image enhancement ii

8/13/2019 Image Enhancement II

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Digital Image Processing

Lecture 4: Image Enhancement II

Dr. Muhammad Amjad Iqbal


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Pixel Operations

for Image Enhancement


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Common Pixel Operations

Image Negatives

Log Transformations

Power-LawTransformations


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Image Negatives

Reverses the gray level order For L gray levels the transformation function is

s =T (r ) = (L - 1) - r


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Image Scaling

s =T (r ) = a.r (a is a constant)


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Log Transformations

Function of s = cLog(1+r )


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Log Transformations

Properties of log transformations –For lower amplitudes of input image the range of gray

levels is expanded

–For higher amplitudes of input image the range of gray

levels is compressed

Application: – This transformation is suitable for the case when the

dynamic range of a processed image far exceeds the

capability of the display device (e.g. display of theFourier spectrum of an image)

– Also called “dynamic-range compression / expansion”


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Log Transformations


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Power-Law Transformation


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For γ < 1: Expands values of dark pixels,compress values of brighter pixels

For γ > 1: Compresses values of dark pixels,expand values of brighter pixels

If γ=1 & c=1: Identity transformation (s = r)

A variety of devices (image capture, printing, display) respondaccording to power law and need to be corrected

Gamma (γ) correction

The process used to correct the power-law responsephenomena


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Gamma Correction


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Power Law Example


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Power Law Example (cont…)

γ = 0.6

00.1

0.2

0.3

0.4

0.5

0.60.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1

Old Intensities

T

r a n s f o r m e d I n t e n

s i t i e s


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γ = 0.4

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1

Original Intensities

T r a n s f o r m e d I n t e

n s i t i e s


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γ = 0.3

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1


T r a n s f o r m e d I n t e

n s i t i e s


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• The images to theright show amagnetic resonance

(MR) image of afractured humanspine

• Different curves

highlight differentdetail

s = r 0.6

s =

r 0 . 4


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Power Law Example


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γ = 5.0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1


T r a n s f o r m e d I n t e n s i t i e s


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Power Law Transformations (cont…)

• An aerial photo

of a runway isshown

• This timepower law

transforms areused to darkenthe image

• Different curves

highlightdifferent detail

s = r 3.0

s =

r 4 . 0

i i i f i


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Piecewise-Linear Transformation

Contrast StretchingGoal:

– Increase the dynamic range of the gray levels for low

contrast images

Low-contrast images can result from

– poor illumination

–lack of dynamic range in the imaging sensor

–wrong setting of a lens aperture during image

acquisition

C S hi E l


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Contrast Stretching Example


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Piecewise-Linear Transformation: Contrast Stretching


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Thresholding


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Gray Level Slicing

•Highlighting a specific range ofGray levels in an image

• First approach

– Display a high value for all the

gray levels in the range of

interest

– Low value for all other gray

levels

– This will produce a Binary Image


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Gray Level Slicing

• 2nd approach

– Brightens the desired range of

Gray Levels but preserves the

Gray Levels of rest of the pixels


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Contrast Stretching


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Contrast Stretching through Histogram

C

If r max and r min are the maximum and minimum gray levelof the input image and L is the total gray levels of output

image The transformation function for contrast stretching

will be


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Histogram Equalization


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Histogram Equalisation(Summary)

Spreading out the frequencies in an image (orequalising the image) is a simple way to improvedark or washed out images

The formula for histogramequalisation is given where

– r k : input intensity

– sk : processed intensity

– k : the intensity range(e.g 0.0 – 1.0)

– n j: the frequency of intensity j

– n: the sum of all frequencies

)( k k r T s

k

j

jr r p1

)(

k

j

j

n

n

1


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Example


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Example: cdf


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Example

Notice that the minimum value (52) is now 0 and the maximum value (154) is now 255.

Initial Image Image After Equalization


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Example


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Histogram Equalization-Examples


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Equalisation Transformation Function

I m a g e s t a k e n f r o m G o n z a l e z & W o o d s , D i g i t a l

I m a g e P r o c e s s i n g ( 2 0 0 2 )


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Edge detection

S i l Fil i f I Sh i


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Spatial Filtering for Image Sharpening

Background: to highlight fine detail in an image or toenhance blurred detail

Applications: electronic printing, medical imaging, industrialinspection, autonomous target detection (smartweapons)......

Foundation:

Blurring/smoothing is performed by spatial averaging(equivalent to integration)

Sharpening is performed by noting only the gray level

changes in the image that is the differentiation

S ti l Filt i f I Sh i


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Spatial Filtering for Image Sharpening

Operation of Image Differentiation Enhance edges and discontinuities (magnitude of

output gray level >>0)

De-emphasize areas with slowly varying gray-levelvalues (output gray level: 0)

Mathematical Basis of Filtering for Image Sharpening

First-order and Second-order Derivatives

Approximation in Discrete-space Domain

Implementation by Mask filtering


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1st Derivative

• The formula for the 1st derivative of a function is as follows:

• It’s just the difference between subsequent values and

measures the rate of change of the function

)()1( x f x f x

f


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First and Second Order Derivatives


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First and Second Order Derivatives

l f


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Example for Discrete Derivatives

Let’s consider a simple 1 dimensional example

l f i i i


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E l f Di D i i


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Various Situations encountered by

Derivatives• Flat Segment f’=0 and f’’=0

• Step f’=0 and f’’=0


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• Ramp

•Ramp or step in 1D profile normally characterize an edge in the image

•f’’ is non-zero on on-set and end of Ramp and produces thin edges

•f’ is non-zero along whole Ramp and produces thick edges


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• Thin Line

• Isolated Point

C i b t f" d f´


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Comparison between f" and f´

f´ generally produces thicker edges in an image

f" has a stronger response to fine detail

f´ generally has a stronger response to a gray-level step

f" produces a double response at step changes in gray

level For image enhancement, f" is generally better suited

than f´

Major application of f´ is for edge extraction; f´ used

together with f" results in impressive enhancement effect

Appl ing First and 2nd Deri ati e sing 1D


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Applying First and 2nd Derivative using 1D

Kernel

E h b 2 d D i i (E l )


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Enhancement by 2nd Derivative (Example)

L l i f I E h t


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Laplacian for Image Enhancement

L l i f I E h t


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Laplacian for Image Enhancement (Example)


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