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數(shù)字圖像處理-圖像的表達(dá)Sampling&Quantisation采樣和量化? 采樣時(shí)要確定好空間分辨率,即DP
I? 量化時(shí)要確定好灰度分辨率,將采樣影像轉(zhuǎn)換為數(shù)值的過程稱為量化。例如,白色是轉(zhuǎn)化為“1”和黑色則轉(zhuǎn)化為“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(jī)是從150
到1440dp
i
(高解析度機(jī)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(jī)使用一種解析度衡量方式,稱為每英吋線數(shù)(
l
p
i
),意思是指每一英吋中可以畫入的線條數(shù)量。這種方式的影用是基於要把半色調(diào)影像,例如相片,分解成點(diǎn)(
或圖素)
。在過去,這種半色調(diào)的顯示是由不同寬度的直線構(gòu)成。在近年,轉(zhuǎn)變成以格子的方式來呈現(xiàn),因此可以把影像分裂成點(diǎn),每英吋線數(shù)的方式也就不適用了。報(bào)紙有
60
lpi的解析度,而雜誌有133-175
lpi的解析度。高品質(zhì)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
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