image restoration · 2020. 10. 28. · image restoration, constrained least squares filtering cse...

Image Restoration

Image Processing

CSE 166

Lecture 8

Announcements

• Assignment 3 is due Nov 2, 11:59 PM

• Quiz 3 is Nov 4

• Assignment 4 will be released Nov 2

– Due Nov 9, 11:59 PM

• Reading

– Chapter 5: Image Restoration and Reconstruction

• Sections 5.1, 5.2, 5.3, 5.4, 5.6, and 5.7

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Model of image degradation

• Spatial domain

• Frequency domain


Noiseimage

Originalimage

Degradedimage

Degradationfunction

Noiseimage

Originalimage

Degradedimage

Degradationfunction

Model of image degradation, then restoration


Estimate of original imageOriginal image

Noise modeled as different probability density functions


Adding noise from different models


Gaussian Rayleigh Gamma

Free ofnoise

Adding noise from different models


Exponential Uniform Salt andpepper

Free ofnoise

Histograms of sample patches

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Sample “flat” patches from images with noise

Identify closest probability density function (pdf) match:

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Gaussian Rayleigh Uniform

Mean filters


Additive Gaussian

noise

Geometric mean

filtered

Arithmetic mean

filtered

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X-ray image

Mean filters


Additivesalt

noise

Additivepeppernoise

Contraharmonicmean filtered

Contraharmonicmean filtered

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Order-statistic filters


Additivesalt and peppernoise

1x median filtered

3x median filtered

2x median filtered

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Order-statistic filters


Min filtered

Max filtered

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Comparing filters


Alpha-trimmed mean filtered

Median filtered

Arithmetricmean

filtered

Geometric mean filtered

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Additive uniform +

salt and peppernoise

Adaptive filters


AdditiveGaussian

noise

Arithmetricmean filtered

Geometric mean

filtered

Adaptive noise reduction

filtered

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Adaptive filters


Additivesalt and pepper

noiseMedian filtered

Adaptive median filtered

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Periodic noise


Conjugate impulses

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Additive sinusoidal noise

DFT magnitude

Notch reject filters

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Notch reject filter

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Filter in frequency

domain

Estimate of original

image

Degraded image

DFT magnitudeConjugate

impulses

Conjugate impulses

Notch reject filter

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Filter in frequency

domain

Estimate of original

image

Degraded image

DFT magnitude

Estimating the degradation function

• Methods

– Observation

– Experimentation

– Mathematical modeling

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Estimation of degradation function by experimentation

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Imaged (degraded) impulseImpulse of light

Estimation of degradation function by mathematical modeling


Atmospheric turbulence

model

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Estimation of degradation function by mathematical modeling


Motion blur model

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Image restoration

• Inverse filtering

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Image restoration, inverse filtering

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FullLimited to

radius of 40

Limited to radius of 70

Limited to radius of 85

Image restoration, Wiener filtering

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Inverse filtering Wiener filtering

Full Radially limited

Image restoration, constrained least squares filtering


Inversefiltering

Wienerfiltering

Degraded image

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Motion blur and

additive noise

Constrained least squares filtering

Less noise

Much less noise

Next Lecture

• Color image processing

• Reading

– Chapter 7: Color Image Processing

• Sections 7.1, 7.2, 7.3, 7.4, 7.5, and 7.6

CSE 166, Spring 2020 29

image restoration · 2020. 10. 28. · image restoration, constrained least squares filtering cse...

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