Soft-proofing Applications for Six and Seven olorants of High-Fidelity Printing Systems Using a Multispectral Approach MailTo : mcl@mail.shu.edu.tw
To bridge the gap between HDR imaging and Hi-Fi color reproduction. The intent of this research has two tasks: 1) to derive an HDR contone to Hi-Fi halftoneconversion model, via fitting spectral-reflectance approach. (isomerism, color-gamut, tone-and-detail) 2) to derive both a contone and a halftone-palate types of image display models, for soft-proofing (simulation) of high-fidelity printing systems.
Methodologies High-Fidelity olor Printing Ideal IE Multispectral amera Model Proofing for Both ontine and Halftone palettes /Dithering
MYKRGB(Press) ~ MYKROG(Proofer) olor Printing - Experiment of 6-colorant/7-ink olor Printing-
High-Fidelity olor Printing Multi-olor Separation (5-8 colors). Two directions suggested and induced: a. Imaging detail, e.g., MYKLcLm. b. Gamut of printability, e.g., MYKRGB, or MYKOG. AdobeRGB b* MYKRGB MYK Gamut Rendering a*
7-Ink MYKRGB Separation (Press) Subdivide the superset of 7-ink into 4 subsets A 4-ink MYK (1617 color; IT8.7/4) Three 5-colorant subsets: MYKR, MYKG, and MYKB (each 1716 colors) Dominant Ink Subgamut Key omponent Black MYK Black (K) Red MYKR Red Green MYKG Green Blue MYKB Blue Table : 4 subsets of 7-ink color separation
7-Ink MYKRGB Separation (PRESS) 7-ink set used: MYK:SAKATA INX T Ecopure J; Red ink: Pantone Red 032; Green ink: Pantone Green ; Blue ink: Pantone Blue 072
Epson Stylus Pro 9900 (Printer) Subdivide the superset 6-ink into 3 subsets A 4-ink MYK (1617 colors; IT8.7/4) Two 5-colorant subsets: MYKO and MYKG (each 1716 colors) Dominant olorant Subgamut Key omponent Black MYK Black (K) Orange MYKO Orange Green MYKG Green Table: 3 subsets of 6-colorant color separation
MYKG MYKO MYK
Printer/Printing haracterization Models Neugebauer-Type Equation Masking-Type Equations A modified type masking-type model using a multispectral approach was carried out here.
All of the colorimetric parameters were converted to colorimetric densities in the use of logarithm method as follows: 0 0 0 lo g lo g lo g r c g m b y X D D X Y D D Y Z D D Z
f(x,y,z)=a 0 +a 1 x+a 2 y+a 3 z f(x,y,z)=a 0 +a 1 x+a 2 y+a 3 z+a 4 xy+a 5 yz+a 6 zx+a 7 x 2 +a 8 y 2 +a 9 z 2 f(x,y,z)=a 0 +a 1 x+a 2 y+a 3 z+a 4 xy+a 5 yz+a 6 zx+a 7 x 2 +a 8 y 2 +a 9 z 2 +a 10 xyz+a 11 x 3 +a 12 y 3 +a 13 z 3 +a 14 xy 2 +a 15 x 2 y+a 1 6 yz2 +a 17 y 2 z+a 18 zx 2 +a 19 xz 2 1... ) ( 1) ( ) (... 1 1 1 1 m a n m n a n m n n m n i m i i m n j j Order Order j j
Masking-Type Equations Simple linear regression f(x,y,z) = D r = a 0 +a 1 x+a 2 y+a 3 z 2nd-order regression f(x,y,z) = D r = a 0 +a 1 x+a 2 y+a 3 z+a 4 xy+a 5 yz+a 6 zx+a 7 x 2 +a 8 y 2 +a 9 z 2 3rd-order regression f(x,y,z) =D r = a 0 +a 1 x+a 2 y+a 3 z+a 4 xy+a 5 yz+a 6 zx+a 7 x 2 +a 8 y 2 + a 9 z 2 +a 10 xyz+a 11 x 3 +a 12 y 3 +a 13 z 3 +a 14 xy 2 +a 15 x 2 y+a 16 yz 2 +a 17 y 2 z+a 18 zx 2 +a 19 xz 2 x=d c =c, y=d m =m, z=d y =y (Principal Density or Equivalent Neutral Density) Note : Forward model for 3-colors MY superimposed
Broadband Type of Third-Order Model (olorant Models) D a c a m a y a c 2 r-3c 1,1 1,2 1,3 1,4 a m a y a cm a cy 2 2 1,5 1,6 1,7 1,8 a my a c a m 3 3 1,9 1,10 1,11 1,12 2 2 2 2 1,13 1,14 1,15 1,16 2 2 1,17 1,18 1,19 a y a c m a c y + a m c a m y a y c a y m a cmy 3 Similar terms are used for the calculation of D g-3c and D b-3c.
