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

PDF

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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