数字图像处理-图像的表达

数字图像处理-图像的表达Sampling&Quantisation采样和量化• 采样时要确定好空间分辨率，即DP

I• 量化时要确定好灰度分辨率，將采样影像转换为数值的过程称为量化。例如，白色是转化为“1”和黑色則转化为“0”。Digital

Image

AcquisitionA physical image, which may be visible orinvisible

to

the

human

eye,

is

normally

a

continuous-tone image with

various shades

blended togethersmoothly having no disruptions. Acquisition of adigital

image

from

a

continuous-tone

image

requiresdigitization

of

spatial

coordinates(Known

as

sampling)and

digitization

of

brightness(Known

as

quantisation).Image

DigitiserConsequently,

an

image

digitiserconsists

of

five

elements:Sampling

aperture

to

allow

the

digitiser

to

access

image

elementsindividuallyScanning

mechanism

to

move

the

sampling

aperture

over

the

image

ins

predetermined

patternLight

sensor

to

measure

the

brightness

of

the

image

at

each

pixelthrough

the

sampling

apertureA/D

converter

to

convert

the

continuous

output

of

the

light

sensor

intoan

integer

valueMemory

to

store

the

gray-level

values

produced

by

the

A/D

converterSamplingandSpatialResolution4If

a

continuous-tone

image

is

approximated

bya

N

lines*M

pixels

digital

image,thenit

requires

decisions

about

values

forN

and

M.

In

practice,N

and

M

arepredetermined

dueto

thelimited

choice

of

available

camerasandimage

acquisition

hardware

and

are

normallyset

to

integerpowers

of

2.As

N

and

M

are

decreased,the

number

of

pixels

in

a

digitalimage

decreased

rapidlygiving

worseapproximation

of

the

originalimage

dueto

lowerspatial

resolutionSamplingandSpatialResolutionHowever,for

a

given

application,

selecting

the

minimum

resolution

necessary

cansignificantly

reduce

storage

and

processing

requirements.

According

to

the

classicalsampling

theorem,

an

image

mustbe

sampled

at

a

rate

atleasttwice

as

fast

as

the

highest

spatial

frequency

(the

frequency

at

which

brightness

cycle

from

dark

to

light

andback

to

dark)

contained

in

theimage.Original

Image

LineSampled

at

a

rate

lessthanhalf

the

spatialfrequencyUndersampledImage

LineSpatial

aliasing

occurswiththe

high

frequency

detailbeing

translatedtoa

lowfrequency

due

to

some

of

itstransitionsare

missedIn

the

selection

of

a

suitable

spatial

resolution,

the

display-observer

distance

is

anotherfactor

for

consideration.As

the

distance

between

animage

and

observer

doublescorrespondingto

a

reduction

of

theimage

size

byon-half,

the

spatial

resolution

can

be

decreased

byon-halfwithout

causing

anyspatial

detail

loss

for

the

observer.Correctly

SampledImage

LineSampled

at

a

rate

2

times

thespatial

frequencyQuantisationandBrightnessResolutionIf

the

intensity

of

a

continuous-tone

image

ata

samplingpoint

isquantised

toaninteger

value

calledthe

gray-level,

thenthe

accuracy

of

the

gray-level

assigneddepends

on

the

numberofbitsusedtorepresent

the

number

of

gray-levels

in

animage.Asthe

number

ofbitsare

decreased,the

imageappearscoarser

due

tolower

brightnessresolutionwithaninsufficient

number

of

gray-levels

insmoothareas

of

theimage.Ex001.mLike

spatialresolution,

the

brightness

resolutionalso

dependsonimage-observer

distance.

Thesmaller

the

imageasitis

placedfurtheraway

from

theobserver,

the

lower

brightness

resolutionneeds

tobe.BrightnessResolution

分辨率• 電腦顯示器的解析度大約為

72dp

i

，印表機是從150

到1440dp

i

(高解析度機種)

，而掃瞄器的解析度是300dp

i

或更高。Pos

t

sc

r

i

p

t

的印表機使用一種解析度衡量方式，稱為每英吋線數(

l

p

i

)，意思是指每一英吋中可以畫入的線條數量。這種方式的影用是基於要把半色調影像，例如相片，分解成點(

或圖素)

。在過去，這種半色調的顯示是由不同寬度的直線構成。在近年，轉變成以格子的方式來呈現，因此可以把影像分裂成點，每英吋線數的方式也就不適用了。報紙有

60

lpi的解析度，而雜誌有133-175

lpi的解析度。高品質的印刷原料可能會超過

200lpi。DigitalImageRepresentationA

digital

image

is

represented

mathematically

bythe

function

f(x,y),

where

x

and

y

areindependent

variables

denoting

spatialco-ordinates,and

the

value

of

fatspatial

co-ordinates

(x,y)

gives

the

intensityof

the

image

atthatpoint.

