On Fuzzy image processing

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Nov 6, 2013 (3 years and 9 months ago)

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On Fuzzy image processing


By


A. Lecture KARRAR DH. MOHAMMED

History

In

the

1970
s,

digital

image

processing

proliferated,

when

cheaper

computers

and

dedicated

hardware

became

available
.

Images

could

then

be

processed

in

real

time,

for

some

dedicated

problems

such

as

television

standards

conversion
.

As

general
-
purpose

computers

became

faster,

they

started

to

take

over

the

role

of

dedicated

hardware

for

all

but

the

most

specialized

and

compute
-
intensive

operations
.

History


With

the

fast

computers

and

signal

processors

available

in

the

2000
s,

digital

image

processing

has

become

the

most

common

form

of

image

processing,

and

is

generally

used

because

it

is

not

only

the

most

versatile

method,

but

also

the

cheapest
.


What is an Image

1.
An

image

f

(
x,

y
)

is

2
-
dimensional

light

intensity

function

,where

f

measures

brightness

at

position

(
x,

y
)
.


2
.

A

digital

image

is

a

representation

of

an

image

by

a

2
-
D

array

of

discrete

samples
.


3
.

The

amplitude

of

each

sample

is

represented

by

a

finite

number

of

bits
.


4
.

Each

element

of

the

array

is

called

a

pixel
.

Terminology

Images:
An image is a two
-
dimensional
signal whose intensity

at any point is a function of two spatial
variables.

Examples are photographs, still video
images, radar and

sonar signals, chest and dental X
-
rays.

An image sequence such as that seen in a


television is a three dimensional signal for


which the image intensity at any point is


a function of three variables: two spatial


variables and time.

1.
Digital image processing
is a term used to describe

the manipulation of image data by a computer.


2. The process of transforming an image to a set of

numbers, which a computer can utilized, is called

digitization
.


3.
Digitization
is to divide an image up into several

picture elements called
pixels
. A pixel is the smallest

resolvable unit of an image which the computer

handles.


4. The value of a pixel is referred to as its gray level and can
be thought of as the intensity or brightness (or darkness)
of the pixel.


5. The number of different gray
-
levels a pixel can have
varies from system to system, and is determined by the
hardware that produces or displays the image.

Why do we process images


Images (and videos) are every where .This
includes different imaging modalities such as
visual, X
-
ray, ultrasound, ] etc. Multimedia
information will be the wave of the future.
Diverse applications in astronomy, biology,


geology, geography, medicine, law enforcement,
defense,


Industrial inspection, require processing of
images.

Grayscale and Color Images

1
.

For

grayscale

image,

256

levels

or

8

bits/pixel

is

sufficient

for

most

applications

2
.

For

color

image,

each

component

(R,

G,

B)

needs

256

levels

or

8

bits/pixel

3
.

Storage

for

typical

images


(a)

512

×

512
,

8

bits

grayscale

image
:

262
,
144
B


(b)

1024
×
768
,

24

bits

true

color

image
:

2
,
359
,
296
B


Grayscale Image

Color Images

X R
(
n,m
)
, X G
(
n,m
)
, X B
(
n,m
)

F
(
x, y
)

F
(
m, n
)
,
0
≤ m ≤ M −
1
,
0
≤ n ≤ N −
1


A digital image can be written as a matrix



























1)

-

N
1,

-

x(M
...

1)

1,

-

x(M
0)

1,

-

x(M

....


....


....

....


....


....

....


....


....
....


....


....
1)

-

N
x(1,
.....

1)

(1,
x
0)

x(1,
1)

-

N
x(0,
.....

1)

(0,
x
0)

x(0,
F
Image

Operations

can

be

classified

as

Linear

and

non
-
linear

Operations
:

H
is a linear operator if if satisfies the
superposition

principle:

H
(
af
+
bg
) =
aH
(
f
)+
bH
(
g
)

for all images
f
and
g
and all constants
a
and
b
.

1. Mean filtering: Linear

2. Median filtering: Non
-
linear

Simple Operations On Images

Digital Negative:
Given an image
F
, the
Digital
Negative
of
F
is defined as

F Negative
(
m, n
) =
255
− F
(
m, n
)

Feature Enhancement by
Subtraction

A Brief History of Lena (Lenna)

Anyone

familiar

with

digital

image

processing

will

surely

recognize

the

image

of

Lena
.

While

going

through

some

old

usenet

discussions,

I

got

to

know

that

Lena

has

a

history

worth

all

the

attention

that

has

been

paid

to

her

over

the

years

by

countless

image

processing

researchers
.

Lena

Sjblom,

(also

spelled

Lenna

by

many

publications)

was

the

Playboy

playmate

in

November

1972

and

rose

to

fame

in

the

computer

world

when

researchers

at

the

University

of

Southern

California

scanned

and

digitized

her

image

in

June

1973
.

(Lena

herself

never

know

of

her

fame

until

she

was

interviewed

by

a

computer

magazine

in

Sweden

where

she

lives

with

her

husband

and

children)
.

A Brief History of Lena (Lenna)

According

to

the

IEEE

PCS

Newsletter

of

May/June

2001
,

they

were

hurriedly

searching

for

a

glossy

image

which

they

could

scan

and

use

for

a

conference

paper

when

someone

walked

in

with

a

copy

of

Playboy
.

The

engineers

tore

off

the

top

third

of

the

centerfold

and

scanned

it

with

a

Muirhead

wire

photo

scanner

(a

distant

cry

from

the

flatbed

scanners

of

today)

by

wrapping

it

around

the

drum

of

the

scanner
.

