=Paper=
{{Paper
|id=Vol-2076/paper-10
|storemode=property
|title=Spectral Reflection Prediction by Artificial Neural Network
|pdfUrl=https://ceur-ws.org/Vol-2076/paper-10.pdf
|volume=Vol-2076
|authors=Oleg B. Milder,Dmitry A. Tarasov
}}
==Spectral Reflection Prediction by Artificial Neural Network==
https://ceur-ws.org/Vol-2076/paper-10.pdf
Spectral Reflection Prediction by Artificial
Neural Network
Oleg B. Milder1 and Dmitry A. Tarasov1,2
1
Ural Federal University, Ekaterinburg, RUSSIA,
datarasov@yandex.ru,
www.urfu.ru
2
Institute of Industrial Ecology UB RAS, Ekaterinburg, RUSSIA
Abstract. Digital image processing requires significant amount of cal-
culations for characterization and profile making. Moreover, enhancing
the computing precision does not always lead to better results, and the
gamut might describe less part of color space than could do. Instead of
expanding the existing methods and color prediction models, we offer a
simple technique for spectral reflection prediction using an artificial neu-
ral network in Matlab. The proposed method is fast and easy-to-operate.
The experimental verification showed its good performance based on
minimization of the color difference CIE Lab dE Lab dE.
Keywords: Gradation trajectories, Profile, Spectral reflection, Image
processing.
1 Introduction
In order to create prints with accurately reproduced colors on a given reproduc-
tion system, it is essential to specify the color response that the system provides
for a given substrate, ink’s type, and with given amounts of inks during the
process of characterization and profile making.
In general, due to the printing process, the deposited ink surface coverage
is larger than the nominal one resulting in a physical dot gain responsible for
the ink spreading, which depends on the inks, on the substrate, and so on [1].
Sometimes, under absence of a competent management system, these limitations
lead to loss in color. In any case, the problem of ink management is crucial. To
solve this problem, manufacturers of image processing software and printing sys-
tems recommend using different criteria, such as: visual evaluation by spreading,
numerical estimation of the optical density of color coordinates that are imple-
mented in a variety of color prediction models (CPMs). CPMs may help the
image processing software to decide, which set of inks is chosen and how to se-
lect and mix them in order to create a determined color on a particular substrate
by particular inks. The models need to be accounted for both the interactions
between dyes, substrates and between light, and the halftone print, as well as
the Fresnel reflections and light scattering. By the present time, a great deal
87
of CPMs have been developed. The models are called up to predict the result-
ing color in print by a set of ink values as specified by reflectance models or
tristimulus values of primaries.
Empirical surface models only take into account superpositions of ink halftones,
which the reflected light is supposed to be a function of the effective ink surface
coverage. These models do not deal with the light propagation within the print
and only demonstrate the relationship between the reflected light and surface
coverages by ink.
Physically inspired models engage a more detailed analysis of light-print inter-
action based on mathematical prediction of how the light goes within a halftone
print and what the resulting fade is.
Ink spreading models describe the physical dot gain as a difference between
the effective and the nominal surface coverages. They show how much an ink dot
spreads out in all ink superposition conditions and rely on ink spreading curves
mapping the nominal surface coverages to the effective surface ones.
Spectral reflection prediction models (SRPM) are helpful in studying the im-
pact of different factors such as inks, substrate, the illumination conditions, and
the halftones influencing the range of printable colors and in creating printer
characterization profiles for the purpose of color management [2]. There are more
complicated spectral CPMs, which deal with spread-based and light propagation
probability.
One of the most cited one is Kubelka–Munk model that is widely used to
predict the properties of multiple layers of ink overlaid at a given location and
given information about each constituent ink’s reflectance and opacity [3]
2
K(λ) (1−R∞ (λ))
= , (1)
S(λ) 2R∞ (λ)
where K is the absorption and S is the scattering coefficients, R is the reflectance
of an infinitely thick sample and the prediction of S and K from reflectance is
made at the given wavelength λ.
Formula (1) allows predicting the combined K and S coefficients for multiple
inks
X l
K (λ) =KB (λ) + ci Ki (λ), (2)
i=1
where B refers to the substrate, l is the number of ink layers, ci is the concen-
tration, and Ki is the absorption coefficient of the i -th layer. The value S (λ) is
computed analogously.
