unit 3 image enhancement-2

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UNIT 3IMAGE ENHANCEMENT

TextbookDigital Image Processingby Gonzales/Woods

AcknowledgementsDr. Rolf Lakaemper

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Image ENHANCEMENTin theSPATIAL DOMAINImage ENHANCEMENTin theSPATIAL DOMAIN




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Spatial domain techniques

Point processing / intensity transformations / gray level transformations> Image Negatives

> Log Transformations

> Power

Law

Transformations

> Piecewise Linear Transformation Functions Contrast stretching

Thresholding Graylevel slicing Bitplane slicing

Mask processing / spatial filtering




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Image Enhancement (Spatial)

Image enhancement:

1. Improving the interpretability or perception of information in images for human viewers

2. Providing `better' input for other automated image processing techniques

Spatial domain methods:

operate directly on pixels Frequency domain methods:

operate on the Fourier transform of an image




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Point Processing The simplest kind of range transformations are

these independent of position x,y :g = T(f)

This is called point processing.

Important: every pixel for himself spatial

information completely lost!




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Remember ?

T transforms the given image f(x,y)into another image g(x,y)

f(x,y) g(x,y)




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Operation on the set of image-pixels

6 8 2 0

12 200 20 10

3 4 1 0

6 100 10 5

Spatial Domain

(Operator: Div. by 2)




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Operation on the set of neighborhoodsN(x,y) of each pixel

6 8 2 0

12 200 20 10

226

Spatial Domain

6 8

12 200

(Operator: sum)




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Operation on a set of images f1,f2,

6 8 2 0

12 200 20 10

Spatial Domain

5 5 1 0

2 20 3 4

11 13 3 0

14 220 23 14

(Operator: sum)



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Chapter 3Image Enhancement in the

Spatial Domain



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Operation on the set of image-pixels

Remark: these operations can also be seen as operations on the

neighborhood of a pixel (x,y), by defining the neighborhood as thepixel itself.

The easiest case of operators g(x,y) = T(f(x,y)) depends only on the value

of f at (x,y)

T is called agray-level or intensity transformation

function

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Spatial Domain



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Spatial Domain



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Basic Gray Level Transformations

Image Negatives Log Transformations Power Law Transformations Piecewise-Linear Transformation

FunctionsFor the following slides L denotes the max. possible gray value of the

image, i.e. f(x,y) [0,L-1]

Transformations w w w . j n t u w or l d . c o m


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Image Negatives: s=L-r-1

Transformations

Input gray level

O u

t p u

t g r a y

l e v e

l



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Log Transformations:s = c * log (1+ r)

Transformations w w w . j n t u w or l d . c o m


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Log Transformations

Transformations

InvLog Log



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Spatial Domain

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Why power laws are popular?

A cathode ray tube (CRT), for example,

converts a video signal to light in a nonlinear way. The light intensity I is proportional to a power ( ) of the source voltage VS

For a computer CRT, is about 2.2 Viewing images properly on monitors requires

correction



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Power Law Transformations orGamma Transformationss= cr

Transformations w w . j n t u w or l d . c o m


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varying gamma ( ) obtains familyof possible transformation curves

> 1 Compresses dark values

Expands bright values < 1

Expands dark values Compresses bright values



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Used for gamma-correction



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Used for general purpose contrast manipulation



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Spatial Domain



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Piecewise Linear Transformations

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Thresholding Function

r1=r2 and s1=0 and s2=L-1g(x,y) = L if f(x,y) > t,

0 elset = threshold level


Input gray level

O u

t p u

t g r a y

l e v e

l

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Gray Level (Intensity level) Slicing

Purpose: Highlight a specific range of gray values

Two approaches:

1. Display high value for range of interest, low valueelse (discard background)

2. Display high value for range of interest, originalvalue else (preserve background)

Piecewise Linear Transformations w . j n t u w or l d . c o m



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Bit-plane Slicing

Extracts the information of asingle bit-plane

Piecewise Linear Transformations w . j n t u w or l d . c o m


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BP 7

BP 5

BP 0



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Spatial Domain



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Spatial Domain



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Spatial filters

Smoothening filters

Low pass filters Median filters

Sharpening filters

High boost filters Derivative filters



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Spatial Domain



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Smoothing linear filters /averaging

filters / low pass filters (linear filter) Uses

Blurring Noise reduction



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Spatial Domain



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Order static filter / (non linear

filter) / median filter Objective:

Replace the valve of the pixel by the median of the intensity values in the neighbourhood of that pixel

Principle function: Force points with distinct intensity levels to be more

like their neighbours

Uses: Noise reduction

Less blurring Reduce impulse noise



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Sharpening spatial filters

Objective:

High light fine details in an image

Applications: Electronic printing Medical imaging Industrial inspection Autonomous target detection



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High boost

filtering

/High frequency emphasis filter /

Unsharp masking Principle:

Subtract an unsharp image from the original image

Uses:

Printing industry Publishing industry



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Process steps:

1. blur the original image 2. subtract the blurred image from the original

(the difference is the mask) 3. add the weighted mask to the original



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Derivative filtering

The derivatives of digital functions are defined

in terms of differences.



