Perception-Based Histogram Equalization for Tone Mapping ...
Histogram equalization
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Transcript of Histogram equalization
BI-HISTOGRAM EQUALIZATION with a plateau limit
FOR DIGITAL IMAGES.
MAHESH MOHAN.M.RGECT S1 ECEROLL NO: 7
GUIDE : Dr.V.S.SHEEBA
OM NAMA SIVAYA
OBJECTIVE
.
TO FAMILARIZE WITH
.HISTOGRAM EQUALIZATION
.DIFFERENT EQUALIZATION METHODS
.THEIR DRAWBACK AND HOW IT IS
RECTIFIED.
FLOW OF SEMINAR.
1.WHAT IS A DIGITAL IMAGE?
2.WHAT IS A HISTOGRAM?
3.WHAT IS HISTOGRAM EQUALIZATION?
4.DIFFERENT EQUALIZATION METHODS AND ITS DRAWBACK.
5.HOW DRAWBACK OF EACH METHOD IS RECTIFED?
• A digital image is a matrix representation of a two-dimensional image.
What is a digital image?
Colour imageGray scale image(Black and white)
dGray Image
Image
What is a gray scale image?
243 121 .34 21 .
. .
Gray level matrix
0 255
Image matrix
Image
What is a colour image?234 212 123
135 231 233 .121 222 . .
243 121 .
. . .
112 167 .
. . .
Red matrix
Green matrix
Blue matrix
.
.
What is a histogram?
Consider a 5x5 image with integer intensities in the range between zero and seven:
0 7 3 2 3
0 0 0 6 7
7 7 2 2 0
1 1 0 4 1
0 0 7 4 1Image matrixImage
0 1 2 3 4 5 6 7
Gray scaleBlack White
What is a histogram?
Consider a 5x5 image with integer intensities in the range between one and eight:
0 7 3 2 3
0 0 0 6 7
7 7 2 2 0
1 1 0 4 1
0 0 7 4 1Image matrixImage
0 1 2 3 4 5 6 7
Grey scaleBlack White
Number of pixel with intensity value 0 [h(r0)] = 8
What is a histogram?
0 7 3 2 3
0 0 0 6 7
7 7 2 2 0
1 1 0 4 1
0 0 7 4 1Image matrixImage
0 1 2 3 4 5 6 7
Grey scaleBlack White
Number of pixel with intensity value 0 [h(r0)] = 8Similarly for 1 h(r1) = 4
What is a histogram?
0 7 3 2 3
0 0 0 6 7
7 7 2 2 0
1 1 0 4 1
0 0 7 4 1Image matrixImage
Similarly
INTENSITY r 0 1 2 3 4 5 6 7
NUMBER of pixels of r h(r)
h(r0)=8 h(r1)=4 h(r2)=3 h(r3)=2 h(r4)=2 h(r5)=0 h(r6)=1 h(r7)=5
r
What is a histogram?
Image matrix
0 1 2 3 4 5 6 7
HISTOGRAM
Intensity values
Number of pixels of intensity r
r 0 1 2 3 4 5 6 7
h(r) 8 4 3 2 2 0 1 5
Histogram plots the number of pixels for each intensity value.
h(r)
What is a histogram?
r 0 1 2 3 4 5 6 7
h(r) 8 4 3 2 2 0 1 5
p(r)h(r)/(5*5)
8/25 4/25 3/25 2/25 2/25 0/25 1/25 5/25
HISTOGRAM - h(r) - Y axis - number of intensitiesNORMALIZED HISTOGRAM - p(r) - Y axis - probability of intensities
SAMPLE IMAGES AND ITS HISTOGRAM
Bright imageIntensity range 0 - 255
SAMPLE IMAGES AND ITS HISTOGRAM
Bright imageIntensity range 0 - 255
0 50 100 150 200 255
Intensity
No:
of
pixe
ls
DARK BRIGHT
h(r)
SAMPLE IMAGES AND ITS HISTOGRAM
Dark imageIntensity range 0 - 255
SAMPLE IMAGES AND ITS HISTOGRAM
Dark imageIntensity range 0 - 255
0 50 100 150 200 255
Intensity
No:
of
pixe
ls
h(r)
SAMPLE IMAGES AND ITS HISTOGRAM
Low contrast imageIntensity range 0 - 255
SAMPLE IMAGES AND ITS HISTOGRAM
Light imageIntensity range 0 - 255
0 50 100 150 200 255
Intensity
No:
of
pixe
ls
h(r)
SAMPLE IMAGES AND ITS HISTOGRAM
Bright image
Dark image
Low contrast image
SAMPLE IMAGES AND ITS HISTOGRAM
High contrast imageIntensity range 0 - 255
0 50 100 150 200 255
Intensity
No:
of
pixe
ls
h(r)
CONCEPT OF HISTOGRAM EQUALIZATION
ORIGINAL IMAGE EQUALIZED IMAGE
MAXIMIZES ENTROPY OF AN IMAGE.
s1 s2
THEORY BEHIND HISTOGRAM EQUALIZATION
TRANSFORMATION FUNCTION THAT MAPS THE INPUT INTENSITY TO ALL AVAILABLE INTENSITIES.
