byst eh-1 dip - ws2002: enhancement in the spatial domain digital image processing bundit thipakorn,...
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BYSTBYSTEh-Eh-11DIP - WS2002: Enhancement in the Spatial DomainDIP - WS2002: Enhancement in the Spatial Domain
Digital Image ProcessingDigital Image Processing
Bundit Thipakorn, Ph.D.Bundit Thipakorn, Ph.D.Computer Engineering DepartmentComputer Engineering Department
Image Enhancement in the Image Enhancement in the Spatial DomainSpatial Domain
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Image EnhancementImage Enhancement
improve the quality of the image / orimprove the quality of the image / or emphasize particular aspects within the imageemphasize particular aspects within the image
EnhancementInput Imagef(x,y)
Output Imageg(x,y)
Application SpecificFeedback
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EnhancementEnhancement
The image enhancement can be performed in either:The image enhancement can be performed in either:
Spatial DomainSpatial Domain: Directly manipulate on the pixels in an : Directly manipulate on the pixels in an image.image.
Frequency DomainFrequency Domain: Modify the Fourier transform of an : Modify the Fourier transform of an image.image.
oror
Cont’d.Cont’d.
The enhancement methods are The enhancement methods are application specificapplication specific as as illustrated in previous diagram. The enhancement illustrated in previous diagram. The enhancement process requires feedback from application.process requires feedback from application.
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EnhancementEnhancementCont’d.Cont’d.
Image enhancement in spatial domain methods Image enhancement in spatial domain methods can be classified into five categories:can be classified into five categories:
1. 1. Point OperationsPoint Operations::Each output pixel’s gray level depends only Each output pixel’s gray level depends only
upon the gray level of the corresponding input upon the gray level of the corresponding input pixel.pixel.
2. 2. Global OperationsGlobal Operations::The global characteristics (statistics) of the The global characteristics (statistics) of the
image array are use to modify the pixel values.image array are use to modify the pixel values.
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EnhancementEnhancementCont’d.Cont’d.
4. 4. Geometric OperationsGeometric Operations::The pixel values are modified according to The pixel values are modified according to
the structural content of the image.the structural content of the image.
5. 5. Temporal (Frame-Based) OperationsTemporal (Frame-Based) Operations::The resulting image is a combination of The resulting image is a combination of
more than one unprocessed image.more than one unprocessed image.
3. 3. Neighbourhood OperationsNeighbourhood Operations::Data from the immediate neighbours is used Data from the immediate neighbours is used
to modify a pixel value.to modify a pixel value.
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Spatial Domain MethodsSpatial Domain Methods
g(x,y) = T[f(x,y)]g(x,y) = T[f(x,y)]
WhereWhere f(x,y)f(x,y) = the input image= the input imageg(x,y)g(x,y)= the processed image= the processed imageTT = an operator.= an operator.
Image enhancement in spatial domain can be expr Image enhancement in spatial domain can be expr essed by the following expression: essed by the following expression:
EnhancementEnhancementCont’d.Cont’d.
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The operator The operator TT is normally defined over some is normally defined over some neigneighborhoodhborhood ofof (x,y)(x,y)..
EnhancementEnhancementCont’d.Cont’d.
yy
xx
00Origin( , )00Origin( , )
(x,y)(x,y)
A traditional defined ne A traditional defined ne ighborhood of a point ( ighborhood of a point (
x,y)x,y)
A square subimage area cent A square subimage area cent ered at (x,y) which is usually ered at (x,y) which is usually
called “ called “maskmask ((kernelkernel , , templatemplatete , or , or windowwindow)”.)”.
Image f(x,y) Image f(x,y)
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The center of the subimage is moved from pixel to pixel an The center of the subimage is moved from pixel to pixel an d the operator d the operator TT is applied at each location (x,y) to yield th is applied at each location (x,y) to yield th e output g(x,y). e output g(x,y).
EnhancementEnhancementCont’d.Cont’d.
yy
xx
00Origin( , )00Origin( , )
(x,y)(x,y)
Image f(x,y) Image f(x,y)
ConvolutionConvolutionProcessProcess
Only the pixels in the area of the image spanned by the neighborhood are utilized.
