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Halftone structure optimization using convex programming

Peter Morovic
Peter Morovic

In a color printing pipeline, the overall properties of a printed pattern depend on how the available inks are used to reproduce a given color. These choices are typically made in ink-space and therefore concern only how much of each ink to use, with halftoning then determining how those ink amounts interact with each other. For a HANS (Halftone Area Neugebauer Separation) pipeline, it is already the color separation the recipes of how inks are used for a given color that determines not only ink amounts but also how to combine them, while halftoning only provides their spatial distribution. Hence, with HANS, halftone properties are to a larger extent determined already by the color separation. This is an important change from traditional pipelines and requires different methods of control. This paper describes an approach to achieving new levels of image quality performance, without incurring complexity in the pipeline. It is based on the realization that certain strategies of halftone composition result in less grainy prints, e.g., when minimizing the amount of blank substrate, and more generally minimizing contrast among constituent, at-pixel drop-states (ink combinations). This is achieved through the mathematical technique of convex optimization, where such strategies can be formulated and efficiently computed. Results are shown for node-by-node LUT optimization; calibrating LUTs from ink-channel ratio data; transforming LUTs to take into account changes in drop-sequences, sets of admissible NPs or the number of possible NPs to use in an on-line pipeline and generating color samples that match in color but vary in grain. This approach is deeply embedded in the first HANS commercial product, the HP DesignJet Z6 and Z9+ series, a portfolio of pro-photo/graphics printers.

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METRIC BASED HALFTONE PATTERN OPTIMIZATION USING CONVEX PROGRAMMING PETER MOROVI, JN MOROVI, VICTOR DIEGO, JAVIER MAESTRO, XAVI FARIA, PERE GASPARIN HP INC., BARCELONA, CATALONIA, SPAIN
INHERENT ASYMMETRY BETWEEN INK-VECTORS AND NPACS: PROBLEM OR OPPORTUNITY? MOTIVATION One ink-vector can result in many different NPacs (NP area coverages) Which do we chose? Can we use this asymmetry for sampling NPacs? Can we define metrics over NPacs that result in a desired property? Once weve chosen NPacs of a given structure (i.e. NP composition), how do we make sure interpolated ones follow? What if we want to calibrate using ink- factors and want to compute new NPacs? Is there a way to do this (and more)? 0% blank (C, M, CM) 30% blank (CM only) 20% blank (C, M, CM) 10% blank (C, M, CM)
DECIDING HALFTONE STATISTICS BEFORE HALFTONING HANS PIPELINE CHOICES Contone Input (RGB) NPacs Halftone (NPs) Tetrahedral interpolation PARAWACS Contone Input (RGB) Ink-vectors Halftone (NPs) Tetrahedral interpolation Error Diffusion or Matrix HALFTONE CONTENTS HALFTONE CONTENTS & SPATIAL DISTRIBUTION SPATIAL DISTRIBUTION
CONSTRAINED MAPPING OF INK-VECTORS TO NPACS CONVEX OPTIMIZATION Y:0.143, YY:0.143, KY:0.143, kY:0.143, kK:0.143, K:0.143, k:0.143 Input NPac kK:0.43, kY:0.57 Output NPacMetric Constraints Convex Optimization Ink-vector change Min || H(NPac) + f(NPac) || Sum(NPac) == 1, 0 <= NPac <= 1 All NPs from Global_NP Set InkVec(NPac) == InkVec(NPac)*factors HANS pipeline controls pixel types (NPs) HP Pixel Control Given an ink-vector (or an NPac), LP allows us to penalize/reward NP types (QP can take it further) Every NPac can be optimized, given such metric, resulting in consistent NPacs
SIMPLE EXAMPLE CONVEX OPTIMIZATION INK-VECTOR: 50% CYAN INK 50% MAGENTA INK NPS: [BLANK, C, M, CM] OBJECTIVE FUNCTION F1 = [100, 0, 0, 0] OBJECTIVE FUNCTION F2 = [0, 100, 100, 0] NPac: 50% C 50% M NPac: 50% CM 50% Blank
OF COURSE, OTHERWISE IT WOULDNT MATTER YES, BUT DOES THIS CHANGE COLOR? -80 -60 -40 -20 0 20 40 60 80 a* -80 -60 -40 -20 0 20 40 60 80 100 b* Default vs W-MAX Yes! Different NPacs, even if they have a constant ink-vector, change in color Simple example case: 854 NPacs processed using a blank space maximization vs blank space minimization: mean 1 95th %tile 2 max 4 E00 Your mileage may vary depending on the system, but expect differences!