I/p intensity
O/p intensity
THEORY BEHIND HISTOGRAM EQUALIZATION
ORIGINAL IMAGE EQUALIZED IMAGE
s1 s2
THEORY BEHIND HISTOGRAM EQUALIZATION
CUMULATIVE DISTRIBUTION FUNCTION T(r)
0 50 100 150 200 255
[76 – 213]
[0 – 48][15 – 100] [25 – 125]
O/P INTENSITY = X0 + [( Xl-1 –X0 )*C(x)]
I/P intensity
DIFFERENT STAGES
GLOBAL HISTOGRAM EQUALIZATION
BI-HISTOGRAMEQUALIZATION
BI-HISTOGRAM EQUALIZATION WITH A PLATEAU LIMIT
GLOBAL HISTOGRAM EQUALIZATION
OBTAIN HISTOGRAM
OBTAIN PDF
OBTAIN CDF
OBTAIN TRANSFORMATIO
N FUNCTION
MAPPING OF NEW INTENSITY VALUES
NEW HISTOGRAM
Original histogram
M*N
1..
CDF
1
x0
XL-1
O/P
x0
XL-1
MappingTransformation function
t1 t2
t2
New histogramt1t1 t2
t2t1t2t1
GLOBAL HISTOGRAM EQUALIZATION RESULTS
GHE
O/P MEAN CONSTANTWHY ?
GLOBAL HISTOGRAM EQUALIZATION DRAWBACK
DO NOT CONSERVE THE MEAN.
WHY MEAN IMPORTANT?
Video frames
GHE
THEORY OF BIHISTOGRAM EQUALIZATION
HISTOGRAM EQUALIZED SEPERATELY AROUND MEAN. THUS CONSERVE THE MEAN.
ORIGINAL HISTOGRAM BIHISTOGRAM EQUALIZED
BIHISTOGRAM EQUALIZATION
OBTAIN PDF(lower subimage)[X0-Xm]
OBTAIN CDF
OBTAIN TRANSFORMATIO
N FUNCTION
MAPPING OF NEW INTENSITY VALUES
NEW HISTOGRAM
DIVIDE HISTOGRAM WITH RESPECT TO INTENSITY MEAN (X m ).
OBTAIN HISTOGRAM
OBTAIN PDF(upper subimage)[Xm-Xl-1]
OBTAIN CDF
OBTAIN TRANSFORMATIO
N FUNCTION
MAPPING OF NEW INTENSITY VALUES
+
GH
E
GHE
Partition
Merging
BI-HISTOGRAM EQUALIZATION RESULTS
BHE
BIHISTOGRAM EQUALIZATION DRAWBACK
LEVEL SATURATION DUE TO HIGH PROBABLE INTENSITY VALUES.
BHE
EXAMPLE
WHY IT HAPPENS ?
THOERY OF BIHISTOGRAM EQUALIZATION WITH A PLATEAU LIMIT .
BIHISTOGRAM CLIPPING HISTOGRAM ABOVE PLATEAU LIMIT
TL PLATEAU LIMITS FOR LOWER HISTOGRAM.TU PLATEAU LIMITS FOR UPPER HISTOGRAM.
SELECT PLATEAU LIMIT
BIHISTOGRAM EQUALIZATION WITH A PLATEAU LIMIT
OBTAIN PDF(lower subimage)[X0-Xm]
OBTAIN CDF
OBTAIN TRANSFORMATION
FUNCTION
MAPPING OF NEW INTENSITY VALUES
NEW HISTOGRAM
DIVIDE HISTOGRAM WITH RESPECT TO INTENSITY MEAN (X m ).
OBTAIN HISTOGRAM
OBTAIN PDF(upper subimage)[Xm-Xl-1]
OBTAIN CDF
OBTAIN TRANSFORMATION
FUNCTION
MAPPING OF NEW INTENSITY VALUES
+
GH
E GHE
Partition
Merging
CLIP WRT AMPLITUDE MEAN
CLIP WRT AMPLITUDE MEAN
Clipping
BIHISTOGRAM EQUALIZATION WITH A PLATEAU LIMIT RESULTS
BHEPL
Simulation results
TEST IMAGES GLOBAL HISTOGRAM EQUALIZATION
BI-HISTOGRAM EQUALIZATION
BIHISTOGRAM EQUALIZATION WITH PLATEAU LIMIT
DARK 86 126 82 91BRIGHT 143 126 154 153LOWCONTRAST 77 124 99 103
MEAN VALUES
Simulation results
LEVEL SATURATION
TEST IMAGES BI-HISTOGRAM EQUALIZATION
BIHISTOGRAM EQUALIZATION WITH PLATEAU LIMIT
WHITE DOT YES NO
d
WHY GRAY SCALE IMAGES INSTEAD OF COLOUR IMAGES?
.
CONCLUSIONhistogram?
IN AN IMAGE
NOTHING WORSE MORE THAN LOW CONTRAST
GLOBAL HISTOGRAM EQUALIZATION
NOTHING WORSE MORE THAN MEAN CONSERVATION
BI-HISTOGRAM EQUALIZATION
NOTHING WORSE MORE THAN ………………?
NOTHING WORSE MORE THAN LEVEL SATURATION
BI-HISTOGRAM EQUALIZATION WITH PLATEAU LIMIT
REFERENCESstogram?Bi-Histogram Equalization with a Plateau Limitfor Digital Image EnhancementChen Hee Ooi, Student Member, IEEE, Nicholas Sia Pik Kong, Student Member, IEEEand Haidi Ibrahim, Member, IEEEIEEE Transactions on Consumer Electronics, Vol. 55, No. 4, NOVEMBER 2009
Contrast Enhancement Using Brightness Preserving Bi-Histogram EqualizationYEONG-TAEG KIM, MEMBER, IEEE
Color Image Enhancement Using Brightness Preserving Dynamic Histogram EqualizationNicholas Sia Pik Kong, Student Member, IEEE, and Haidi Ibrahim, Member, IEEE.
Preserving brightness in histogram equalizationbased contrast enhancement techniquesSoong-Der Chen a, Abd. Rahman Ramli
Digital image processing by Gonzalez and Woods
NAMASIVAYA
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