n order -SVD Equation 3 rd -SVD Equation (MB) m M Y K E R R R R R 3 5 0 ( ) 1 56 i i H Note: 1) BB: Broadband,MB: Multispectral;2) R 5c is the outcome for 3 rd -SVD equation in multispectral model (forward process); 3) SVD: Singular Value Decomposition method Polynomial Models using SVD method In MYKOG Model 1 ),,,, ( 1 ),,,, ( 2 ),,,, ( 3 5 1 6 2 7 3 6 2 7 3 6 2 7 3 7 3 7 3 1 1 1 E K Y M st j j E K Y M nd j j E K Y M rd j j R R R R R a R R R R R a R R R R R a 0 ( ) 1 n m i i H 1... ) ( 1) ( ) (... 1... 1 2 1 1 1 1 m n a m n a Order j j Order j j n m n n m n n m n n m n order Parameters No. of Term Polynomial Regression Model
Polynomial Models using SVD method In MYKOG Model mn1 n j 1 a j n Order ( m) mn1 n j mn1 n mn2 n1 a... j... 1 ( n 1) Order ( m)... 1 7 7 6 3 3 2 rd nd aj R RM R Y RK RE aj R RM R Y RK RE j1 j 1 3 (,,,, ) 2 (,,,, ) 7 6 5 3 2 1 7 6 3 2 j 1 7 3 st a 1( R, R, R, R, R ) 1 j M Y K E
The gray component is the determination of black-ink channel (K channel) for reversal model. onditional rules for GR (e.g): if (D (4, min) <0.6 D 4 < Fullolor 3 ) D GR =.0 (D 3 =D 4 ); if (D (4, min) >= K 100 ) D GR = K 100 ; else D GR = D (4, min) * 0.7; Density Value The minimum density Replacement Ratio Dr Dg Db K 70% 100% Figure : A schema figure of Gray omponent Replacement
1 0.9 0.8 Degree of GR 0.7 0.6 0.5 0.4 0.3 n=4 n=1 n=2 0.2 0.1 n=3 0 0 20 40 60 80 100 L Y Adaptive Type of GR: =[(100-L*)/80] n
Get FDA of Key olor omponent Using Look Up Table ompute ratio_distance =computedistanceandratio2keyolor(lch_pixel.h); extraomponent.e= ((Math.pow((1 ratio_distance),n_adjkr_oncave))) *extraomponent.e;
Hue Red E-Orange Yellow Green E-Green yan Blue Magenta Red L h i 52.0 97.5 39.7 66.5 110.4 55.6 94.6 106.9 94.8 41.6 85.0 161.5 83.5 61.9 163.1 51.3 70.2 243.6 13.4 78.1 306.0 52.7 84.6 356.3 52.0 97.5 399.7 L h i 64.0 127.7 41.6 98.0 96.5 97.2 86.0 158.2 150.8 90.0 98.0 194.2 40.0 122.7 291.9 72.0 122.1 330.5 64.0 127.7 401.6
Polynomial Models using SVD method In MYKOG Model KR or GR
Summary of Prediction performances of the multi-spectral 2 nd -SVD model (MYKOG) Subset MYK MYKO MYKG Process F R F R F R Max 4.44 4.97 3.53 4.98 4.25 4.43 Average 0.80 0.88 0.76 1.44 0.74 1.43 E 00 >6 ount 0 0 0 0 0 0 RMSE (Mean) 9.70 E-4 0.0017 7.92 E-4 0.0021 9.54 E-4 0.0040 in terms of mean E 00, of four derived Models for transform processes of both the forward (denoted as F) and the reverse (denoted as R) under the D 50 condition.
