Graininess of Color Halftones

1
Graininess of Color Halftones

• Howard Mizes
• Xerox Corp.
• October 18, 2000

http//chester.wrc.xerox.com/mizes
2
Image Graininess
Graininess is the subjective impression of image
noise

• Quantifying Graininess
• From the eyes point of view
• From the printers point of view
• Modeling Graininess
• From the toners point of view
• Graininess of Color images
• Extending the metric
• Obtaining the parameters
• Applying the metric
• Graininess of different color separations
• Graininess of color blends

3
Metrics for Image Graininess

• Dooley-Shaw (1978)

Amplitude
Amplitude
Frequency
Frequency
Density
Fourier transform of density
Visual Transfer Function

• Modifications of Dooley-Shaw
• Engeldrum et al, Hino et al, Mishra et al, others
• Different density scaling.
• 2D vs. 1D integration.
• Removal of nonrandom effects.
• Different visual transfer functions
• Different metrics dont change nature of
  graininess metric - just use it consistently.

4
Halftone Image Graininess

• If optical density of dots are uncorrelated
• Weiner spectrum is white noise (independent of
  frequency)
• Integral over visual transfer function becomes a
  constant

Convert to L
u

• Randomness arises from toner number variation

RefH. A. Mizes, "Particle size effects in
halftone image graininess", Proc. SPIE 1912, 454
(1993).
5
Models of toner number fluctuations

• Random sequential absorption
• Fill halftone dot randomly with toner until no
  more toners fit.
• Randomness from geometry.

• Neutralization of halftone dot
• Toners deposit at rate proportional to the
  development voltage for finite time
• Randomness from Poisson statistics

qt

qch
Deposition rate l(qch-qt)/qch toners/sec

• Xerographic systems model
• Apply step by step model of xerographic
  subsystems to calculate mass distribution on
  paper.
• Convert mass to toner number by applying
  statistical development.

6
Color vs. Black and white graininess

• Metric based only on lightness not sufficient to
  describe perception of grainy color images
• Subjective evaluated levelsimproved greatly
  compared with the case where color noise is not
  considered
• K. Sakatani T. Itoh, Color Noise Analysis, PICS
  1999

Noise varies in L
Noise varies in a
Noise varies in b

• Perception of graininess in color space is
  smaller, but significant.

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Color Graininess Metric - Itoh et al

• Itoh Generalization

(same graininess metric)
L a b
uniform color image
low pass filter
Psychophysical experiments give k2.76
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Color Graininess Metric - Halftone based

• Specific for halftones
• Chroma and Luminosity enter in symmetric ways

Gray
Color

• Determine sa and sb from color visual transfer
  functions.

L
a
b
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Color visual transform functions
Hirose measurements, 1993
Goodman/Klassen measurements, 2000

• Graininess sensitivity constants
• Hirose sa0.332, sb0.110
• Goodman/Klassen sa0.240, sb0.121

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Application to color separations

• Source of graininess is toner number
  fluctuations.
• Toner color affects the perception of
  granularity.
• Express color graininess formula in terms of area
  coverage.

Area coverage fluctuations, from models
Measure from toner reproduction curves
Color graininess formula extracts interplay
between mass fluctuations, color perception, and
color space.
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Application to color blends

• Highlight colors achieved from blending 2 or more
  toners in second development station.

• Number of toners in each dot follows binomial dist

• toners/dot and toner ratio fluctuate dot to dot
  leading to increase in graininess

12
Color and blend ratio

• Color is complicated function of blend ratio

Measured color of cyan yellow blends as function
of blend ratio - 100 coverage
L
a
b
L

• Toner number fluctuation gives variation along
  toner reproduction curve.
• Toner ratio fluctuation gives variation off toner
  reproduction curve.

b
a
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Graininess formula for toner blends

• Graininess formula contains color sensitivities
  to toner number and blend ratio fluctuations.

• Results for cyan-yellow blend

Graininess
toners/dot constant
toners/dot fluctuates
6.0
4.0
2.0
0.0
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Conclusions

• Proposed graininess metric for color halftones.
• Evaluated parameters from psychophysical
  measurements.
• Applied color halftone metric
• Graininess of single color separations.
• Graininess of toner blends.

• Acknowledgements
• Frank Bonsignore - toner blend color
  measurements.
• Kristen Natale, Victoria Rook - toner
  reproduction curves.
• Nancy Goodman, Vic Klassen - Color sensitivity
  psychophysical measurements.