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A relational approach to color
1.
© Copyright 2016
HP, Inc. A RELATIONAL APPROACH TO COLOR Peter Morovič HP Inc. 24th Color & Imaging Conference San Diego (CA), November 2016 [Redacted]
2.
© Copyright 2016
HP, Inc. OUTLINE • Metamer Sets • HANS • Beyond print control
3.
© Copyright 2016
HP, Inc. METAMER SETS
4.
© Copyright 2016
HP, Inc. COLOR FORMATION (RETINAL) • Color is the result of the relationship between light, (a surface) and an observer [necessary conditions for color perception] • Arbitrary* changes in any one of the components results in a change of the resulting XYZ • However, possible to find S/ E/Xi so that XYZ doesn’t change: metamerism E(λ) S(λ) Xi(λ) ∫E(λ) S(λ) X1(λ) dλ = X1 ∫E(λ) S(λ) X2(λ) dλ = X2 ∫E(λ) S(λ) X3(λ) dλ = X3
5.
© Copyright 2016
HP, Inc. METAMERISM 5 Human Observer under daylight All reflectances that match: Different observer, camera or light [...and vice versa] XYZ
6.
© Copyright 2016
HP, Inc. MACBETH COLORCHECKER
7.
© Copyright 2016
HP, Inc. MACBETH COLORCHECKER 30 38 43 35 43 52 22 38 22 25 36 24 32 37 14 22 23 43 8 39 47 40 32 23 Worst case DE76 (D65 to CIE A)
8.
© Copyright 2016
HP, Inc. CONVEX COMBINATIONS Given all possible reflectances, color a unit area with a subset in varying proportions (adding up to 1) to match a given color: naturalness constraint The set of all metameric reflectances (for a given illuminant and observer) form a convex set
9.
© Copyright 2016
HP, Inc.
10.
© Copyright 2016
HP, Inc. THE PURPOSE OF A COLOR PIPELINE Primaries (e.g. inks) Mechanism & Constraints Drops/ink Pixels/color Substrate (paper) Ink-limits Spatial resolution System Error … Desired Result + grain, banding, smoothness, detail, speed, ink-use (efficiency), …
11.
© Copyright 2016
HP, Inc. HANS Side view Subtractive Additive Halftone Area Neugebauer Separation Side view Colorants Substrate Appearance W C M Y Neugebauer primaries Materials Example halftone C M Y CMY + + = NP areas W=1/9 C=1/9 M=2/9 CM=2/9 CY=1/9 MY=1/9 CMY=1/9Colorant vector [C,M,Y]=[5/9, 6/9,3/9]
12.
© Copyright 2016
HP, Inc. NEUGEBAUER PRIMARY AREA COVERAGES A pattern C, formed by combining some of a printing system’s NPs, can be characterized by its NP area coverage (NPac) vector – NPacC 1/3! 2/9! 2/9! 2/9! k – number of colorant levels / colorant / pixel n – number of colorants, (i.e., the weights are convex) NPi – the i-th NP T() – color (e.g., Yule-Nielsen-corrected XYZ)
13.
© Copyright 2016
HP, Inc. ASSOCIATIVITY • Convex combination of relative area coverage weighted NP colors can also be seen as the convex combination of two constituent patterns – CA and CB, where wCi = wCBi + wCAi =! *1/3+! *2/3! 1/3! 2/9! 2/9! 2/9! 1/3! 2/3! 1/3! 1/3! 1/3! 1/9! 2/9! 2/9! 2/9!2/9! *1/3! *2/3!
14.
© Copyright 2016
HP, Inc. CONSEQUENCES OF ASSOCIATIVITY • As a consequence of associativity, we can perform convex combinations not only of at-pixel states (i.e., the Neugebauer Primaries), but also of a pattern’s sub-patterns • New NPacs can be constructed by convexly combining other NPacs, and this process can, in principle, go on ad infinitum. 0! 10! 20! 30! 40! 50! 0! 20! 40! 60! 80! lightness! chroma! ink! area coverage! Yn 0! 25! 50! areacoverage(%)! C! W! CM! K! M! Xn
15.
© Copyright 2016
HP, Inc. HERZOG’S CUBE-SHAPED GAMUT
16.
