Removing Camera Shake from a Single Photograph

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Removing Camera Shake from a Single Photograph

• Rob Fergus, Barun Singh, Aaron Hertzmann,
• Sam T. Roweis and William T. Freeman
• ACM SIGGRAPH 2006, Boston, USA
•  

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Outline

• Overview
• Proposed method for camera shake removing
• Simulation results

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Image blur due to camera shake
Desired image
Degraded image
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Image formation process

?

Blurry image
Sharp image
Blur kernel
Gaussian noise
Desired output
Input to algorithm
Convolutionoperator
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Image formation process

• A linear imaging model is assumed in this paper,
  that is

Prior for blur kernel
Observation model
Prior for image
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Prior model for nature image (1)

• Characteristic distribution of sharp image with
  heavy tails

Histogram of image gradient
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Prior model for nature image (2)

• Use parametric model for sharp image statistics

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Prior model for blur kernel (1)

• The characteristics of blur kernel are positive
  and sparse

?
Blur kernel
Blurry image
Sharp image
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Prior model for blur kernel (2)

• Assume the probability distribution of the
  element of blur kernel is the mixture of
  exponential distributions

Exponential distribution
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Model transformation

• The imaging model need to be transformed before
  we using the image gradient prior, that is

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Variational Baye (1)

• Illustration for Bayesian mean squared error
  estimator (Minimum mean squared error estimator,
  MMSE)

Parameter space ?
Observed data
?1
?3
Process
d
?2
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Variational Baye (2)

• Apply MMSE estimator for blur kernel estimation

It may be difficult to find the integration
result of the posterior probability
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Variational Baye (3)

• Factorize the previous posterior probability
  for blur kernel inference
  operation

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Variational Baye (4)

• The factorization of the posterior probability
  could be modeled as an optimization problem

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Original photograph
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Blur kernel
Proposed method
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Original photograph
Matlabs deconvblind
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Original photograph
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Matlabs deconvblind
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Proposed method
Blur kernel
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Original photograph
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Proposed method
Blur kernel
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Original photograph
Proposed method