Another famous CPM is the Neugebauer model, which predicts the CIE XYZ
tristimulus values of a color halftone patch as the sum of the tristimulus values
of their individual colorants [4]. Since the Neugebauer model does not take into
account the lateral propagation of light within the paper and internal reflections
at the paper-air interface, it is considered to be inaccurate.
Today, the most applicable model is the Yule–Nielsen modified spectral Neuge-
bauer model (YNSN) where the Yule–Nielsen relationship is applied to the spec-
88
tral Neugebauer equations [5, 6]
p n
X 1
R (λ) =( wi Pi (λ) n ) , (3)
i=1
where R(λ) is the reflectance of a halftone pattern neighborhood that is optically
integrated as it is being viewed, wi is the relative area coverage of the i -th
Neugebauer primary P, n is the Yule-Nielsen non-linearity that is accounted for
the optical dot-gain.
The Enhanced YNSN accounts the ink spreading connected with the respec-
tive physical dot-gains in different conditions (from 1 to 4 colorants superposi-
tion). The model engages multiple ink spreading (tone reproduction) curves to
characterize the physical dot-gain [7].
Current CPMs accounting the physical dot-gain and are able to predict re-
flectance spectra as a function of ink surface coverage for 3–4 inks [1, 8]. The
criterion for assessing the model’s performance is minimization of the difference
metric between measured and predicted reflection spectrum for each superpo-
sition condition. The most applicable difference metric used is the CIE Lab dE
(or ∆E ) color difference [9].
All mentioned approaches have their advantages and drawbacks. Majority of
models are too complicated to be embedded in a real digital image processing
workflow without substantial development and adjustment that takes time. For
instance, the YNSN-based models are extremely critical to selection of the pa-
rameter n that is usually fitted by brute force, and is utterly laborious except
some approaches [10]. An alternative is an empirical gradation approach.
Gradation scales are known as an unaltered attribute of contemporary digital
image processing systems [11, pp. 88–89]. At the same time, the authors express
doubts about the rational use of its features. The main problem is the fact that
using the gradation curves in conventional 2D embodiment significantly reduces
the quantity and quality of information extracted from them. In work [12], the
3D gradation trajectories are introduced as a further development of the gra-
dation curves. Implication the apparatus of differential geometry for gradation
trajectories analysis in the 3D CIE Lab space allows one to reveal their intrinsic
features of curvature that help to improve ink management.
Nevertheless, precise color prediction is still the issue that should be resolved.
One of the promising way to build the color prediction model is not model
variation at all. This is the artificial neural network (ANN) approach. Works
on this topic had started at early 1990th . Most of researchers were focusing
on application of ANN to the Kubelka-Munk approach [13–15]. The work [16]
also employs fundamental color stimulus for improving performance of color
prediction system based on the ANN. All studies have confirmed vast prospective
for ANN-based techniques in color prediction models.
This work is devoted to further development of the ANN technique applied
to color prediction. We work with an ANN training algorithm, define the ap-
plicability of the technique for spectral prediction, and guess how preliminary
linearization affects the accuracy.
89
1. Experimental
For the experiment, we use the 4-color (CMYK) wide-format ink-jet printer
Mimaki CJV30-160BS. Print mode: 720×720 dpi, variable dot. Substrate: a
vinyl banner fabric as a weak-absorbent substrate. The measurement tools: spec-
trophotometer x-Rite iOne iSis + x-Rite ProfileMaker package. Charts genera-
tion is made in the ArgyllCMS package.
We describe the approach as follows: print a specially developed test chart →
Measure CIE Lab coordinates of the patches → Build ANN → Predict spectral
reflectance ρ(λ) by ANN using test chart patches recipes as ANN inputs →
Assess the quality of prediction by the color difference formula dE 94 [9, 17].
For the ANN development, we use Matlab 16 package. The ANN type is mul-
tilayer perceptron with one hidden layer, and 10 hidden neurons. The training
techniques are the Levenberg–Marquardt (L-M) method and bayesian regular-
ization [18]. The trained network is stored in the form of a Matlab function.
Further statistical operations are carried out in the MS Excel and Statistica 10.