© Copyright 2016
HP, Inc. THE 8-VERTEX COLOR SEPARATION BLACK YELLOW GREEN BLUE CYAN RED MAGENTA WHITE BLACK RED MAGENTA WHITE CYAN GREEN BLUE YELLOW Device RGB Interface Yule-Nielsen XYZ measurments of HANS NPac characterisation chart Print & measure NPs and NPacs Select 8 vertices in correspondence with RGB cube Apply tetrahedral RGB tessellation to 8 vertices in XYZn Do tetrahedra in XYZn overlap? RGB-NPac- XYZ LUT YES NO
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HP, Inc. A HANS PIPELINE (SIMPLIFIED VIEW) Print & measure Neugebauer primary (NP) CIE XYZs Compute convex hull & tetrahedralize hull NPs Find printable color’s enclosing tetrahedron Printable color 20% W 30% C 25% M 0% Y 25% CM 0% CY Barycentric coordinates are vertex NP areas Select one NP per pixel & diffuse NPac-NP error Due to linearity in XYZ/XYZN W C CM M
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HP, Inc. NICE THEORY… DOES IT ACTUALLY WORK? HANS +31% Gamut Colorant pipeline Current HANS
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HP, Inc. TESSELLATIONS Points (NP colorimetries) Convex Hull Example Tessellations [triangular/rectangular/...] 42 possible polygons if we allow overlapping • Tessellating NPs can be done in different ways - not a unique solution • A given XYZ (within the convex hull) is contained in many tessella • Each tessella gives rise to a new NP area NP1 NP2 NP3 NP4 NP5 NP6 NP7 ?
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HP, Inc. COMBINATORIAL SOLUTION • Given a set N NPs and their measured XYZs there are ∑[ p=4 to N](N over p) polyhedra • In the case of CMY, there are 70 tetrahedra, 56 pentahedra, 28 hexahedra, etc... = 163 polyhedra Tetrahedra All polyhedra CMYK@1dpp 1,820 64,839 CMYK@2dpp 1,663,740 ~1024 CMYKcm@2dpp A lot! Even in CMY (8 NPs) there are many polyhedra, leading to metamerism.
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HP, Inc. • How many NPacs are there? • Given a set of N NPs and an encoding precision d (e.g. d=255 for 8bits), how many vectors w are there? w = [w0, w1, w2, … wN-1] such that SUM(wi) = d and all wi are in the range of [0 … d] • Solution: (N + (d-1)) choose N • How many ink-vectors are there? • For M inks there are d M ink vectors NPAC SPACE CARDINALITY Ink-vectors NPacs CMY 1dpp 8bit 1.7 x 107 4.9 x 1014 CMYK 2dpp 8bit 4.2 x 109 ~1.5 x 1079 CMYK 2dpp 12bit 2.8 x 1014 ~1.5 x 10172
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HP, Inc. COMPUTATIONAL OPTIMISATION • For a given XYZ (sampling printable gamut) • check all polyhedra that contain it • compute the resulting NPac • evaluate each NPac for optimality (e.g. ink-use) • Conceptually: we compute the metamer set and choose the best candidate from within • Challenging: large number of tetrahedra; large metamer sets (still only sampling)
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HP, Inc. TRICHROMACY • Trichromatic color reproduction is the use of one colorant/light-source per cone type • additive: RGB light sources, varying in intensity of output, control intensity of response from LMS cones • subtractive: CMY filters, varying in level of absorption, control intensity of response from LMS cones • For each color that can be matched, there is one and only one RGB / CMY combination that matches it • Alternatives (metamers) are only available when more than three colorants/light-sources are available (e.g., adding K to CMY, adding W to RGB)
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HP, Inc. CMY METAMERS 115 NPacs (formulations) that produce a mid-gray 12% W 35% C 0% M 29% Y 24% CM 0% CY 0% MY 0% CMY 12% W 51% C 3% M 32% Y 2% CM 2% CY 10% MY 0% CMY Each column represents an NPac that matches a mid-gray, the color of the segments corresponds to NPs and their length to the relative area coverages
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HP, Inc. TWO EXAMPLES (HALFTONES) Two out of 115 metamers: left patch uses 11 base NPacs (out of 14) – right patch uses 5 base NPacs [shown in pseudo-color] Target LAB
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HP, Inc. INK-USE OPTIMISATION • Print and measure 544 LAB- uniform samples spanning the whole CMY color gamut • Perform computational optimisation (tetrahedral search for each sample over extended base NPac set - 244 samples) • 14,4 x106 tetrahedra evaluated • Min vs Max ink-use over all 544 samples = 12.66% ink use range −60 −40 −20 0 20 40 60 −40 −20 0 20 40 60 80 a* b* Printed and Measured LABs
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HP, Inc. 6-INK INDUSTRIAL PRINTING SYSTEM CMYKcm ink-set, up to 3 drops per pixel = 4096 NPs
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HP, Inc. NOT JUST PRINT-CONTROL Simulation Print photo Mimír: a display pixel preview of a halftone corresponds to a local distribution of NPs in the halftone, which is an NPac. Zoom-dependent, dynamic re-computation of halftone NPac to display pixels + a color model allow for a WYSIWYG halftone preview (ICC profile level accuracy)
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HP, Inc. NOT JUST PRINTING Display design: decompose backlight into atomic states (monochromatic signals) and convexly combine them to generate full variety via optically additive mechanism.
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HP, Inc. THANK YOU ☺ Ján Morovič, Graham Finlayson, Jordi Arnabat, Juan Manuel Garcia Reyero, Xavier Fariña, Hector Gomez, Pere Gasparin, David Gaston, Annarosa Multari, Africa Real, Rafael Gimenez, Albert Serra, Ramon Pastor