class5 image restoration

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ImageAcquisition

ImageEnhancement

ImageRestoration

ImageCompression

DIP Components

Image

Segmentation

Representation& Description

Recognition &Interpretation

Knowledge Base

Preprocessing low level

ImageCoding

MorphologicalImage Processing

WaveletAnalysis


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What Is Image Enhancement?

Image enhancement is the process ofmaking images more useful

The reasons for doing this include: Highlighting interesting detail in images Removing noise from images Making images more visually appealing


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Image Enhancement ExamplesImagestakenfromGonzalez&Woods,DigitalImageProcessing(2

002)


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Image Enhancement Examples(cont)

ImagestakenfromGonzalez&Woods,DigitalImageProcessing(2

002)


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002)


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002)


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Spatial & Frequency Domains

There are two broad categories of imageenhancement techniques

Spatial domain techniques Direct manipulation of image pixels

Frequency domain techniques Manipulation of Fourier transform or wavelet

transform of an image


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Image Histograms

The histogram of an image shows us thedistribution of grey levels in the image

Massively useful in image processing,

especially in segmentation

Grey Levels

Fre

quencies


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Histogram ExamplesImagestakenfromGonzalez&Woods,DigitalImageProcessing(2

002)


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Histogram Examples (cont)ImagestakenfromG

onzalez&Woods,DigitalImageProcessing(2

002)


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002)

Dark image


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002)

Dark image

Dark Bright


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002)

Bright image


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002)

Bright image

Dark Bright


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002)

Low contrastimage


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onzalez&Woods,DigitalImageProcessing(2002)

High contrastimage


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High contrast image

Dark Bright


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Histogram Examples (cont)

A selection of images andtheir histograms

Notice the relationshipsbetween the images andtheir histograms

Note that the high contrastimage has the mostevenly spaced histogram

ImagestakenfromG



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Histogram Equalisation

Spreading out the frequencies in an image(or equalising the image) is a simple way toimprove dark or washed out imagesThe formula for histogramequalisation is given where

rk: input intensity

sk: processed intensity

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

nj: the frequency of intensity j

n: the sum of all frequencies

)( kk rTs =

=

=k

j

jr rp

1

)(

=

=k

j

j

n

n

1


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Equalisation Transformation Function

ImagestakenfromG



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Equalisation ExamplesImagestakenfromG


1


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Equalisation Transformation Functions

The functions used to equalise the imagesin the previous exampleImagestakenfromG


1. Dark2. Bright3. Low

contrast4. High

contrast


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Equalisation ExamplesImagestakenfromG


2


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The functions used to equalise the imagesin the previous exampleImagestakenfromG



contrast4. High

contrast


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Equalisation Examples (cont)ImagestakenfromG


3

4


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Equalisation Examples (cont)ImagestakenfromG


3

4


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The functions used to equalise the imagesin the previous examples

ImagestakenfromG



contrast4. High

contrast


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Chapter 3Image Enhancement in the

Spatial Domain


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Contrast Stretching

We can fix images that have poor contrastby applying a pretty simple contrastspecification

The interesting part is how do we decide onthis transformation function?


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Spatial Domain


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Spatial Domain

Log transformationS=c log(1+r)

Image negatives

S=L-1-r

Power LawtransformationS=c r


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Spatial Domain


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Spatial Domain


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Spatial Domain


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Spatial Domain


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Spatial Domain


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Spatial Domain

Low contrast image


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Spatial Domain

Low contrast image-Poor illumination-Lack of dynamicrange in image sensor-Wrong setting of lens

aperture

Binary image(thresholding)r1= r2

s1= 0, s2 = L-1


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Spatial DomainGrey level slicing


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Spatial Domain


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Spatial Domain


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Spatial Domain


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Spatial Domain


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Spatial Domain


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Spatial Domain


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Spatial Domain


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Spatial Domain


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Spatial Domain


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Spatial Domain


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Spatial Domain


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Spatial Domain


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Spatial Domain


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Spatial Domain


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Spatial Domain


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Degradation Models

Image degradation can occur for many reasons, some typicaldegradation models are

2 2

2

2

2 2 2

2

1 0( , )

0

( , )

1,

( , ) 2 2

0

1

( , )

0

i j

ai bjh i j

otherwise

h i j Ke

L Li j

h i j L

otherwise

i j Rh i j R

otherwise

+

+ ==

=

=

+ =

Motion Blur: due to camerapanning or subject moving quickly.

Atmospheric Blur: long exposure

Uniform 2D Blur

Out-of-Focus Blur

CGU IPAM 2003: Inverse Problems


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Noise sources

Image acquisition Image transmission


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Noise models

Spatially independent noise models Gaussian noise Rayleigh noise

Erlang (Gamma) noise Exponential noise Impulse (salt-and-pepper) noise

Spatially dependent noise model Periodic noise


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Noise Models

Most noise models assume the noise is some known probabilitydensity function. The density function is chosen based on theunderlining physics.

Gaussian: poor illumination.

Rayleigh: range image

Salt andPepper: faulty switch during imaging

Gammaor Exp: laser imaging

CGU IPAM 2003: Inverse Problems

22 2/)(1)(

= zezp


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2)(

= ezp

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