An Input-Level Dependent Approach To Color Error Diffusion

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An Input-Level Dependent Approach To Color Error
Diffusion
2004 SPIE/IST Symposium on Electronic Imaging
1Mr. Vishal Monga, 2Dr. Niranjan Damera-Venkata
and 1Prof. Brian L. Evans
1Embedded Signal Processing LaboratoryThe
University of Texas at AustinAustin, TX
78712-1084 USA bevans,vishal_at_ece.utexas.edu

• 2Hewlett-Packard Laboratories1501 Page Mill
  RoadPalo Alto, CA 94304 USA
• damera_at_exch.hpl.hp.com

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Grayscale Error Diffusion Halftoning
Background

• 2- D sigma delta modulation Anastassiou, 1989
• Shape quantization noise into high freq.
• Several Enhancements
• Variable thresholds, weights and scan paths

Error Diffusion
current pixel
weights
Spectrum
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Direct Binary SearchAnaloui, Allebach 1992
Background
- Computationally too expensive for real-time
applications e.g. printing - Used in screen
design - Practical upper bound for achievable
halftone quality
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Tone Dependent Error Diffusion
Grayscale TDED

• Train error diffusionweights and
  thresholdmodulationLi Allebach, 2002

Highlights and shadows
FFT
Graylevel patch x
Halftone pattern for graylevel x
FFT
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Input-Level Dependent Color Error Diffusion
Color TDED

• Extend TDED to color?
• Goal e.g. for RGB images obtain optimal (in
  visual quality) error filters with filter weights
  dependent on input RGB triplet (or 3-tuple)
• Applying grayscale TDED independently to the 3
  (or 4) color channels ignores the correlation
  amongst them
• Processing channel-separable or vectorized
• Error filters for each color channel (e.g. R, G,
  B)
• Matrix valued error filters Damera-Venkata,
  Evans 2001
• Design of error filter key to quality
• Take human visual system (HVS) response into
  account

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Input-Level Dependent Color Error Diffusion
Color TDED

• Problem(s)
• (256)3 possible input RGB tuples
• Criterion for error filter design?
• Solution
• Design error filters along the diagonal line of
  the color cube i.e. (R,G,B) (0,0,0) (1,1,1)
  (255,255,255)
• 256 error filters for each of the 3 color planes
• Color screens are designed in this manner
• Train error filters to minimize the visually
  weighted squared error between the magnitude
  spectra of a constant RGB image and its
  halftone pattern

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Color HVS Model
Perceptual Model Poirson, Wandell 1997

• Separate image into channels/visual pathways
• Pixel based transformation of RGB ? Linearized
  CIELab
• Spatial filtering based on HVS characteristics
  color space

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Linearized CIELab Color Space
Color TDED

• Linearize CIELab space about D65 white point
  Flohr, Kolpatzik, R.Balasubramanian, Carrara,
  Bouman, Allebach, 1993
• Yy 116 Y/Yn 116 L 116
  f (Y/Yn) 116
• Cx 200X/Xn Y/Yn a 200
  f(X/Xn ) f(Y/Yn )
• Cz 500 Y/Yn Z/Zn b 500
  f(Y/Yn ) f(Z/Zn )
• where
• f(x) 7.787x 16/116 0 x lt
  0.008856
• f(x) x1/3
  0.008856 x 1
• Color Transformation
• sRGB ? CIEXYZ ? YyCx Cz
• sRGB? CIEXYZ obtained from http//white.stanford.e
  du/brian/scielab/

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HVS Filtering
Color TDED

• Filter chrominance channels more aggressively
• Luminance frequency response Näsänen and
  Sullivan, 1984
• L average luminance of display
• weighted radial spatial frequency
• Chrominance frequency response Kolpatzik and
  Bouman, 1992
• Chrominance response allows more low frequency
  chromatic error not to be perceived vs. luminance
  response

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Perceptual Error Metric
Color TDED
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Perceptual Error Metric
Color TDED

• Find error filters that minimize TSE subject to
  diffusion and non-negativity constraints, m
  r, g, b a ? (0, 255)

(Floyd-Steinberg)
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Results
Color TDED
(a) Original Color Ramp Image
(b) Floyd-Steinberg Error Diffusion
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Color TDED
Results
(c) Separable application of grayscale TDED
(d) Color TDED
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Color TDED
Results

• Halftone Detail
• Blue section of the color ramp

Floyd-Steinberg
Grayscale TDED
Color TDED
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Original House Image
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Floyd Steinberg Halftone
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Color TDED Halftone
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Color TDED
Conclusion Future Work

• Color TDED
• Worms and other directional artifacts removed
• False textures eliminated
• Visibility of halftone-pattern minimized (HVS
  model)
• More accurate color rendering (than separable
  application)
• Future Work
• Incorporate Color DBS in error filter design to
  enhance homogenity of halftone textures
• Design visually optimum matrix valued filters

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Back Up Slides
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Floyd Steinberg Yy component
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Floyd Steinberg Cx component
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TDED Yy component
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TDED Cx component
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Color TDED
HVS Filtering contd

• Role of frequency weighting
• weighting by a function of angular spatial
• frequency Sullivan, Ray, Miller 1991

where p (u2v2)1/2 and
w symmetry parameter
reduces contrast sensitivity at odd multiples of
45 degrees
equivalent to dumping the luminance error
across the diagonals where the eye is least
sensitive.