MINIMIZE NP CONTRAST FOR ALL NPACS OF A LUT IMPACT ON GRAIN EXAMPLE: IQ OPTIMIZATION LUT USING 200 NPS VIA OPTIMISATION FAVOURING OVERPRINTING AND PENALISING BLANK SPACE LUT USING 31 NPS VIA AN NP REDUCTION AND SIDE-BY-SIDE OPTIMIZATION HIGH SPEED HIGH QUALITY
REPURPOSE IMPORTED INK-VECTOR LUT TO IMPROVE IQ EXAMPLE: LUT IMPORTING Native (TDFED, ink-channels) HANS (PARAWACS, NPacs) ~.5 cm SMOOTHNESS COMPARISON (APPROXIMATELY AT 100% ZOOM) GRAIN COMPARISON (CROP APPROX. 0.5 CM WIDTH)
SAME INK-VECTOR, DIFFERENT NPACS, DIFFERENT GRAIN EXAMPLE: GRAIN SAMPLES MINIMIZING OVERPRINTING (SINGLE-INK NPS OR LOW DROP STATES MOST COMMON) GIVEN AN INK-VECTOR, COMPUTE DIFFERENT ALTERNATIVE NPACS THAT VARY IN GRAIN (MORE OR LESS OVERPRINTING, MORE OR LESS BLANK SPACE, ETC.). MAXIMIZING OVERPRINTING (MULTI-INK NPS OR HIGHER DROP STATES MOST COMMON)
FROM MEASURED INK-VECTOR RATIOS TO IQ-MAINTAINING CHANGED NPACS EXAMPLE: CALIBRATION -80 -60 -40 -20 0 20 40 60 a* -60 -40 -20 0 20 40 60 80 100b* Color difference (vs reference printer) before calibration -80 -60 -40 -20 0 20 40 60 a* -60 -40 -20 0 20 40 60 80 100 b* Color difference (vs reference printer) after calibration CALIBRATED MED: 0.7 95%: 1.4 MAX: 1.9 UNCALIBRATED MED: 1.2 95%: 2.7 MAX: 3.5
CONCLUSIONS Convex optimization provides a powerful and flexible framework for algorithmically dealing with the relationship of ink-vectors and NPacs It allows us to introduce NPac structure that directly affects print attributes We successfully applied this approach to: ink-vector sampling, LUT node optimization, local grain sampling, ink-factor based color calibration HP Pixel Control HP Pixel Control HP Pixel Control Photos 息 Lee Jeffries
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Halftone structure optimization using convex programming

  • 1. METRIC BASED HALFTONE PATTERN OPTIMIZATION USING CONVEX PROGRAMMING PETER MOROVI, JN MOROVI, VICTOR DIEGO, JAVIER MAESTRO, XAVI FARIA, PERE GASPARIN HP INC., BARCELONA, CATALONIA, SPAIN
  • 2. INHERENT ASYMMETRY BETWEEN INK-VECTORS AND NPACS: PROBLEM OR OPPORTUNITY? MOTIVATION One ink-vector can result in many different NPacs (NP area coverages) Which do we chose? Can we use this asymmetry for sampling NPacs? Can we define metrics over NPacs that result in a desired property? Once weve chosen NPacs of a given structure (i.e. NP composition), how do we make sure interpolated ones follow? What if we want to calibrate using ink- factors and want to compute new NPacs? Is there a way to do this (and more)? 0% blank (C, M, CM) 30% blank (CM only) 20% blank (C, M, CM) 10% blank (C, M, CM)
  • 3. DECIDING HALFTONE STATISTICS BEFORE HALFTONING HANS PIPELINE CHOICES Contone Input (RGB) NPacs Halftone (NPs) Tetrahedral interpolation PARAWACS Contone Input (RGB) Ink-vectors Halftone (NPs) Tetrahedral interpolation Error Diffusion or Matrix HALFTONE CONTENTS HALFTONE CONTENTS & SPATIAL DISTRIBUTION SPATIAL DISTRIBUTION
