , H(u,v)=0.5When D(u,v)= , H(u,v)=0.50D

nDvuDvuH

20 ]/),([1

1),(




Gaussian Lowpass filterGaussian Lowpass filter

letlet

22 2/),(),( vuDevuH

20

2 2/),(),( DvuDevuH

0D



Sharpening Frequency Domain Sharpening Frequency Domain FiltersFilters

IdealIdeal ButterworthButterworth GaussianGaussian

),(1),( vuHvuH lphp

Sharpening Frequency Domain Sharpening Frequency Domain FiltersFilters

Ideal Highpass FiltersIdeal Highpass Filters

Ideal highpass filterIdeal highpass filter

0

0

),( 1

),( 0 {),(

DvuDif

DvuDifvuH

Butterworth Highpass FiltersButterworth Highpass Filters

nvuDDvuH

20 )],(/[1

1),(

Gaussian Highpass FiltersGaussian Highpass Filters

20

2 2/),(1),( DvuDevuH

The Laplacian in the Frequency The Laplacian in the Frequency DomainDomain

)()()(

uFjudx

xfd nn

n

),()(

),()(),()(),(),(

22

222

2

2

2

vuFvu

vuFjuvuFjuy

yxf

x

yxf

),()(),( 222 vuFvuyxf

)(),( 22 vuvuH

])2/()2/[(),( 22 NvMuvuH

)},(])2/()2/[({),( 2212 vuFNvMuyxf



),(),(),( 2 yxfyxfyxg

Unsharp Masking, High-Boost Filtering, and Unsharp Masking, High-Boost Filtering, and High-Frequency Emphasis FilteringHigh-Frequency Emphasis Filtering

Unsharp masking :Unsharp masking : High-Boost filtering :High-Boost filtering :

High-Frequency Emphasis FilteringHigh-Frequency Emphasis Filtering

),(),(),( yxfyxfyxf lphp

),(),(),( yxfyxAfyxf lphb

0.21.5 ,5.00.25 valuetypical,,0

),(),(

baaba

vubHavuH hphfe

),()1(),(

),(1),(

vuHAvuH

vuHvuH

hphb

lphp



Documents

Local Enhancement Histogram processing methods are global processing, in the sense that pixels are modified by a transformation function based on the gray-level