2. point processes computer engineering, sejong university...

Image Processing

2. Point Processes

Computer Engineering, Sejong University

Dongil Han

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Spatial domain processing

g(x,y) = T[f(x,y)]

f(x,y) : input imageg(x,y) : processed imageT[.] : operator on f, defined over some neighborhood of (x, y)

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Point Processes

The simplest form of T[.]•• processed output depends only on the value of f at (x, y)

s = T(r)

r : gray-level of f(x,y)s : gray-level of g(x,y)T[.] : operator on f, becomes a gray-level mapping function

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Some basic point processing techniques

• Arithmetic operations

•

• Look-up table processing

• Histogram

• Contrast stretching

• Intensity transform

Point Processes

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Arithmetic Operations

Addition, Subtraction, Multiplication, Division operations over pixels by a constant value

•

g(x,y) = f(x,y) + c

• multiplication, division operations : adjusting the contrast

g(x,y) = a * f(x,y)

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<Original> <Original+50> <Original-60>

Addition, Subtraction Operations•• Subtracting to a pixel : darkens the image• Nothing to increase/decrease the local contrast

e.g.) g(x,y) = f(x,y) + 50, g(x,y) = f(x,y) - 60


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Multiplication, Division Operations•• Multiplication : increase the local contrast • Division : decrease the local contrast

e.g.) g(x,y) = 1.5 * f(x,y), g(x,y) = f(x,y)/1.5

<Original> <Original *1.5> <Original/1.5>


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Problems•• Subtraction : : can exceeds the min. value of image range• Multiplication : can exceeds the max. value of image range

=> simple solution: clampinge.g.) negative value : set to 0, greater than 255: set to

255 => may generates saturated image

original saturated


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Logical Operations

XOR (Exclusive OR) Operation

AND Operation

OR Operation

A XOR B A = 0 A = 1

B = 0

B = 1

0

1

1

0

A AND B A = 0 A = 1

B = 0

B = 1

0

0

0

1

A OR B A = 0 A = 1

B = 0

B = 1

0

1

1

1

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XOR operation in image processing• used to find all pixels of a certain value•

if f(x,y) = c then g(x,y) = 0 else g(x,y) = f(x,y)

• application example- generates cursor- extracts certain value in an image- Pseudo-color image processing

Logical Operations

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<ORIGINAL> <ORIGINAL XOR 128>

<ORIGINAL XOR 250>

Logical Operations

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Pseudo color image processing

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Look-up Table

Look-up Table(LUT)•• array index : current pixel value• array output : generated new pixel value

advantage• easy to use(Software : array, Hardware : Memory)• complex mathematical expression : just LUT

programming (e.g.: y = sin x, y = log x)

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Graphical representation of LUT• x axis : index of array (input pixel value)•• y axis : LUT output (processed pixel value)

x

y

0 1 2 3 4 5 6 7input image

output image

76543210

Look-up Table

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LUT example : Gamma correction

Look-up Table

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Gamma correction• CRT devices have a non-linear intensity-to-voltage response•• low voltage region : darker than intended• gamma correction : the process used to correct this response

voltage(gray-level)

brightness

display characteristics

of CRT

Look-up Table

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Gamma correction

•

• Inverse response curve is adapted in camera system(L : luminance, V : output voltage of camera, : determines the gain)

10812.0099.1

)099.0(

VforV

L

0812.005.4

VforV

L

1018.0099.0099.1 )/1( LforLV

018.00500.4 LforLV

Look-up Table

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Display gamma

Camera gamma

Gamma correction

• variations of response dependent on the gamma value

Final display characteristics

Look-up Table

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Gamma correction• Gamma > 1 : darker image

=>

• Gamma < 1 : brighter image=> intentionally adjusted characteristics of Camera

• Gamma = 1 : normal image=> final display image

Gamma > 1darker image

Gamma = 1normal image

Gamma < 1brighter image

Look-up Table

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display before gamma

correction

original image

gamma correction(Camera)

display after gamma

correction

Look-up Table

Gamma correction

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Broadcasting block diagram using gamma correction

Look-up Table

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• separate gamma correction for R, G, B signal in color TV• incorrect gamma correction may generate unintended color

signal for gray images

Look-up Table

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Problems of gamma correction

• Each display device has different gamma characteristics=>

• PDP : linear curve between input voltage and output luminance

• camera signal renders gamma corrected signal : PDP needs inverse gamma response

input voltage

luminance

input voltage

luminanceCRT PDP

Look-up Table

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Image enhancement using gamma curve

Look-up Table

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Image enhancement using LUT

Look-up Table

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Image enhancement using LUT

Look-up Table

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Histogram

imagehistogram

Mathematical definition• graphical representation of the distribution data•

Histogram in image processing• graphical representation used to view the intensity profile

of an image- X-axis : possible pixel intensity values- Y-axis : number of occurrences for each intensity

