Approaches for Retinex and Their Relations

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Approaches for Retinex and Their Relations

• Yu Du
• March 14, 2002

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Presentation Outline

• Introductions to retinex
• Approaches for retinex
• The variational framework
• Relation of these approaches
• Conclusions

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What Is Retinex

• Lightness and retinex theory
• E. H. Land 1971
• Visual system of human
• Retina the sensory membrane lining the eye that
  receives the image formed by the lens (Webster)
• Reflectance and illumination
• Edges and independent color senstion

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Model of retinex (1)
The given image
The illumination part
The reflectance part
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Model of retinex (2)

Log
Exp
Input Image
Estimate the Illumination
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Three Types of Previous Approaches

• Random walk algorithms
• E. H. Land (1971)
• Homomorphic filtering
• E. H. Land (1986), D. J. Jobson (1997)
• Solving Poisson equation
• B. K. P. Horn (1974)

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Random Walk Algorithms (1)

• First retinex algorithm
• A series of random paths
• Starting pixel
• Randomly select a neighbor pixel as next pixel on
  path
• Accumulator and counter

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Random Walk Algorithms (2)

• Adequate number of random paths
• Cover the whole image
• Small variance
• Length of paths
• gt200 for 10x10 image (D. H. Brainard)

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Special Smoothness of Random Walk

• The value in the accumulator
• The illumination part

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Homomorphic Filtering

• Assume illumination part to be smooth
• Apply low pass filter

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Poisson Equation Solution (1)

• Derivative of illumination part close to zero
• Reflectance part to be piece-wise constant
• Get the illumination part
• Take the derivative of the image
• Clip out the high derivative peaks

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Poisson Equation Solution (2)

• Solve Poisson equation
• Iterative method
• Apply low-pass filter (invert Laplacian operator)

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Comments on Above Approaches

• Random walk algorithm
• Too slow
• Homomorphic filtering
• Low-pass filtering first or log first?
• More work needed to be done on Poisson equation
  solving

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Variational Framework

• Presented by R. Kimmel etc.
• From assumptions to penalty function
• From penalty function to algorithm

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Assumptions On Illumination Image

• Spatial smoothness of illumination
• Reflectance is not pure white
• Illumination close to intensity image
• Spatial smoothness of reflectance
• Continues smoothly beyond boundaries

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Penalty Function and Restrictions

• Goal to minimize
• Subject to
• And on

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Solve the Penalty Function (1)

• Euler-Lagrange equations
• And

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Solve the Penalty Function (2)

• Projected normalized steepest descent (PNSD)
• Iteratively to get illumination part

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Multi-resolution

• Make PNSD algorithm converges faster
• Illumination part is smooth
• Coarse resolution image first
• Upscale coarse illumination as initial of finer
  resolution layer
• Not multi-scale technique

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Relationship of Different Approaches (1)

• Random walk and Homomorphic filtering
• R. Kimmels words on Homomorphic filtering
• and remove constraint

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Relationship of Different Approaches (2)

• Apply appropriate scaling on images, Homomorphic
  filtering satisfies constrain
• and
• Poisson equation approach

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Conclusions

• Retinex is trying to simulate human vision
  process
• Different approaches are from same assumptions
• Implementation details are important for results

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Thank You

• March 14, 2002