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Gray-Scale ModificationGray-Scale Modification
LetLet r = the gray level of f(x,y) at x,yr = the gray level of f(x,y) at x,yand and s = the gray level of g(x,y) at x,y.s = the gray level of g(x,y) at x,y.
s = M(r)s = M(r)
WhereWhere M = a gray-level or mapping transformation function. M = a gray-level or mapping transformation function.
Gray-scale modification is a type of point operations that Gray-scale modification is a type of point operations that will change the pixel’s values by a mapping equation as shwill change the pixel’s values by a mapping equation as shown in the following:own in the following:
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That is, only one pixel is used and g(x,y) depends on the gr That is, only one pixel is used and g(x,y) depends on the gr ay value at (x,y). ay value at (x,y).
Cont’d.Cont’d.Gray-Scale Gray-Scale ModificationModification
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1. Image Negative1. Image Negative
1:1 Mapping1:1 Mapping
Negative MappingNegative Mapping
Input Gray LevelInput Gray Level
Output Output Gray LevelGray Level
Let Let n be the number of gray level bits usedn be the number of gray level bits used
S = 2S = 2nn - r - r
Cont’d.Cont’d.Gray-Scale Gray-Scale ModificationModification
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The primary operations applied to the gray scale of The primary operations applied to the gray scale of an image are to compress or stretch.an image are to compress or stretch.
Cont’d.Cont’d.Gray-Scale Gray-Scale ModificationModification
CompressCompress Uninterested gray-scale rUninterested gray-scale ranges.anges.
StretchStretch Gray-scale ranges containing Gray-scale ranges containing desired information.desired information.
Gray-scale compression or stretching can be performed by Gray-scale compression or stretching can be performed by changing the slope of the mapping equations to be lower or changing the slope of the mapping equations to be lower or greater than one, respectively. greater than one, respectively.
2. Gray-Scale Compression and Stretching2. Gray-Scale Compression and Stretching
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Cont’d.Cont’d.Gray-Scale Gray-Scale ModificationModification
Input Gray LevelInput Gray Level
Output Output Gray LevelGray Level
1:1 Mapping1:1 Mapping
255255
255255
00
aa
bb
Gray-Scale CGray-Scale Compressionompression
Gray-Scale SGray-Scale Stretchingtretching
Slope > 1: Slope > 1: StretchingStretching
Slope < 1: CoSlope < 1: Compressingmpressing
(0-b)(0-b) (0-255)(0-255)
(0-255)(0-255) (0-a)(0-a)
““a” and “b” < 255a” and “b” < 255
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Cont’d.Cont’d.Gray-Scale Gray-Scale ModificationModification
InputInputGray LevelGray Level
Output Output Gray LevelGray Level
Slope = 1Slope = 1
255255
255255
00aa bb
Gray-Scale SGray-Scale Stretchingtretching
Stretching gray-scales Stretching gray-scales between a to b.between a to b.
Slope = 1Slope = 1
aa bb 255255
255255
Output Output Gray LevelGray Level
InputInputGray LevelGray Level
00
Gray-Scale SGray-Scale Stretchingtretching
Stretching with clipping at Stretching with clipping at ends.ends.
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Cont’d.Cont’d.Gray-Scale Gray-Scale ModificationModification
InputInputGray LevelGray Level
Output Output Gray LevelGray Level
Slope = 1Slope = 1
255255
255255
00 aa bbHighlighting gray values bHighlighting gray values between a to b.etween a to b.
Slope = 1Slope = 1
aa bb 255255
255255
Output Output Gray LevelGray Level
InputInputGray LevelGray Level
00
Highlighting gray values between Highlighting gray values between a to b and dimming others.a to b and dimming others.
Intensity-Level Slicing
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To reduce contrast of brighter regions by using a To reduce contrast of brighter regions by using a logarithmic curve as the mapping function.logarithmic curve as the mapping function.