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Mathematical representation of histogram•

nk = h(rk), rk : kth level, 0 < k < 255

Here, nk can have values between 0 < nk < 64x64(4096)

Histogram Normalization• histogram is divided by the total number of pixels

If we let the total number of pixels be n

nk/n = p(rk), rk : kth level, 0 < k < 255

Here, p(rk) can be considered probability density function

Histogram

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Properties of Histogram• renders the intensity profile of an image• can estimate the contrast information of an image•• brightness image : Histograms are right shifted• contrast is low: Histograms are crowded in a narrow area• contrast is high: Histograms are extended out in a wide area

Histogram

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Histogram vs. Arithmetic Operation• addition operation: brightens the image

=> • subtraction operation : darkens the image

=> Histogram : shift left

originalOriginal + 40 Original - 40

Histogram

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Histogram vs. Arithmetic Operation• multiplication operation : increase the local contrast

=> • division operation : decrease the local contrast

=> Histogram : shrink narrower

originalOriginal * 1.2 Original / 1.2

Histogram

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Color image histogram• histogram processing is conducted in each R, G, B signal

Histogram

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Cumulative Distribution Function(CDF:누적 분포 함수)•

w : dummy variable for integrationr : random variable of CDF

Mathematical Properties of CDF T(r)• monotone increasing function in region

•

•

• may not have an inverse function

r

010 ,)( r(w) dwprTs r

10 r

1010 rfor T(r)

11 )T(

Histogram

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Properties of CDF T(r)• dark image =>

• bright image => bends downwards

0 1

1

0 1

0

1

0 1

1

0 1

1

“histogram”

“histogram”

“CDF curve”

“CDF curve”

0

0 0

Histogram

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Histogram

Image correction using CDF• use CDF as a LUT

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Image correction using CDF• dark image => LUT =>

• bright image => LUT => increase the dark portion

0 1

1

0 1

0

1

0 1

1

0 1

1

“histogram”

“histogram”

“CDF curve”

“CDF curve”

0

0 0

Histogram

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Histogram Equalization

Histogram Equalization(HE)• goal : obtain a uniform histogram by redistribution of

original histogram- HE example

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Histogram Equalization process1.2. calculate normalized sum of histogram(CDF)3. transform input image to output image using CDF

1 2 3


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Properties of HE•• mostly, generates images with maximum contrast• work well on images with fine details in dark region• can not change the frequency of each luminance level• Automatic!! : Good quality images can be degraded by

HE


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Histogram Specification

desiredhistogram

Histogram Specification• The method used to generate a processed image that has a

specified histogram• can lighten or darken an image or make more contrast of an

image•• histogram equalization + inverse histogram equalization• also called “Histogram matching”

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The procedure of Histogram Specification1.2. calculate normalized sum of histogram(CDF) T(r)

3. calculate normalized sum of desired histogram G(z) that it has G(z)-1

4. perform histogram equalization using an input image, after that, perform inverse histogram equalization using the CDF of the desired histogram

r

r dwwprTs0

.)()(

z

z dwwpzGv0

.)()(

)(1 sGz )]([1 rTGz


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Contrast Stretching

Contrast•

lowhigh

lowhighContrast

Contrast stretching• stretch a histogram to fill the full dynamic range of

image• good contrast image exhibits a wide range of pixel

values

low contrast high contrast

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Basic contrast stretching•• works best on images that have all pixels concentrated

in one part of the histogram

Contrast Stretching

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End-In-Search• must specify that a certain percentage of the pixels must

be saturated to full white or full black•• High : converted to full white

Contrast Stretching

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Original Image

Original Image

Basic Contrast Stretching

End-in Search

Contrast Stretching

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Piecewise-Linear Stretching• transform function is divided into several piecewise linear

function•• parameter setting: clamping, thresholding, etc.• clamping : • thresholding :

Lubvbu

buavau

auu

v

LvLuufv

b

a

)(

)(

0,

],0[],,0[)(

0 ],[ bautba

Contrast Stretching

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5.0

5.0

5.1

5.1

5.0

5.0

5.0

5.1

5.0

Piecewise-Linear Stretching

Contrast Stretching, a = 80, b= 160

Contrast Stretching

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Contrast Stretching

Piecewise-Linear Stretching

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Intensity Transform

Intensity Transform• converts an old pixel into a new pixel based on some

predefined function•

Simple intensity transform example• null transform

y = x

• negative transformy = 255 - x

• gamma correction

• stretching

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Intensity Transform

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Intensity transform example • compression

-- reduce the dynamic range of an image

• posterizing- reduce the number of gray levels in an image- can reduce the size of an image

• thresholding- posterizing with the number of gray levels is reduced 2- generates binary images

Intensity Transform

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Intensity Transform

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Intensity transform example • bounded thresholding

-- treats the other input pixels as null transforms

• iso-intensity contouring- sets particular input intensity values to black or white- uses to find certain intensity level

• solarizing- negative transform for the bright part of an image

Intensity Transform

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Intensity Transform

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