  • 4. CONSTRAINED MAPPING OF INK-VECTORS TO NPACS CONVEX OPTIMIZATION Y:0.143, YY:0.143, KY:0.143, kY:0.143, kK:0.143, K:0.143, k:0.143 Input NPac kK:0.43, kY:0.57 Output NPacMetric Constraints Convex Optimization Ink-vector change Min || H(NPac) + f(NPac) || Sum(NPac) == 1, 0 <= NPac <= 1 All NPs from Global_NP Set InkVec(NPac) == InkVec(NPac)*factors HANS pipeline controls pixel types (NPs) HP Pixel Control Given an ink-vector (or an NPac), LP allows us to penalize/reward NP types (QP can take it further) Every NPac can be optimized, given such metric, resulting in consistent NPacs
  • 5. SIMPLE EXAMPLE CONVEX OPTIMIZATION INK-VECTOR: 50% CYAN INK 50% MAGENTA INK NPS: [BLANK, C, M, CM] OBJECTIVE FUNCTION F1 = [100, 0, 0, 0] OBJECTIVE FUNCTION F2 = [0, 100, 100, 0] NPac: 50% C 50% M NPac: 50% CM 50% Blank
  • 6. OF COURSE, OTHERWISE IT WOULDNT MATTER YES, BUT DOES THIS CHANGE COLOR? -80 -60 -40 -20 0 20 40 60 80 a* -80 -60 -40 -20 0 20 40 60 80 100 b* Default vs W-MAX Yes! Different NPacs, even if they have a constant ink-vector, change in color Simple example case: 854 NPacs processed using a blank space maximization vs blank space minimization: mean 1 95th %tile 2 max 4 E00 Your mileage may vary depending on the system, but expect differences!
  • 7. MINIMIZE NP CONTRAST FOR ALL NPACS OF A LUT IMPACT ON GRAIN EXAMPLE: IQ OPTIMIZATION LUT USING 200 NPS VIA OPTIMISATION FAVOURING OVERPRINTING AND PENALISING BLANK SPACE LUT USING 31 NPS VIA AN NP REDUCTION AND SIDE-BY-SIDE OPTIMIZATION HIGH SPEED HIGH QUALITY
  • 8. REPURPOSE IMPORTED INK-VECTOR LUT TO IMPROVE IQ EXAMPLE: LUT IMPORTING Native (TDFED, ink-channels) HANS (PARAWACS, NPacs) ~.5 cm SMOOTHNESS COMPARISON (APPROXIMATELY AT 100% ZOOM) GRAIN COMPARISON (CROP APPROX. 0.5 CM WIDTH)
  • 9. SAME INK-VECTOR, DIFFERENT NPACS, DIFFERENT GRAIN EXAMPLE: GRAIN SAMPLES MINIMIZING OVERPRINTING (SINGLE-INK NPS OR LOW DROP STATES MOST COMMON) GIVEN AN INK-VECTOR, COMPUTE DIFFERENT ALTERNATIVE NPACS THAT VARY IN GRAIN (MORE OR LESS OVERPRINTING, MORE OR LESS BLANK SPACE, ETC.). MAXIMIZING OVERPRINTING (MULTI-INK NPS OR HIGHER DROP STATES MOST COMMON)
  • 10. FROM MEASURED INK-VECTOR RATIOS TO IQ-MAINTAINING CHANGED NPACS EXAMPLE: CALIBRATION -80 -60 -40 -20 0 20 40 60 a* -60 -40 -20 0 20 40 60 80 100b* Color difference (vs reference printer) before calibration -80 -60 -40 -20 0 20 40 60 a* -60 -40 -20 0 20 40 60 80 100 b* Color difference (vs reference printer) after calibration CALIBRATED MED: 0.7 95%: 1.4 MAX: 1.9 UNCALIBRATED MED: 1.2 95%: 2.7 MAX: 3.5
  • 11. CONCLUSIONS Convex optimization provides a powerful and flexible framework for algorithmically dealing with the relationship of ink-vectors and NPacs It allows us to introduce NPac structure that directly affects print attributes We successfully applied this approach to: ink-vector sampling, LUT node optimization, local grain sampling, ink-factor based color calibration HP Pixel Control HP Pixel Control HP Pixel Control Photos 息 Lee Jeffries