3. Logarithm Operator3. Logarithm Operator
Cont’d.Cont’d.Gray-Scale Gray-Scale ModificationModification
S = c log(|r|) or S = c log(1+|r|)S = c log(|r|) or S = c log(1+|r|)
rr
SS
Where c is the scaling Where c is the scaling constant which is constant which is selected so that the selected so that the maximum output value maximum output value is 255.is 255.
M(r)
A logarithmic transform A logarithmic transform stretches the lower values stretches the lower values while compresses the while compresses the higher values.higher values.
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Cont’d.Cont’d.Gray-Scale Gray-Scale ModificationModification
An original image.An original image. A enhanced image after A enhanced image after applying the logarithm applying the logarithm operator.operator.
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To enhance high intensity pixel values by using a To enhance high intensity pixel values by using a exponential curve as the mapping function.exponential curve as the mapping function.
4. Exponential Operator4. Exponential Operator
Cont’d.Cont’d.Gray-Scale Gray-Scale ModificationModification
S = c bS = c brr or S = c(b or S = c(brr - 1) - 1) WhereWhere b = the basisb = the basis
rr
SS
M(r)
A exponential transform A exponential transform stretches the higher values stretches the higher values while compresses the lower while compresses the lower values.values.
c = the scaling constantc = the scaling constant
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Cont’d.Cont’d.Gray-Scale Gray-Scale ModificationModification
An original image.An original image. A enhanced image after A enhanced image after applying the exponential applying the exponential operator.operator.
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An alternative method: “An alternative method: “Raised to the PowerRaised to the Power””
Cont’d.Cont’d.Gray-Scale Gray-Scale ModificationModification
S = c rS = c rii
In this alternative method, the input intensity “In this alternative method, the input intensity “rr” is a basis of ” is a basis of the exponential mapping function. Hence the new pixel the exponential mapping function. Hence the new pixel intensity value is equal to the input intensity value raised to the intensity value is equal to the input intensity value raised to the value of “value of “ii”. ”.
IfIf i > 1 i > 1 An exponential transform. An exponential transform.
i < 1 i < 1 A logarithmic transform. A logarithmic transform.
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The brightness of the image can be easily adjusted The brightness of the image can be easily adjusted by adding or subtracting f(x,y) with some constant by adding or subtracting f(x,y) with some constant gray-level gray-level (sliding the histogram to the bigger or the (sliding the histogram to the bigger or the smaller gray-level)smaller gray-level)..
S = r + A ; S = r - A
5. Brightness Modification5. Brightness Modification
WhereWhere A = the enhancement factor (constant).A = the enhancement factor (constant).
Cont’d.Cont’d.Gray-Scale Gray-Scale ModificationModification
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To improve the contrast in an image by linearly To improve the contrast in an image by linearly stretching the intensity values that image contains to span stretching the intensity values that image contains to span within a desired range of values.within a desired range of values.
LetLet a = the lowest gray level (0)a = the lowest gray level (0)b = the highest gray level (255)b = the highest gray level (255)c = the lowest pixel value in the present imagec = the lowest pixel value in the present imaged = the highest pixel value in the present image. d = the highest pixel value in the present image.
Therefore;Therefore;
S = [(r-c)(b-a)/(d-c)] + aS = [(r-c)(b-a)/(d-c)] + a
6. Contrast Stretching6. Contrast Stretching
Cont’d.Cont’d.Gray-Scale Gray-Scale ModificationModification
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A plot of the gray-level values versus A plot of the gray-level values versus
the number of pixels at that value.the number of pixels at that value.
# of pixels
gray-level
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Given an image f, the histogram of f over the gray levels ranged from 0 to L-1 is defined as:
P(g) =N(g)
MWhere P(g) = the histogram probability
N(g) = the number of pixels at gray level gM = the total number of pixels in the
image.
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# of pixels
Gray Level
# of pixels
Gray Level
Note: 0 = White255 = Black
DarkImage
BrightImage
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# of pixels
Gray Level
# of pixels
Gray Level
Note: 0 = White255 = Black
Low- ContrastImage
High- ContrastImage
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Histogram processing (modification) is a type of global Histogram processing (modification) is a type of global operations that will modify the dynamic range and contrasoperations that will modify the dynamic range and contrast of the original image.t of the original image.
