AM-FM Screen DesignUsing Donut Filters

Niranjan Damera-Venkata and Qian LinHewlett-Packard Laboratories1501 Page Mill Road, MS 1203Palo Alto CA 94304

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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– optimized “donut” filters

• Green-noise error diffusion– 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 andbanding inhighlights

clumping in themidtones results

In grain

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AM-FM halftoning (a.k.a. “green-noise”)

• AM-FM– Dot size and dot

frequency varies• Advantages

– Promise of the “best of both worlds”

• Disadvantages– Design depends on

particular dot formation characteristics

– Difficult design problem

highlights

midtones

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Green-noise statistics [Lau et al.]

Spectral Spatial

G=0.10 G=0.25

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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

Spatial

2

2

2 rree

Spectral

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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

3y

x

2y

4y

1y

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Deriving the optimal donut filter

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Results

G=22/255 G=42/255 G=62/255 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

Add shifted version of FG2to earlier filtered result

Desired concentration of minority pixels?

No

stopYes

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Optimal Multifilters for color screens

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Optimal Multifilters for color screens

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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

Existing minority dots from level G1 in C and M

Generate parametric matrix-valued 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?

No

stopYes

Color design algorithm

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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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