What are Good Apertures for Defocus Deblurring?

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What are Good Apertures for Defocus Deblurring?
Changyin Zhou Shree K. Nayar
Columbia University ICCP 2009, San Francisco
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Geometry of Defocus
Lens
Object
Sensor
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Formulation of Defocus
In the Spatial Domain
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Formulation of Defocus
In the Fourier Domain
Focused Image
Captured Image
PSF
Image Noise
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Various Aperture Coding Techniques
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What are Good Apertures for Defocus Deblurring?
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Outline
- Background
- Evaluation Criterion for Aperture Patterns
- Pattern Optimization
- Experiments
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How to Evaluate Aperture Patterns?
Captured Image
Focused Image
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How to Evaluate Aperture Patterns?
Captured Image
Focused Image
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The Optimal Linear Deblurring Algorithm

• For white noise and L2 distance, Weiner filter
  is optimal

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The Optimal Linear Deblurring Algorithm

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How to Evaluate Aperture Patterns?
Captured Image
Focused Image
An Optimal Deblurring Algorithm
Deblurred Image
Linear system
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Evaluation Criterion for Aperture Pattern
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Evaluate Patterns Using the Criterion
R Curve of Circular Pattern
R
Noise Level
Noise Level
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Evaluate Patterns Using the Criterion
Curves of Relative R R(K)/R(K0)
Noise Level

• Coded apertures help more when noise level is
  low.
• Circular aperture is better when noise level is
  high.

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Outline
- Background
- Evaluation Criterion for Aperture Patterns
- Pattern Optimization
- Experiments
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Pattern Optimization

• Difficult to solve analytically
• Patterns evaluated in the Fourier domain, but
  strictly constrained in the spatial domain
  .

• Difficult to do brute force search
• For binary patterns of resolution N x N, the
  number of possible solutions is huge,

when N 13, if evaluating one pattern takes 1
millisecond, the brute force search requires
1045 yrs.
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Pattern Optimization
Pattern Evolution in Genetic Algorithm 13 x 13
binary patterns 8 different noise levels
2nd Run
3nd Run
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Evaluate the Optimized Patterns
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Evaluate the Optimized Patterns
Relative R curves of the Optimized Patterns
Image
s 0.001
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Outline
- Background
- Evaluation Criterion for Aperture Patterns
- Pattern Optimization
- Experiments
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Implementation
Precision Laser Photoplot (1 micron)
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Implementation
Canon EF 50mm f/1.8 Lens
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Implementation
Image Pattern
Veeraraghavan et al.s Pattern
Levin et al.s Pattern
Circular Pattern (wide open)
Our Optimized Pattern
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Comparison Experiments on a CZP Chart
Captured Images
Focused Image
Circular Pattern
Veeraraghavan et als Pattern
Image Pattern
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Comparison Experiments on a CZP Chart
Deblurred Images
Focused Image
Circular Pattern
Levin et al.s Pattern
Veeraraghavan et als Pattern
Image Pattern
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Shrek
Captured Image using the Optimized Pattern
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Shrek
Captured Image using the Optimized Pattern
Deblurring Result
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On the Street
Captured Image Using the Optimized Pattern
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On the Street
Captured Image Using the Optimized Pattern
Deblurring Result
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Traffic Scene
Captured Image Using the Optimized Pattern
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Traffic Scene
Captured Image Using the Optimized Pattern
Deblurring Result
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Summary

• Main Contributions
• Aperture Evaluation Criterion for Defocus
  Deblurring
• Aperture Pattern Optimization for Defocus
  Deblurring

• Future Work
• Optimize gray-level patterns
• Apply Criterion to other PSF Engineering Problems
  
• Extend Analysis to Account for Diffraction

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Thank You!
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Genetic Algorithm for Pattern Optimization
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Genetic Algorithm for Pattern Optimization
Noise level 0.005
1st Run
2nd Run
3nd Run