The modification is performed by altering the histograThe modification is performed by altering the histogram of the original image to have the desired shape.m of the original image to have the desired shape.
Histogram modification can perform using non-linear oHistogram modification can perform using non-linear or non-monotonic mapping functions.r non-monotonic mapping functions.
Histogram ProcessingHistogram Processing
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1. Histogram Equalization1. Histogram Equalization
Ideally: The output image contains a uniform distributionIdeally: The output image contains a uniform distribution
of intensities ( a flat histogram).of intensities ( a flat histogram).
N(g) = Max { 0, Round ( ) -1}2l x c(g)m x n
WhereWhere l = the number of bits;l = the number of bits; m x n = the image resolutionm x n = the image resolutionN(g) = the new intensity valueN(g) = the new intensity valuec(g) = the cumulative pixel count up to old intensity value gc(g) = the cumulative pixel count up to old intensity value gRound( ) = a rounding to the nearest integer function. Round( ) = a rounding to the nearest integer function.
Cont’d.Cont’d.
HistogramHistogram
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Examples m=n=8 and l = 3
g f c(g) N(g)0
1
2
3
4
5
6
7
8
22
20
2
30
2
8
2
0
8 0
50
52
54
62
64
64
3
5
5
6
7
7
7
Cont’d.Cont’d.
HistogramHistogram
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An original image.An original image. A enhanced image after A enhanced image after applying the histogram applying the histogram equalization method.equalization method.
Cont’d.Cont’d.
HistogramHistogram
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2. Histogram Specification (Matching)2. Histogram Specification (Matching)
The output image contains a desired shape of the output The output image contains a desired shape of the output
intensity distribution (histogram).intensity distribution (histogram).
Histogram specification will map the intensity distributHistogram specification will map the intensity distribut
ion of the original image into a desired intensity distributioion of the original image into a desired intensity distributio
n by using a histogram equalized image as the intermediatn by using a histogram equalized image as the intermediat
e stage.e stage.
Cont’d.Cont’d.
HistogramHistogram
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Histogram specification can be performed as following Histogram specification can be performed as following steps:steps: Apply the histogram equalization to the original image Apply the histogram equalization to the original image (Row H in the following table).(Row H in the following table).
Specify the histogram of the new image.Specify the histogram of the new image.
Apply the histogram equalization to the desired histograApply the histogram equalization to the desired histogram in step 2 (Row S).m in step 2 (Row S).
Map each value of row H to the closest value in row S aMap each value of row H to the closest value in row S and then using the corresponding row in O for the new valund then using the corresponding row in O for the new value of gray level (Row M).e of gray level (Row M).
Cont’d.Cont’d.
HistogramHistogram
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Examples:Step 1: Result of applying histogram equalization to the original image.
Original Gray-Scale Value (O) Histogram Equalized Values (H)
0
1
2
3
4
5
6
7
1
2
4
4
6
6
7
7
Cont’d.Cont’d.
HistogramHistogram
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Examples:Step 2: The desired histogram.
Gray-Scale Value Number of Pixels in Desired Histogram
0
1
2
3
4
5
6
7
1
5
10
15
20
0
0
0
Cont’d.Cont’d.
HistogramHistogram
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Examples:Step 3: Result of applying histogram equalization to the desired histogram.
Gray-Scale Value Histogram Equalized Values (S)
0
1
2
3
4
5
6
7
0
1
2
4
7
7
7
7
Cont’d.Cont’d.
HistogramHistogram
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Examples:Step 4: Mapping result
O H S M
0
1
2
3
4
5
6
7
1
2
4
4
6
6
7
7
0
1
2
4
7
7
7
7
1
2
3
3
4
4
4
4
Cont’d.Cont’d.
HistogramHistogram
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Local EnhancementLocal Enhancement
Histogram equalization and histogram specification preHistogram equalization and histogram specification pre
viously discussed will viously discussed will enhance an image globallyenhance an image globally since pixel since pixel
s are modified by a transformation function based on the gs are modified by a transformation function based on the g
ray-level distribution over an entire image.ray-level distribution over an entire image.
