8色光谱分离法：多色打印机色彩校准新方法

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"Spectral-based color separation method for a multi-ink printer" 这篇研究论文主要探讨了一种基于光谱的多色墨水打印机色彩分离方法。在彩色打印系统中，颜色分离是至关重要的，它涉及到将图像的色彩信息分解成不同颜色的墨水组合，以便打印机能够准确再现原始图像的色彩。传统的色彩分离方法通常基于XYZ色彩空间，但这种方法在预测多墨打印的色彩配方时可能会存在不准确的问题。作者开发了一个8色墨水的特性化模型，该模型结合了5种3色和6种4色的组合，利用了细胞结构的Yule-Nielsen光谱Neugebauer模型，并辅以一种配方选择策略。Yule-Nielsen光谱Neugebauer模型是一种广泛用于描述颜色混合的理论，它考虑了不同颜色墨水在光谱级别的相互作用，从而更精确地预测颜色混合效果。在实际应用中，研究者通过打印测试样本对前向模型（预测颜色配方）和后向模型（从已知打印结果反推颜色配方）的性能进行了评估。结果显示，基于光谱的方法在色彩预测和还原上优于传统的XYZ色彩空间方法。这表明，利用光谱信息可以提高多墨打印的色彩准确性，特别是在处理复杂色彩组合时。此外，根据后向模型的性能，研究者提出了一种快速的配方选择算法，旨在优化打印过程中的颜色匹配和效率。这种算法对于提高多色打印系统的色彩管理和生产效率具有重要意义，尤其是在大规模生产和专业图形设计领域。这篇论文揭示了基于光谱的色彩分离方法在多墨打印中的优势，为色彩科学和打印技术提供了新的理论基础和技术手段。通过这种先进的方法，打印设备可以更精确地模拟和再现各种颜色，从而提升打印质量和用户体验。

COL 9(6), 063301(2011) CHINESE OPTICS LETTERS June 10, 2011

Spectral-based color separation method for

a multi-ink printer

Binyu Wang (

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1,2

, Haisong Xu (

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∗

, M. Ronnier Luo

, and Jinyi Guo (

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1,2

State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Hangzhou 310027, China

Department of Colour Science, University of Leeds, Leeds, LS2 9JT, UK

∗

Corresponding author: chsxu@zju.edu.cn

Received November 12, 2010; accepted December 17, 2010; posted online April 28, 2011

A sp ectral-based 8-ink characterization model is developed to accurately predict the recipe for a multi-ink

printer. The 8-ink color separation method is a union of ﬁve 3-ink and six 4-ink combinations based on

the cellular Yule-Nielsen spectral Neugebauer model with a recipe selection strategy. The performance

levels of the forward and backward models are evaluated for individual ink combinations using printed

testing samples. Furthermore, the spectral-based method performs bett er compared with the XYZ-based

approach. On the b asis of the backward model performance, a novel fast recipe selection strategy is

proposed and estimated.

OCIS codes: 330.1690, 300.6550, 330.1710, 330.1715.

doi: 10.3788/COL201109.063301.

In printer systems, two major approaches are used, i.e.,

the analytical and generic methods, to derive a character-

ization model. The analytical metho d is based on mod-

eling physical phenomena, such as Kubelka-Munk the-

ory and Neugebauer equations. The parameters of the

model are usually obtained from a relatively small num-

ber of samples, while the accuracy depends on the e x-

tent to which the model describes the actual behavior of

the device; some of these models are diﬃcult to invert.

The generic method requires a large set o f training data

to build the model, as in three-dimensional (3D) look-

up table with interpolation

[1]

. Because the spectral data

contain all color information compared with tristimulus

values, the spectral-based approach achieves higher ac-

curacy and lower illuminant metamerism than does the

XYZ-based method at the expense of more calculations.

Typical 4-ink color printers have sma ll color gamut and

limited deg rees of freedom; thus, the use o f more inks not

only incre ases color gamut and the number of degrees of

freedom, but also improves accuracy

[2,3]

In this letter, the cellular Yule-Nielsen spectral Neuge-

bauer (CYNSN)

[2,4]

model is implemented to character-

ize a HP Desig njet Z3200ps 44 -inch photo printer, which

uses 12 inks

[5]

. For s implicity, 8 inks are used in the

exp eriment, including grey (Gy), photo black (K), light

cyan (C), magenta (M), yellow (Y), chromatic red (R),

green (Gn), and blue (B). The 8-ink color separation al-

gorithm is a union of ﬁve 3-ink and six 4-ink sets based

on the CYNSN model

[6]

with a recipe selection strat-

egy, containing the ink combinations of CMY, RMY,

CGnY, CMB, RGnB, CMYK, RMYK, CGnYK, CMBK,

RGnBK, a nd CMYGy. A large number of training and

testing hardcopy samples were prepared and measured,

and then the performa nce levels of the forward and back-

ward models were individually evaluated. In addition,

the spec tral-based method was compared with the XYZ-

based approach in terms of color diﬀerence, reﬂectance

root mean square

[7]

(RRMS) error, and metamerism in-

dex (MI). Finally, a novel fast recipe selection strategy

with high accuracy is proposed for the printer.

In 1937, Neugebauer developed a method for modeling

CMY halftone printing

[4]

. It was based on improving the

Murray-Davies

[2]

model and can be extended to use mor e

inks. Afterward, two main improvements

[2]

were pre -

sented. One is the Yule-Nielsen n-factor describing the

light sca ttering. The classical CMY Neugebauer model

modiﬁed by the Yule-Nielsen eﬀect is expressed as

R(λ) =

(

i=1

(λ)]

1/n

)

, (1)

where R

(λ) is the reﬂectance of the ith primaries (i =

1, 2, · · ·, 8) at wavelength λ, w

denotes the weighting

coeﬃcient for the ith primary deﬁned by the Demichel

equation

[8]

, n-factor is usually determined by optimiza-

tion, and the typical value of n-factor rang e s from 1 to

4. The other improvement is called the cellular Neuge-

bauer model. Firstly, the entire color space (e.g. CMY,

CMYK) is divided into smaller sub-spaces called ce lls,

and then the classical Neugeba uer model is applied in

the selec ted cell dependent on the input ink amounts.

Combining these two improvements with the classical

Neugebauer model forms the CYNSN model, in which

predicting ac c uracy drama tically increases.

The Yule-Nielsen spectral Neugebauer (YNSN) model

is not analytically invertible; thus, its inversion is usually

solved using iteratio n. A well-known method was pr o-

posed by Urban and Grigat, in which linear regres sion

iteration was used

[9]

, based on which Li et al. introduced

“QR” decomposition, further reducing computational

costs

[10]

. Therefore, Li algorithm was employed in this

letter.

Before conducting the backward YNSN model, deter-

mining the optimal cell is an indispensable step, within

which the most accurate recipe can be predicted by the

backward model. Urban et al. developed a cellular lin-

ear regression iteration algorithm, which dramatically

decreased the number of cells tr ied but did not guaran-

tee that the selected cell was the actual optimal cell

[11]

Later, Guo et al. proposed a cell searching method,

which ensured that the optimal cell was found at the

1671-7694/2011/063301(4) 063301-1

 2011 Chinese Optics Letters

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