Image enhancement

Image enhancement belongs to image pre-processing methods.

Objective of image enhancement – process the image (e.g. contrast improvement, image sharpening ,…) so that it is better suited for further processing or analysis

P. Strumiłło, M. Strzelecki

Image enhancement methods are based on subjective image quality criteria.

No objective mathematical criteria are used for optimizing processing results.

subjective perception

Image enhancement

Pseudo

colouring

False

colouring

Linear filters

Nonlinear filters

Edge detection

Zooming

Contrast

enhancement

Histogram modelling

Image

averaging

Image enhancemet methods

Point processing

Spatialfiltering

Imagecolouring

M, N – image dimensions f(i,j) – gray level value at (i,j)

∑∑

∑∑

= =

= =

−=

=

M

i

N

j

M

i

N

j

JjifMN

C

jifMN

J

1 1

2

1 1

]),([1

),(1Brightness

Contrast

Image enhancement

J=29, C=38J=112, C=47

Image brightness and contrast influence image subjective quality perceptionJ=194, C=29

Image histogram

Image histogram

Image : array[1..M,1..N] of byte;

Hist : array[0..L-1] of longint;

...

Hist:=0;

for i:=1 to M do for j:=1 to N do

Inc( Hist[ Image[i, j] ] );…

0 50 100 150 200 250

0

200

400

600

800

0 50 100 150 200 250

0

200

400

600

800

0 50 100 150 200 250

0

500

1000

1500

0 50 100 150 200 250

0

200

400

600

800

1000

1200 darkdark

Source Source imageimage

brightbright

Image histogramrepresents statistical distribution of image pixel brightnesses

Image histogram

L-1

L-1

d

m

0 f

g

Linear gray scale transformation

OUTPUT IMAGE

SOURCE IMAGE

g f

g(i,j) = m f(i,j) + d

m ~ contrast

d ~ brightness POINT OPERATION

MATLAB Demo – image histogram

Histogram „stretching”

g(i,j) =

0 f(i,j)<fMIN

L-1 f(i,j)>fMAX

L-1fMAX- fMIN

(f(i,j)- fMIN), fMIN≤≤≤≤ f(i,j) ≤≤≤≤fMAX

POINT OPERATION?

L-10 f fM A X

fM I N

g

0 50 100 150 200 250

0

1000

2000

3000

4000

5000

0 50 100 150 200 250

0

1000

2000

3000

4000

5000

fMIN=110, fMAX=225

Histogram „stretching” - example

Grayscale inversion

L-1

L-10 f

g

OUTPUT IMAGE

SOURCE IMAGE

g f

g(i,j) = T( f(i,j))

Grayscale normalization!

γ correction

Nonlinear grayscale transformation

POINT OPERATION

L-1

L-1

exp(x)

ln(x)

x2

sqrt(x)

0 f

g

Source image

Nonlinear grayscale transformation - example

0 50 100 150 200 250

0

200

400

600

800

1000

0 100 200

0

500

1000

1500

T=x2

0 100 200

0

200

400

600

800

1000

1200T=sqrt(x)

Nonlinear grayscale transformation - example

0 100 200

0

500

1000

1500

0 100 200

0

500

1000

1500

2000T=ex

T=log(x)

Nonlinear grayscale transformation - example

Example: square function

normalization: minimum value - 0 -> 0

maximum value - 255 -> 2552

Normalization coefficient: norm=1/255

...

for i:=1 to M do for j:=1 to N do

g[i,j]:=round(sqr(f[i,j])*norm);

...

Nonlinear grayscale transformation - algorithm

Example: square function (using look-up-table)

lut : array[0..255]of byte;

...

for k:=0 to 255 do lut[k]:=round(k*k*norm)

for i:=1 to M do for j:=1 to N do

g[i,j]:=lut[(f[i,j])];

...

Nonlinear grayscale transformation - algorithm

Enhacement of a telescope moon image

T=b log( ax)

Consider a noisy image:

( ) ( ) ( )jijifjig ,,, η+=

contaminated by additive noise η(i,j) of zero average an variance σh

2 that is not correlated to the image.

We will show that after N averagings (acquisitions) of

the noisy image g(i,j) the variance of noise

component will be reduced to:

N

22 ηη

σσ =

Image ehancement by image averaging

Image ehancement by image averaging

∑∑==

+=+=N

kk

N

kk jin

Njifjinjif

Njig

11),(

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

1),(

1N

+ +...+ =

WARNING ! – grayscale range

Noise variance in the averaged image:

( ){ }22

21

22

1

22

2212

2

12

2

1

2

111

211

11

ηη=

≠=

==η

σ=σ=

η=

=

ηη+η⋅=η++η+η⋅=

=

η⋅=

η=σ

∑

∑∑

∑∑

NN

NE

N

EN

EN

ENN

E

N

kk

N

pkpk

N

kkN

N

kk

N

kk

K

=0

Image ehancement by image averaging

One can also show that the pick value of noise {n} is reduced by a factor of √Nafter N image averagings

N=1

N=8 N=16

N=2

Microscope image of a cell

Additive Gaussian noise

Addison-Wesley

Image averaging – example

Cumulative histogram

ensionsimageNM

LiMNkhistihistc

ofarrayhists

ofarrayhist

histogramcumulativehistchistogramimagehist

i

k

dim,

1,...,0,/])[(][

;]255..0[:

]255..0[:

,

0

−

−==

−−

∑=

single

longint;

0 50 100 150 200 250

0

0.5

1

1.5

0 50 100 150 200 250

0

200

400

600

800

1000

Histogram Cumulative histogram

Cumulative histogram

Histogram equalization

By histogram equalization one gets:

• contrast enhancement

• image normalization

Histogram equalization aims at obtaining uniform statistical distribution of image gray levels (uniform probability density function)

L-10 f

p (f)f

L-1

1/(L-1)

0 g

p (g)g

pf(f)=hist[f]/MN pg(g)=1/(L-1)

Histogram equalization

][)1(][

)1()()1(

12,1,0,1

)(

1,011

1

1

1)(

)()(

00

0

0 00

fhistcLMN

ihistLipLg

,...,L-gfL

gip

LgfL

gu

Ldu

Ldhhp

duupdhhp

f

i

f

if

f

if

f gg

f

gf

−=−=−=

=−

=

−≤≤−

=−

=−

=

=

∑∑

∑

∫ ∫

∫∫

==

=

Histogram equalization

Histogram equalization

0 50 100 150 200 250

0

500

1000

1500

2000

2500

3000

3500

4000

0 50 100 150 200 250

0

0.5

1

Histogram

Cumulativehistogram

Equalizedhistogram

][)1( fhistcLg −=

g

f

Cumulative histogram - algorithm

hist : array[0..255] of longint;

histc : array[0..255] of single;

...

histc[0]:=hist[0];

for k:=1 to 255 do

histc[k]:=histc[k-1]+hist[k];

...

0 50 100 150 200 250

0

1000

2000

3000

4000

5000

6000

Histogram equalization

0 50 100 150 200 250

0

1000

2000

3000

4000

5000

6000

7000

0 50 100 150 200 250

0

1000

2000

3000

4000

5000

6000

7000

Histogram equalization - example

0 50 100 150 200 250

0

1000

2000

3000

4000

5000

6000

7000

MATLAB Demo – intensity adjustment

Correction of nonuniform illumination