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First derivative:1. Must be zero in areas of constant intensity2. Must be non zero at the onset of an intensity

step or ramp3. Must be non zero along the ramps

Second derivative 1. Must be zero in areas of constant intensity2. Must be non zero at the onset and end of an

intensity step or ramp3. Must be zero along the ramps of constant slope



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Using the first order derivatives for (non

linear) image

sharpening

The

Gradient

First derivatives

in

image

processing

are

implemented using magnitude of the gradient.

Uses: Industrial inspection Enhance defects Eliminate slowly changing background features



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Using the second derivatives for (linear) image sharpening The Laplacian

Uses Highlights intensity discontinuities in an image Deemphasizes regions with slowly varying intensity

levels.



S ti l Filt i g w w w .j


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Spatial Filtering

Different variants of the Laplacian

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Histogram processing



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Histogram processing

Histogram equalization Histogram matching / specification



Histograms w w w .jn


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Histograms

Remember:The histogram shows the number of

pixels having a certain gray-value

n u m

b e r o

f p

i x e

l s

Gray-value (0..1)



Histograms w w w . j n


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Histograms

The NORMALIZED histogram is thehistogram divided by the total number

of pixels in the source image.

The sum of all values in the normalizedhistogram is 1.

The value given by the normalizedhistogram for a certain gray value canbe read as the probability of randomlypicking a pixel having that gray value





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Histograms

What can the (normalized)

histogram tell about theimage ?





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Histograms

1. The MEAN VALUE (or average graylevel)

M = g g h(g)1*0.3+2*0.1+3*0.2+4*0.1+5*0.2+6*0.1=

2.60.30.20.1

0.01 2 3 4 5 6





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Histograms

The MEAN value is the average grayvalue of the image, the overall

brightness appearance.

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Histograms

2. The VARIANCE

V = g (g-M) 2 h(g)

(with M = mean)or similar:

The STANDARD DEVIATION

D = sqrt(V)

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Histograms w w w . j nt


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Histograms

The STANDARD DEVIATION is a valueon the gray level axis, showing theaverage distance of all pixels to themean

0.30.20.1

0.0

0.30.20.10.0

D1 > D2

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Histograms

VARIANCE and STANDARD DEVIATIONof the histogram tell us about theaverage contrast of the image !

The higher the VARIANCE (=the higherthe STANDARD DEVIATION), thehigher the images contrast !



I Hi t w w w . j nt


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Image Histograms

x axis values of intensities rky axis h(rk) or p(rk)



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Histogram equalization t u w or l d . c o m


In probability theory , a probability density function (abbreviated as w w w . j nt
http://en.wikipedia.org/wiki/Probability_theoryhttp://en.wikipedia.org/wiki/Probability_theoryhttp://en.wikipedia.org/wiki/Probability_theoryhttp://en.wikipedia.org/wiki/Probability_theory


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In probability theory , a probability density function (abbreviated aspdf , or just density ) of a continuous random variable is a function

that describes

the

relative

likelihood

for

this

random

variable

to

occur at a given point in the observation space. The probability of a random variable falling within a given set is given by the integral of its density over the set.

A random variable X has density , where is a non negative

Hence, if F is the cumulative distribution function of X , then:

The probability density function (PDF) of a continuous distribution is

defined as the derivative of the cumulative distribution function [source : wikipedia]



http://en.wikipedia.org/wiki/Probability_theoryhttp://en.wikipedia.org/wiki/Probability_theoryhttp://en.wikipedia.org/wiki/Probability_theoryhttp://en.wikipedia.org/wiki/Random_variablehttp://en.wikipedia.org/wiki/Random_variablehttp://en.wikipedia.org/wiki/Random_variablehttp://en.wikipedia.org/wiki/Random_variablehttp://en.wikipedia.org/wiki/Random_variablehttp://en.wikipedia.org/wiki/Random_variablehttp://en.wikipedia.org/wiki/Cumulative_distribution_functionhttp://en.wikipedia.org/wiki/Cumulative_distribution_functionhttp://en.wikipedia.org/wiki/Cumulative_distribution_functionhttp://en.wikipedia.org/wiki/Cumulative_distribution_functionhttp://en.wikipedia.org/wiki/Cumulative_distribution_functionhttp://en.wikipedia.org/wiki/Cumulative_distribution_functionhttp://en.wikipedia.org/wiki/Random_variablehttp://en.wikipedia.org/wiki/Random_variablehttp://en.wikipedia.org/wiki/Probability_theory


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g

Histogram Equalization:

Preprocessing technique toenhance contrast in natural

images Target: find gray leveltransformation function T totransform image f such that thehistogram of T(f) is equalized



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Histogram Equalization (Idea)

Idea: apply a monotone transform resulting in an approximately uniform histogram



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g q

Example:

We are looking for

this transformation !

T



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Histogram Equalization w w w . j n t u


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g q

Discrete:

g1 is mapped to the (normalized)

number of pixels havinggray-values 0..g1 .

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Histogram Equalization w w w . j n t u


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Histogram Equalization u w or l d . c o m


Histogram matching or w w w . j n t u


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Histogram matching or

Histogram specification

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Chapter 3

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Spatial Domain

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Chapter 3

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Spatial Domain

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Chapter 3

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Spatial Domain

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Chapter 3

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Spatial Domain

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unit 3 image enhancement-2

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