We predict spectral reflectance by test chart patches recipes. A preliminary
experiment stage consists of training the ANN by the training data set (training
chart). The training set contains 2448 patches, which recipes are obtained from
a discrete sequence {0; 16.8; 33.3; 50.2; 66.7; 83.1; 100} for each color in all
possible combinations (so-called a ‘multicube’). For ANN prediction, the test
chart with 2496 patches is developed in the ArgyllCMS. The patches recipes
take random values evenly distributing the fields in the color space of the ideal
CMYK-device. This data set acts as input for the ANN. The ANN output is the
predicted spectrum. For each spectra, the CIE Lab coordinates are calculated.
The test chart is then measured and the actual values of the CIE Lab coordinates
are established. The color difference between predicted and measured values for
each patch of the test chart is calculated by the dE 94 formula.
The preliminary stage revealed that 6–7% of predicted spectra have negative
values of individual spectral components, which is physically impossible. This
occurs in cases where the actual value of the reflection coefficient is close to
zero. Under the absence of restrictions, the network selects patterns in this way.
However, we do not yet have grounds for introducing restrictions.
We study several options of this problem solution. The simplest case is ig-
noring of the negative values and removing them from further consideration.
However, this can steep the results of the prediction.
The other option may be an increase in the samples sizes for both train-
ing and test sets. The sample volumes are artificially increased by a three-fold
measurement of the scales. The results of measurement are placed in a single
protocol. This option also did not bring significant results, except for a significant
increase in the training time of the network. Similar results are also obtained in
attempts to use the averaged values for training and predicting.
A variant of the solution of the problem is the transition from the spectral
reflection coefficients ρi (λ) to the spectral optical density Di (λ)(4)
90
Di (λ) = −log10 ρi (λ), ∀ i, λ , (4)
where i is the counter of patches, λ is the wavelength, λ = {380, 390, . . . ,
730} nm.
The final experiment is the following. The training set consists of the results
of triple measurements of the training scale. Thus, each patch is included in
the training set three times with the same composition of predictors, but with a
statistically different composition of spectral components. The additional benefit
of this approach is the ability to train the network on statistically blurred data.
Such, we train the ANN with spectral density D and predict also its values.
After prediction, the spectral density D values are recalculated back into the
spectral reflectance
ρi (λ) =10−Di (λ) , ∀ i, λ. (5)
The predicting quality is assessed by the color difference dE 94 . The list of per-
formed experiments and their brief description are given in Table 1.
1. Results and discussion
For comparison of the results obtained in each experiment, arrays of dE 94
are fitted by different distributions (see Table 2 and Fig. 1). Goodness of fit is
assessed by the χ2 criterion.
The distribution that fit dE 94 best in most cases is lognormal. We use an-
alytical distribution only for the ability to evaluate median and 95% quantile.
Median shows the mean value of the color difference in the test set. The quantile
is the upper border of the color difference with 95% probability. Analysis of plots
in Fig. 1 confirms validity of such estimate.
We also build the dependencies of the dE 94 from the total ink parameter (see
Fig. 2). The plots allow assessing where the ANN predicts better, in “lights” or
in “shades”.
As it can be seen from Fig. 2a, the ANN badly predicts spectral reflectance.
In some cases, the dE 94 exceeds 6 that is completely unacceptable in real print
production. Moreover, color difference is distributed unevenly in relation with the
total ink parameter: the prediction error increases in the “shades”. The determi-
nation coefficient and trend in the figure accentuate such increase. Nevertheless,
as Table 2 shows, the mean value of the color difference is just about 2 and 95%
quantile is less than 5 that is quite good. At the same time, existence of the
negative spectral components in some predictions does not allow us to consider
this experiment successful. In further experiments, we replace the prediction of
spectral reflectance ρi (λ) with one of spectral density Di (λ) without changes in
the ANN.
Figure 2b shows the results of predictions by the ANN trained with non-
linearized printer sample. Table 2 reveals the awesome results of the third experi-
ment where 95% values of color difference are less or equal 1.5. Notwithstanding,
in this case, we also observe the dependence of the color difference and the total
ink parameter. “Lights” are predicted much worse than “shades”. This might
91
be explained with the assumption that a non-linearized printer exceeds the ink
supply for highly saturated tones. The reason why the network predicts these
formulations better is the excessive number of dark patches in the training set.
Figures 2c and 2d show the results of prediction for the ANN trained by
data from the linearized printer. The determination coefficients in these cases are
significantly lower than previous ones. This can be interpreted as the complete
absence of the dependence of the color difference on the total ink parameter.