However,

there

are

threedifferent

spatialco-ordinate

systems

being

used

in

digitalimage

processing:Cartesian

co-ordinate

systemMatrix

co-ordinate

systemPixel

co-ordinate

systemxy0 12 3 4210xy12 3 4 5123111

2 3 4 51 0 1 1 1 02

0 1 0 3 1 0 111ColumnRowOriginalPixel8DigitalImageRepresentationinMatlab9Matlab

uses

a

rectangular

matrix

(two-dimensional

array)

to

represent

adigital

image.

There

are

four

basic

types

of

images

supported

by

Matlab,namely,intensity

(gray-level)

images,

binary

images,

RGB

imagesandindexed

images.IntensityImages

(Gray-ScaleImages)10Matlab

uses

a

single

matrix

to

represent

an

intensity

image

with

the

magnitude

value

ofeach

element

inthe

matrix

corresponding

tothe

gray-level

of

each

pixel

in

the

image.Two

differentdata

types

are

available

in

Matlab

to

represent

the

gray-level:double(double

precision):

the

gray-level

values

rang

from

0

(corresponding

to

black)

to

1

(corresponding

to

white),

and

it

is

used

forperforming

mathematical

operations.uint8(unsigned

8

bit

integers):

the

gray-level

values

range

from

0

(corresponding

to

black)

to

255(corresponding

to

white),

and

it

is

used

to

save

memory

as

it

requires

only1/8

the

memory

for

a

double

precision

array

(no

mathematical

operations

are

defined

forthis

data

type).Actual

gray-level

0

128

192

255

In

uint8

formatNormalised

gray-level00.5020

0.7529

1In

double

formatGray-ScaleImages11BinaryImagesMatlab

used

asingle

matrix

to

represent

a

binary

image

(aspecial

kind

ofintensity

image)

with

the

magnitude

valued

ofeach

element

in

the

matrixbeing

either

0

(black)

or

1(white).Binary

Image12Gray-ScaleImage13RGBImagesAll

colours

can

formed

by

various

combination

of

the

three

primary

colours,namely,

red(R),

green(G)

and

blue(B).In

Matlab,a

colour

image

isrepresented

by

three

separate

matriceswith

thesame

row

and

column

dimensions

to

represent

the

corresponding

red,

greenand

blue

components.0

.

75

0

.50

1 0 0 1 1 0 0

.50

0

01101010

.50010110

.50Red

Matrix 255002552550128255Green

Matrix025502550255128192

Blue

Matrix 002550255255128128

RGBImages14IndexedImages15In

the

indexed

image

representation,

Matlab

used

two

matrices,namely,

acolour

map

matrix

and

an

image

matrix,

to

represent

a

colour

image.

Thecolour

map

matrix

is

a

look-up

table

(LUT)

containing

n-row

by

3-columnelements,where

n

rowsspecify

the

number

of

possible

coloursand

3

columnsspecify

the

intensity

of

the

red,

green

and

blue

components

of

each

colour

(theintensity

of

each

colour

isspecified

on

the

interval

form

0

to

1).

The

value

ofeach

element

inthe

image

matrix

isused

as

an

index

to

look

up

the

desiredcolour

in

the

colour

map

for

each

image

pixel.

8 7 6 5 41 2 3 4 5G0101010.5020 0.5020

70.7925 0.5020

8B00

21

30 1

51

6

4Row

110.5020R100110ColorMap

MatrixImage

MatrixColor

ImageTutorialProblems(a)

For

digital

image

with

512x1024

pixels,

plot

the

memory

requirements

against

the

number

of

bits(from

1to

8)

usedtorepresent

a

pixel

value.If

c

computer

has

an

available

memory

of

1Mbyte,

determine

the

number

of

images

which

can

bestoredat

differentresolutions.(a)A

1024x1024

digita