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

SPIE Electronic Imaging Conference - 01/22/04 4/25/2017 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 SPIE Electronic Imaging Conference - 01/22/04 HP_presentation_template

Conventional AM halftoning 4/25/2017 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 SPIE Electronic Imaging Conference - 01/22/04 HP_presentation_template

FM halftoning (a.k.a. “blue-noise”) 4/25/2017 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 clumping in the midtones results In grain SPIE Electronic Imaging Conference - 01/22/04 HP_presentation_template

AM-FM halftoning (a.k.a. “green-noise”) 4/25/2017 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 SPIE Electronic Imaging Conference - 01/22/04 HP_presentation_template

Green-noise statistics [Lau et al.] 4/25/2017 Green-noise statistics [Lau et al.] G=0.10 G=0.25 Spatial Spectral SPIE Electronic Imaging Conference - 01/22/04 HP_presentation_template

SPIE Electronic Imaging Conference - 01/22/04 4/25/2017 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 SPIE Electronic Imaging Conference - 01/22/04 HP_presentation_template

SPIE Electronic Imaging Conference - 01/22/04 4/25/2017 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 SPIE Electronic Imaging Conference - 01/22/04 HP_presentation_template

SPIE Electronic Imaging Conference - 01/22/04 4/25/2017 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 SPIE Electronic Imaging Conference - 01/22/04 HP_presentation_template

SPIE Electronic Imaging Conference - 01/22/04 4/25/2017 Optimal donut filters Maximum Likelihood solution for dot placement problem is equivalent to finding min/max of filter output SPIE Electronic Imaging Conference - 01/22/04 HP_presentation_template

Deriving the optimal donut filter 4/25/2017 Deriving the optimal donut filter SPIE Electronic Imaging Conference - 01/22/04 HP_presentation_template

SPIE Electronic Imaging Conference - 01/22/04 4/25/2017 Results G=22/255 G=42/255 G=62/255 G=82/255 SPIE Electronic Imaging Conference - 01/22/04 HP_presentation_template

SPIE Electronic Imaging Conference - 01/22/04 4/25/2017 Results SPIE Electronic Imaging Conference - 01/22/04 HP_presentation_template

SPIE Electronic Imaging Conference - 01/22/04 4/25/2017 Results SPIE Electronic Imaging Conference - 01/22/04 HP_presentation_template

Grayscale design algorithm 4/25/2017 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 FG2 to earlier filtered result Desired concentration of minority pixels? No stop Yes SPIE Electronic Imaging Conference - 01/22/04 HP_presentation_template

Optimal Multifilters for color screens 4/25/2017 Optimal Multifilters for color screens SPIE Electronic Imaging Conference - 01/22/04 HP_presentation_template

Optimal Multifilters for color screens 4/25/2017 Optimal Multifilters for color screens SPIE Electronic Imaging Conference - 01/22/04 HP_presentation_template

Color design algorithm 4/25/2017 Color design algorithm 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 stop Yes SPIE Electronic Imaging Conference - 01/22/04 HP_presentation_template

SPIE Electronic Imaging Conference - 01/22/04 4/25/2017 Results C,M=62/255 SPIE Electronic Imaging Conference - 01/22/04 HP_presentation_template

Results (epxand images to see dot structure) 4/25/2017 Results (epxand images to see dot structure) Optimized donut filter Gaussian donut filter [Lin] SPIE Electronic Imaging Conference - 01/22/04 HP_presentation_template

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