To enhance details over small areas, gray-level values wiTo enhance details over small areas, gray-level values wi
thin an image can be modified locally by applying histograthin an image can be modified locally by applying histogra
m modification techniques to the image on a m modification techniques to the image on a block-by-blockblock-by-block
basis (7x7, 15x15, etc.). This technique is called “basis (7x7, 15x15, etc.). This technique is called “local enhlocal enh
ancementancement”.”.
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Local EnhancementLocal EnhancementCont’d.Cont’d.
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Local EnhancementLocal Enhancement
Original ImageOriginal Image Image after global histoImage after global histogram equalization.gram equalization.
Cont’d.Cont’d.
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Local EnhancementLocal Enhancement
Image after local histogram eImage after local histogram equalization (7x7).qualization (7x7).
Image after local histogram Image after local histogram equalization (15x15).equalization (15x15).
Cont’d.Cont’d.
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Adaptive Contrast EnhancementAdaptive Contrast Enhancement
Modify the histogram by a transformation function basModify the histogram by a transformation function bas
ed on the gray-level distribution over small areas (Local ened on the gray-level distribution over small areas (Local en
hancement).hancement).
Adaptive Contrast Enhancement (ACE) method is based Adaptive Contrast Enhancement (ACE) method is based
on the intensity on the intensity meanmean and and variancevariance (or S.D.) of the pixel int (or S.D.) of the pixel int
ensities in a neighborhood.ensities in a neighborhood.Let f(x,y) = an input image,Let f(x,y) = an input image,
g(x,y) = a new image,g(x,y) = a new image,
M = the global mean of f(x,y),M = the global mean of f(x,y),
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Adaptive Contrast EnhancementAdaptive Contrast Enhancement
(x,y) = the gray-level standard deviation (S.D.),(x,y) = the gray-level standard deviation (S.D.),
Cont’d.Cont’d.
m(x,y) = the gray-level mean,m(x,y) = the gray-level mean,
kk11 and k and k22 = constants and 0 < k = constants and 0 < k11, k, k22 < 1. < 1.
Where Where (x,y) and m(x,y) are calculated in a neighborhood (x,y) and m(x,y) are calculated in a neighborhood centered at (x,y).centered at (x,y).
The transformation function of ACE method is defined as The transformation function of ACE method is defined as follows:follows:
)y,x(mk)y,x(m)y,x(f)y,x(
Mk)y,x(g 21
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Adaptive Contrast EnhancementAdaptive Contrast EnhancementCont’d.Cont’d.
The termThe term)y,x(
Mk1
is called the “local gain”. is called the “local gain”.
(x,y)(x,y))y,x(
Mk1
High contrastHigh contrast
(x,y)(x,y))y,x(
Mk1
Low contrastLow contrast
Thus, areas with low contrast will have larger local gain.Thus, areas with low contrast will have larger local gain.
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Arithmetic/Logic OperationsArithmetic/Logic Operations
Image 1, …, n are normally the identical scenes but may Image 1, …, n are normally the identical scenes but may
be acquired at be acquired at different timesdifferent times or through or through different spectral fdifferent spectral f
iltersilters..
Arithmeticor Logic Operations
1Image 1Image
2Image 2Image
Image n Image n
RRRRRRRRRRRRRRRRRRRRRR
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Arithmetic/Logic OperationsArithmetic/Logic Operations
Arithmetic/logic operations will operate on a Arithmetic/logic operations will operate on a pixel-by-pixpixel-by-pix
elel basis between two or more images. basis between two or more images.
The result image is a new image whose pixel at coordinaThe result image is a new image whose pixel at coordina
tes (x,y) is the result of applying arithmetic or logic operatites (x,y) is the result of applying arithmetic or logic operati
ons to the pixels in the same location.ons to the pixels in the same location.
Image subtraction and division are more widely used thImage subtraction and division are more widely used th
an image addition and multiplication.an image addition and multiplication.
The The ANDAND or or OROR operations are used for selecting subim operations are used for selecting subim
ages in an image (ages in an image (maskingmasking).).
Cont’d.Cont’d.
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Arithmetic/Logic OperationsArithmetic/Logic OperationsCont’d.Cont’d.