(Now

you

know

why

the

image

shows

only

a

small

part

of

the

entire

picture
..

discounting

of

course,

the

fact

that

the

complete

picture

would

raise

quite

a

few

eyebrows
.

Linear Stretching

1
.

Enhance

the

dynamic

range

by

stretching

the

original

gray

levels

to

the

range

of

0

to

2
.

Example

(a)

The

original

gray

levels

are

[
100
,

150
]
.

(b)

The

target

gray

levels

are

[
0
,

255
]
.

(c)

The

transformation

function


g
(
f
)

=

((
f



100
)
/
50
)



255

for
100



f



150

Illustration of Linear Stretching

Image/video Processing Methods

1
. Image Enhancement

2
. Image Restoration

3
. Compression

4
. Image reconstruction

5
. Morphological image processing

6
. Feature extraction and recognition,
computer vision

Other Image Operations

Image algebra includes mathematical
comparisons, altering values of pixels,
thresholding, edge detection and noise
reduction.

1
.
Neighborhood averaging
is to avoid extreme
fluctuations in gray level from pixel to pixel. It is
also very effective tool for noise reduction.

2
.
Image Scaling
is a means of reducing or
expanding the size of an image using existing
image data.

3
.

Histogram

Equalization

is

an

adjustment

of

gray

scale

based

on

gray
-
level

histogram
.

This

is

effective

in

enhancing

the

contrast

of

an

image
.

4
.

Edge

Detection

is

an

operation

of

measuring

and

analyzing

the

features

in

an

image

by

detecting

and

enhancing

the

edges

of

the

features
.

The

most

common

edge

detection

method

is

gradient

detection
.

5
.

Image

Restoration
:

Given

a

noisy

image

y
(
m,

n
)

y
(
m,

n
)

=

x
(
m,

n
)+
v
(
m,

n
)

where

x
(
m,

n
)

is

the

original

image

and

v
(
m,

n
)

is

noise
.

The

objective

is

to

recover

x
(
m,

n
)

from

y
(
m,

n
)
.

Color Restoration

Photo Restoration

6
.
Contrast Enhancement:
how to enhance the
contrast of an image?

1
. Low contrast image values concentrated near
narrow range (mostly dark, or mostly bright, or
mostly medium values)

2
. Contrast enhancement change the image value

distribution to cover a wide range

3
. Contrast of an image can be revealed by its
histogram

Histogram
The histogram of an image with
L
possible

gray levels,
f
=
0
,
1
, · · · , L −
1
is defined as:




where



nl
is the number of pixels with gray level l.



n
is the total number of pixels in the image.

n
nl
l
p

)
(
Examples of Histograms

Applications

Astronomy:
Hubble Space Telescope : This
telescope has limitation in resolution due to
atmospheric turbulence.

Optical

problem

in

a

telescope

results

in

blurred,

out

of

focus

image
.

Digital

image

processing

is

normally

used

to

recover

the

desired

information

from

these

images
.

Applications

Medical Imaging:
Most of advanced
medical imaging tools are based on DSP
tools. X
-
Ray computerized Tomography
(X
-
ray CT) is capable of generating a
cross
-
sectional display of the body. This
involves X
-
ray generation, detection,
digitization, processing and computer
image reconstruction. Similarly, NMRCT
(nuclear magnetic resonance).

MRI

Ultrasound

Fingerprint

In
1684
, an English plant morphologist

published the first scientific paper reporting

his systematic study on the ridge and pore structure

in fingerprints.


A fingerprint image may be
classified as:

(a) Offline: Inked impression of the fingertip on a


paper is scanned

(b) Live
-
scan: Optical sensor, capacitive sensors,


ultrasound sensors, ...

At the local level, there are different local ridge


characteristics. The two most prominent ridge


characteristics, called minutiae, are:

(a) Ridge termination

(b) Ridge bifurcation

At the very
-
fine level, intra
-
ridge details (sweat pores) can
be detected. They are very distinctive; however, very
high
-
resolution images are required.

Face Recognition

Face Recognition Methods

(a) Template matching using minimum
-
distance


classifiers metrics

(b) Linear discriminants

(c) Bayesian approach

Watermarking

The World Wide Web and the

progress in multimedia storage and transmission

technology expanded the possibility of illegal copying

and reproducing of digital data. Digital watermarking

represents a valid solution to the above

problem, since it makes possible to identify the

source, author, creator, owner, distributor or authorized

consumer of digitized images, video recordings

or audio recordings. A digital watermark

is an identification code, permanently embedded

into digital data, carrying information pertaining

to copyright protection and data authentication.

(a) Copyright protection and authentication

Image Compression Techniques

1
. JPEG
2000
standard is based on wavelets

2
. JPEG (original) is based on the Discrete Cosine

An Example of Image Compression

What does Fuzzy Image
Processing mean
?

Fuzzy image processing is not a unique theory. It is a
collection of different fuzzy approaches to image
processing. Nevertheless, the following definition can be
regraded as an attempt to determine the boundaries
:


Fuzzy image processing is the collection of all
approaches that understand, represent and process the
images, their segments and features as fuzzy sets. The
representation and processing depend on the selected
fuzzy technique and on the problem to be solved
(

From
:
Tizhoosh, Fuzzy Image Processing
,
Springer

(
1997
)


Fuzzy image processing has three main stages: image
fuzzification, modification of membership values, and, if
necessary, image defuzzification


see figure below

The general structure of fuzzy image processing
.