This document discusses using an extended Neugebauer spectral model to efficiently characterize color printers with fewer color patches. It explains that traditional color profiling requires printing and measuring hundreds of patches, but an extended Neugebauer model using a Yule-Nielsen correction can predict colors with as few as 44 patches. The model provides a better physical explanation for allowing negative Yule-Nielsen factor values and performs color prediction more accurately for dye-based inks than pigment-based inks. Future work could expand the model to handle multiple ink systems and improve estimating colors beyond the inks' limits.

1. © 2006 Hewlett-Packard Development Company, L.P.
The information contained herein is subject to change without notice
Efficient Color Printer Characterization
Based on Extended Neugebauer Spectral
Models
Pau Soler and Jordi Arnabat
Hewlett-Packard Large Format Printing Division - Barcelona,
Spain

2. 2 Jan 31, 2007 Electronic Imaging '07 Extended Neugebauer Models
The need for color profiling
Strong demand of m e dia
fle xibility in photographic and
fine arts markets
•+100 paper types
•If same color profile is used,
differences can be up to 30dE
canvas
litho
coated
glossy
satin
Colorprofiles determine
the amount of ink
needed foreach media,
ensuring accurate
colors.
Using colorprofile

3. 3 Jan 31, 2007 Electronic Imaging '07 Extended Neugebauer Models
Building color profiles
Typically, to create a color
profile a big target (~1000
patches) needs to printed,
measured and processed.
And it takes time… (~2 hour)
Printers with embedded color
sensors enable users to easily
create colorprofiles.
But it takes time… (~20
minutes)
Ink space (e.g. CMYK) CIE L*a*b*

4. 4 Jan 31, 2007 Electronic Imaging '07 Extended Neugebauer Models
Goal: reduce the number of patches
color
prediction
model
small target
(~50 patches)
Standard IT8.7/3
large target (~700 patches)
The goal is to use a color model with less number of sampling points, reducing:
• Time of operation
• Media usage
• Ink usage

5. 5 Jan 31, 2007 Electronic Imaging '07 Extended Neugebauer Models
Neugebauer Spectral Model
The human visual system
‘averages’ halftone pattern
colors
where:
ai: area covered by each colorant
Ri(λ): spectral reflectance of Neugebauer colorants
Ř (λ): estimated spectral reflectance of halftone pattern
Neugebauer model predicts such ‘average’.

6. 6 Jan 31, 2007 Electronic Imaging '07 Extended Neugebauer Models
Yule-Nielsen Correction
where:
n : Yule-Nielsen factor
Actually, light propagates within
the media. This phenomena is
known as o pticaldo t g ain.
Yule-Nielsen proposed a
parametric non-linear correction
to compensate this effect.

7. 7 Jan 31, 2007 Electronic Imaging '07 Extended Neugebauer Models
The valid range for n
Originally linked to dot gain, n is supposed to be positive.
Experimental fit to data improves as n  ∞ .
Which is the valid range of values for n ?
Data fitting improves as n  ∞
Viggiano [ICIS ‘06] and
Lewandowski e t al. [J. Opt. Soc. 06]
suggest the use of negative values.
where:
n : Yule-Nielsen factor

8. 8 Jan 31, 2007 Electronic Imaging '07 Extended Neugebauer Models
The valid range for n (2)
As internal scattering is higher,
light interacts more with
pigments, decreasing the
reflectance of the patch.
The actual reflectance spectra
lays between Neugebauer
estimation (no optical dot gain)
and the minimum of the
colorant’s spectra (infinite
scattering).
n positive sets an arbitrary limit
to this range, which might not
suffice to match the actual
color.
colorant 1
colorant 2
Neugebauer estimation
Actual color
validrange

9. 9 Jan 31, 2007 Electronic Imaging '07 Extended Neugebauer Models
Yule-Nielsen as generalized averaging
Yule-Nielsen is actually a
generalized averaging of the
colorant spectra, for the particular
case of and .
As function of n varies from min to
max:
General form of generalized averaging
Particular case for
n = 1 /α
∞
1
1/2
0+
-1
0-
validrange
n
neugebauer (n=1)
min

10. 10 Jan 31, 2007 Electronic Imaging '07 Extended Neugebauer Models
Practical considerations:
Physical dot gain correction
Extra primary patches are printed and measured to correct area coverage:
No area coverage correction With area coverage correction
Area coverage computed with DeMichel’s equation:

11. 11 Jan 31, 2007 Electronic Imaging '07 Extended Neugebauer Models
Practical considerations:
Ink limits
Fully saturated colors can not be printed due to ink limiting.
Neugebauer colorants are estimated using the closest printable color and
the other colorants, as:
Maximum values of CY… …corresponding CIEL*a*b* values

12. 12 Jan 31, 2007 Electronic Imaging '07 Extended Neugebauer Models
Results
color
prediction
model
Printer:
HP designjet 2500CP
(inkjet CMYK)
Spectrophotometer:
Minolta-CM508c
(45/0, D50, 8mm)
n value optimized for each case
Better results with dye inks than pigment inks
44 patches

13. 13 Jan 31, 2007 Electronic Imaging '07 Extended Neugebauer Models
Conclusions
•We gave a numerical explanation for negative n values.
•Yule-Nielsen is a form of generalized averaging
•n values with physical meaning are (−∞ , 1] U [1,∞ , 1).
•Probably optimize 1/α makes more sense than n.
•Extended Neugebauer model performs better with dye inks than pigmented
inks.
•Feasible approach to reduce number of patches to create a color profile
•Future work includes:
• extend to multiple ink system
•improve colorant estimation
•many other Neugebauer extensions (e.g. cellular).