Gradient%20Domain%20High%20Dynamic%20Range%20Compression

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Gradient Domain High Dynamic Range Compression

• Raanan Fattal
• Dani Lischinski
• Michael Werman

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The Dynamic Range Problem

• Whats wrong with these images?
• What would your eye see?
• How could you put all this information into one
  image?

3
Whole Image Solutions

• Tone Reproduction Curves
• Re-mapping of luminance values
• Easy to compute
• Suffer from quantization
• Examples
• Linear scaling
• Gamma correction
• More sophisticated models

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Ward Larson Model

• One of the best total image methods
• Based on models of display capabilities and human
  vision
• Still suffers from loss of local contrast
• Notice washed-out appearance of the outside area

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Local Solutions

• Tone Reproduction Operators
• Take local context into account
• Attempt to solve the local contrast problem
• Older Methods
• Based on estimating illuminance and reflectance
  for each part of the image
• Suffer from artifacts, dark halos

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Low Curvature Image Simplifier

• Tumblin and Turk, 1999
• Scale luminance of smoothed image
• Add back details
• 8 parameters
• Computationally intensive

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Gradient Domain Method
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Basic Assumptions

• The eye responds more to local intensity
  differences than global illumination
• A HDR image must have some large magnitude
  gradients
• Fine details consist only of smaller magnitude
  gradients

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Basic Method

• Take the log of the luminances
• Calculate the gradient at each point
• Scale the magnitudes of the gradients with a
  progressive scaling function (Large magnitudes
  are scaled down more than small magnitudes)
• Re-integrate the gradients and invert the log to
  get the final image

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1D Example

• Original Signal F(x) - Dynamic range 24151

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1D Example

• ln F(x)

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1D Example

• F(x)

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1D Example

• G(x) F(x) after applying the attenuating
  function

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1D Example

• I(x) Integrate G(x)

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1D Example

• eI(x) - New dynamic range 7.51

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Changes for 2D

• Use gradients instead of derivatives
• May produce a non-integrable vector field after
  scaling
• Transform scaled vectors into a conservative
  field whose gradients are closest to G(x)

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Attenuation Map
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Attenuation Details

• Images contain edges at multiple levels of detail
• How do we handle this?
• Compute gradients for many different resolutions
  of the image
• The set of different resolution images composes a
  Gaussian pyramid

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Creating the Final Image

• How do we recombine the different resolution
  levels?
• Start with coarsest image
• Calculate scaling factors
• Linearly interpolate those factors for each point
  in the next image, and multiply with the local
  scaling factor
• Apply the combined factors to the highest
  resolution image

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The Attenuation Function

• a average gradient magnitude for each level
  times 0.1
• ß adjustable gain (between 0.8 and 0.9)

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Performance

• On an 1800 MHz Pentium 4
• Computing a 512x384 image takes 1.1 seconds
• Computing a 1024x768 image takes 4.5 seconds
• LCIS takes 8.5 minutes to compute a 751x1130 image

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Examples

• Streetlight on a foggy night
• Dynamic range 100,0001

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Examples

• Stanford Memorial Church
• DR 250,0001

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Applications

• Enhancing contrast for LDR images
• Combining photographs of different exposure
  levels to enhance detail or stitch together for
  panoramas
• Medical image enhancements

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Panoramas
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Medical Imaging
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Questions / Credits

• Any questions?
• All pictures in this presentation are from the
  original paper