AM-FM Screen Design
Using Donut Filters
Niranjan Damera-Venkata and Qian Lin
Hewlett-Packard Laboratories
1501 Page Mill Road, MS 1203
Palo Alto CA 94304
Outline
•
Halftoning methods
–
•
why use green-noise (AM-FM) halftoning?
Statistical properties of green-noise
patterns
–
spatial statistics
– spectral statistics
•
Design of optimal green-noise screens
–
•
Green-noise error diffusion
–
–
–
•
optimized “donut” filters
analysis of Levien error diffusion
noise shaping: role of the “donut” filter
new green noise error diffusion methods
Status
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Conventional AM halftoning
•
Indigo’s “Sequin” halftoning
–
–
•
Dot frequency is fixed
Dot size varies to represent
tone
Disadvantages
–
–
–
–
Rosette patterns
Tone jumps
Detail rendition suffers
Scan quality suffers
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FM halftoning (a.k.a. “blue-noise”)
•
Photo printers
–
–
•
Dot size is fixed
Dot frequency varies
Advantages
–
Does not cause Moiré
– Rosette patterns eliminated
– Tone jumps not abrupt
– Better detail rendition
– Better quality at consumer
grade scan resolutions
•
Disadvantages
–
Depends heavily on fidelity of
isolated dot reproduction
dot dropout and
banding in
highlights
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clumping in the
midtones results
In grain
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AM-FM halftoning (a.k.a. “green-noise”)
•
AM-FM
–
•
Advantages
–
•
highlights
Dot size and dot frequency
varies
Promise of the “best of both
worlds”
Disadvantages
–
–
Design depends on particular
dot formation characteristics
Difficult design problem
midtones
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Green-noise statistics [Lau et al.]
G=0.10
G=0.25
Spatial
Spectral
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AM-FM Screen design
•
Filter based methods
–
Donut Filters [Lin]
• Optimal void and cluster approach
• Donut filter parameters must be empirically chosen for each
graylevel
–
ColorSmooth Dither [Lin and Allebach]
• Computationally very expensive
• Handles joint design for a set of colorants
• Several parameters must be set empirically
•
Optimal method
–
Green Noise Mask [Lau, Arce and Gallagher]
• Approximates green-noise Markov statistics in Maximum
Likelihood sense
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Donut filters
•
•
Dots added one at a time
Start off with well distributed dot centers and then grow
them
–
Filter existing pattern with filter
– Choose minimum location and add a dot there
– Donut filter’s characteristic promotes dot clustering
Spectral
Spatial
 2 r 2
 r 2 

  e
e



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Donut filters
•
•
Dots added one at a time
Start off with well distributed dot centers and then grow
them
–
Filter existing pattern with filter
– Choose minimum location and add a dot there
– Donut filter’s characteristic promotes dot clustering
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Optimal donut filters
•
Maximum Likelihood solution for dot placement problem
is equivalent to finding min/max of filter output
y1
y2
x
y3
y4
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Deriving the optimal donut filter
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Results
G=22/255
G=42/255
G=62/255
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G=82/255
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Results
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Results
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Grayscale design algorithm
Existing minority dots from
level G1
Generate parametric linear
filter FG2 for level G2
Filter existing dot pattern for
level G1 using FG2 and
circular convolution
Find majority pixel where
the result is minimum and
convert it to a minority pixel
Desired concentration
of minority pixels?
Yes
stop
No
Add shifted version of FG2
to earlier filtered result
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Optimal Multifilters for color screens
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Optimal Multifilters for color screens
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Color design algorithm
Existing minority dots from
level G1 in C and M
Generate parametric matrixvalued linear filter FG2
Filter existing dot pattern for level
G1 using matrix-valued filter FG2.
Find majority pixel in C, M where
the result is minimum and convert
it them to a minority pixel
Desired concentration
of minority pixels?
Yes
stop
No
Add circularly shifted versions of impulse response
vector (for impulses in C and M) of FG2 and add to
earlier filtered vector result for C,M
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Results
C,M=62/255
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Results (epxand images to see dot structure)
Optimized donut filter
Gaussian donut filter [Lin]
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