Suchwise, the ANN predicts the spectrum of any patch recipe with equal success.
The only difference between Figures 2c and 2d is the algorithm of ANN training:
Experiment 4 uses the Levenberg-Marquardt method while Experiment 5 applies
the Bayesian regularization.
Table 1. Summary table of the experiments description
ExperimentA brief experiment description
number
1 The test set is printed on a linearized printer and measured three times.
7488 dE 94 values are calculated. dE 94 of each patch from the triple aver-
age is obtained. The lowest border of prediction accuracy is evaluated.
2 The test set is printed on a linearized printer and measured three times.
The ANN is trained to predict ρ(λ) value according to the recipe of the
patch. The L-M algorithm is applied. 7059 recipes are predicted without
negative values of ρ(λ). Estimation of direct prediction of ρ(λ) is done.
3 The test set is printed on a non-linearized printer and measured once.
The ANN is trained to predict the spectral D value according to the
patch recipes. The L-M algorithm is applied. Estimation of indirect pre-
diction of ρ(λ) is done. We compare the prediction results of a linearized
and non-linearized printing system.
4 The test set is printed on a linearized printer and measured three times.
The ANN is trained to predict the spectral D value according to the
patch recipes. The L-M algorithm is applied. Estimation of indirect pre-
diction of ρ(λ) is done. We compare the prediction results of a linearized
and non-linearized printing system.
5 The test set is printed on a linearized printer and measured three times.
The ANNis trained to predict the spectral D value according to the patch
recipes. The Bayesian regularization algorithm is applied. We compare
network learning algorithms.
As it can be seen from Table 2, the spreading of color differences dE 94 in
Experiment 4 is not fitted well by both lognormal and normal distributions.
At this stage, the correlation with the total ink parameter is not high, but 1.4
times higher than in the case of Experiment 5. Moreover, there is an inexplica-
ble border around dE 94 =3 (see Fig. 2c). Consequently, it can be argued that, in
general, for all experiments, the Levenberg-Marquard training algorithm shows
unsatisfactory results. The lowest correlation with the total ink and even distri-
92
bution of low dE 94 are obtained in Experiment 5 with the Bayesian regularization
for the ANN training method.
Fig. 1. Distribution fitting according to Table 1: a) Experiment 1, b) Experiment 2,
c) Experiment 3, d) Experiment 4 - lognormal, e) Experiment 4 - normal,
f) Experiment 5
93
Fig. 2. dE 94 vs total ink parameter for: a) Experiment 2, b) Experiment 3, c) Experi-
ment 4, d) Experiment 5
Table 2. Statistical processing results
ExperimentType of χ2 Parameters of the theo- Median, 95% quan-
number distribu- retical distribution, µ / d tile, d
tion σ
1 Log- 66 –3.0275 / 0.4893 0.05 0.11
normal
2 Log- 80 0.7369 / 0.4916 2.09 4.69
normal
3 Log- 11 –0.1349 / 0.3325 0.87 1.51
normal
4 Log- 1304 0.3625 / 0.3005 1.44 2.36
normal
4 Normal 501 1.6327 / 0.5570 1.63 2.55
5 Log- 291 0.2108 / 0.3142 1.23 2.07
normal
1. Conclusion
We offer a technique for spectral reflection prediction using an artificial neural
network. The proposed method is easy-to-operate and does not involve sophis-
ticated color prediction models. The experimental verification showed its good
performance based on minimization of the color difference CIE Lab dE 94 .
94
Application of artificial neural networks for solving the problem of color pre-
diction by its recipe shows the excellent result subject to certain conditions.
First, the color reproduction system must be linearized prior to the predic-
tion. Next, we strongly recommend training the network not for prediction the
spectral reflectance but for the spectral density, since there are probability of
appearance of negative values during the ANN prediction.
Additional benefits of our study are the following: we first use the uniformity
of the dE distribution from the total ink as a criterion for prediction quality
assessment. Our approach solve the problem of the Black (K) channel generation
automatically as we use the CMYK patches as inputs and outputs while common
color prediction models operate in CMY recipes only, which requires additional
efforts for the CMY-CMYK converting.
The results obtained are preliminary. Some issues remain unsolved. We would
expect that the prediction could be even more precise when the appropriate
training algorithm and sample volume were selected.
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