Summary of Prediction performances of the multi-spectral 2 nd -SVD model (MYKRGB) Subset MYK MYKR MYKG Process F R F R F R Max 5.27 4.85 5.33 5.34 4.89 4.97 Average 1.15 0.92 1.26 1.85 0.99 1.67 E 00 >6 ount 0 0 0 0 0 0 RMSE (Mean) 0.0013 0.0018 0.0011 0.0028 0.0011 0.0027 in terms of mean E 00, of four derived Models for transform processes of both the forward (denoted as F) and the reverse (denoted as R) under the D 50 condition.
Summary of Prediction performances of the multi-spectral 2 nd -SVD model (MYKRGB) Subset Process MYKB F R Max 6.47 4.94 Average 1.00 1.61 E 00 >6 ount 1 0 RMSE (Mean) 9.78 E-4 0.0026 in terms of mean E 00, of four derived Models for transform processes of both the forward (denoted as F) and the reverse (denoted as R) under the D 50 condition.
Sample omparisons & Patches Analysis Examples of spectral reflectance (SR) estimated, and comparisons between the original and the predicted (MYKO set; red line: the Originals; green line: the Predicted)
Ideal IE amera Model A spectra sensing model, virtually equipped with the simulated IEXYZ three-band filters (with a set of ideal spectral responses) i.e. IE 1931 olor Matching Function. 2.0 z 1.0 y x 0.0 400 500 600 700 λ
Ideal IE amera Model 1. An appropriate real spectral color dataset Munsell Book Glossy was used in this research 2. SVD and Winner Method Basis vectors: using SVD method oefficients: approximated by using the wellknown Winner-inverse solution 2.0 z 1.0 y x 0.0 400 500 600 700 λ Ideal spectral responses Munsell Book Glossy
omputational Procedures of Spectral Hi-Fi 6-colorant/ink Separation Algorithm
7 6 4 Optimization 4 no Optimization
Original 7 4 6
Soft-proofing Using Adobe-Type Display (BenQ) Via Halftone Palletter Dithering
http://en.literateprograms.org/floyd-steinberg_dithering_(java)
Implement the core algorithm Based on the concept of error diffusion The nearest palette color is chosen to the current pixel in question, and Then compute the difference of that color from the original color in each RGB channel. Pieces of this difference are dispersed throughout several adjacent pixels not yet visited. SO: in MY APPROAH: Using 00 instead of the difference of RGB MYKRGB2 7 =128 palettes MYKROG2 6 =64 palettes
<< >>= public static byte[][] floydsteinbergdither(rgbtriple[][] image, RGBTriple[] palette) { Implement the core algorithm RGBTriple currentpixel = image[y][x]; } return result;
4 Dithering Methods Floyd-Steinberg Jarvis, Judice & Linke Stucki Atkinson Based on the concept of error diffusion
7to6_DitheringProcess Soft-proofing omputational Procedures from Spectral 7-ink Separation Algorithm to 6-colorant Dithering Process
Satisfactorily derived: 1) An HDR contone to Hi-Fi halftone-conversion model, via fitting spectral reflectance approach. 2) The IEXYZ type of camera (sensing) model 3) Both ontone and Halftone-palate types of image display models, for soft-proofing of simulation of high-fidelity printing system, Using MYKRGB and MYKOG colorants.
Future Work
Process of Scanner
R G B Gray Balancing (1DLUT) R G B hromatic Lightness- Division (3 rd _SVD) Highlight Near-Neutral- Division (3 rd _SVD) Shadow Near-Neutral- Division (3 rd _SVD) Achromatic Gray Balance Algorithm (3DLUT) Lab
Original ((after GB Approach No_GB GB L 4 L7 GM Mean 2.76 2.31 1.53 0.96 1.17