Mathematical Problems of Computer Science 57, 18–29, 2022.

doi: 10.51408/1963-0083

UDC 004.932

A New Image Decolorization Evaluation Quality

Metric

Hrach Y. Ayunts1 and Sos S. Agaian2

1Yerevan State University, Yerevan, Armenia
2College of Staten Island (CSI), City University of New York, New York, USA

e-mail: hrach.ayunc@gmail.com, sos.agaian@csi.cuny.edu

Abstract

Image decolorization, the process of color-to-gray conversion, plays a crucial role in
single-channel processing, computer vision, digital printing, and monochrome visual-
ization. This process induces new artifacts, the impact of which on visual quality has
to be identified. While visual quality assessment has been the subject of many stud-
ies, there are still some open questions regarding new color-to-gray conversion quality
metrics. For example, computer simulations show that the commonly used grayscale
conversion quality metrics such as CCPR, CCFR, and E-score depend on parameters
and may pick different best decolorization methods by changing the parameters.

This paper proposes a new quality metric to evaluate image decolorization methods.
It uses the human visual properties information and regression method. Experimental
results also show (i) strong correlations between the presented image decolorization
quality metric and the Mean Opinion Score (MOS), (ii) more robust than the existing
quality metrics, and (iii) help to choose the best state-of-the-art decolorization methods
using the presented metric and existing quality metrics.

Keywords: Color-to-gray conversion, Decolorization, Grayscale, Regression, Qual-
ity metric.

1. Introduction

Image decolorization aims to convert a color image into a grayscale image to improve the
image’s visual appearance or provide a “better” gray-level representation for the future
automated image. The overall purpose of image decolorization is to preserve the visible
color contrast, which usually suffers from information loss. It plays an essential role in
single-channel image processing (analysis, detection, segmentation, and recognition), com-
puter vision, monochrome printing, e-ink display, etc. [1]. The analysis of the existing image
decolorization techniques shows the common problems that need to be solved because such
methods introduce certain artifacts. It isn’t easy to evaluate decolorization methods and
select their optimal parameters. There are various quality metrics for color images [2, 3].

18



H. Ayunts and S. Agaian 19

Thus, these types of metrics are not suitable for the evaluation of color-to-gray conversion.
There is also no efficient measure that can be served as a building criterion for image decol-
orization.

Practically, all quality metrics for image decolorization are based on the fact that the
human visual system cannot perceive color differences smaller than a certain threshold [4,
5, 6]. Extensive computer simulations show that (i) commonly used grayscale conversion
quality metrics such as CCPR, CCFR and E-score depend on the color difference parameter,
and (ii) by changing the parameter, we pick a different decolorization method. Thus, one
needs to develop a new robust threshold-independent quality metric that does not require a
reference image.

This paper makes several key contributions:

1. Propose a non-parametric, robust, monotonic, and non-reference quality metric for
image decolorization.

2. Present extensive computer simulation results.
3. Present qualitative and perceptual evaluation of state-of-the-art decolorization meth-

ods.

The structure of this paper is organized as follows. Section 2 discusses the existing image
decolorization methods and quality metrics. Section 3 presents a new non-parametric quality
metric. Section 4 provides the results of extensive computer simulation. Section 5 validates
the new metric using preference scores from the user study. Finally, Section 6 concludes the
work.

2. Background

This section presents the existing color-to-gray conversion methods and quality metrics.
Traditional color-to-gray conversion methods usually use a linear combination of R (red),
G(green), B (blue) channels of a color image. It is based on the theory of T. Young (1802),
which states that any color can be created by combining three primary colors: R, G, and B.
Gray = aR + bG + cB [7], were a, b, c coefficients are calculated as

(i) Lightness method: Gray =
max(R,G,B)+min(R,G,B)

2

(ii) Average method: a = b = c = 1/3, or Gray = R+G+B
3

(iii) Luminosity method: a = 0.21, b = 0.72, c = 0.07, or Gray = 0.21R + 0.72G + 0.07B.

These are the most popular and straightforward conversions used in electronic displays,
printers, computer vision, image processing, and many other algorithms as a preprocessing
step.

However, Fig. 1 shows that the grayscale conversion suffers from information loss (many
details didn’t preserve, and the color contrast was lost in the grayscale images). It is natural
to ask.

(a) Can we have a better decolorization algorithm?
(b) How to quantitatively evaluate the performance of different methods or choose the

parameters such as a, b, and c?
(c) How do you improve the quality of a color image using decolorized images?

More advanced decolorization methods use the values of other pixels to specify color
orders to preserve the color contrast. Local methods rely on local chrominance edges to
enhance the contrast [8, 9]. Most recent notable decolorization methods are based on the
parametric decolorization model and its modification [5, 4, 10].



20 A New Image Decolorization Evaluation Quality Metric

Source Lightness Average Luminosity We need this

Fig. 1. Comparison of traditional grayscale conversion methods. Decolorized images can lose

can lose the contrast and become hardly visible.

Parametric Decolorization Model(PDM). The basic idea here is to convert a
color image into gray using a combination of a polynomial of R, G, and B components:
{R, G, B, RG, RB, GB, R2, G2, B2}. It generalizes commonly used linear and nonlinear
color-to-gray conversion/mapping systems. More details on this method one can find in [5].

There are also neural network solutions to this problem [11].

Decolorization needs quantitative evaluation to understand the performance of different
methods.

Exiting decolorization quality metrics. The most commonly used decolorization
quality metrics are based on the fact that the human visual system cannot perceive color
difference δ smaller than a certain threshold. For example, the Color Contrast Preserving
Ratio (CCPR) (suggested by Lu et al. [4]), defined as

CCPR =
#{(x, y)|(x, y) ∈ Ω, |gx − gy| ≥ τ}

||Ω||
, (1)

where Ω is the set of all pixel pairs with δx,y ≥ τ, and gx, is the value of the x pixel after
decolorization.

CCPR shows the percentage of distinctive pixel pairs after the conversion, but it does not
necessarily indicate if the grayscale image was “distorted” after conversion. To complement
CCPR, Lu et al. [4] suggested Color Content Fidelity Ratio (CCFR). It is defined as

CCFR = 1 −
#{(x, y)|(x, y) ∈ Θ, δx,y ≤ τ}

||Θ||
, (2)

where Θ is the set of all pixel pairs with |gx − gy| > τ. This metric shows how much the
converted image has changed in terms of structure.

Finally, the combination of CCPR and CCFR, E-score [4], is defined as

E-score =
2 · CCPR · CCFR
CCPR + CCFR

. (3)

kind of quality



H. Ayunts and S. Agaian 21

3. Proposed Quality Metric

This section shows the shortcomings of the existing decolorization metrics and suggests a
better quality metric for quantitative evaluations.

Table 1: E-score metric for some threshold values for different decolorization methods

Image Method τ = 3 τ = 5 τ = 7 τ = 9 τ = 15 τ = 25

PDM 0.9934 0.9776 0.9759 0.9737 0.9644 0.9551

LUM 0.9613 0.9174 0.8526 0.7990 0.5956 0.3997

SPD 0.9862 0.9769 0.9751 0.9713 0.9475 0.9192

SVD 0.9896 0.9821 0.9765 0.9744 0.9279 0.8514

PDM 0.9726 0.9502 0.9272 0.9035 0.8298 0.6647

LUM 0.9646 0.9356 0.9046 0.8704 0.7447 0.4993

SPD 0.9777 0.9550 0.9275 0.8956 0.7823 0.5662

SVD 0.9745 0.9525 0.9279 0.9003 0.7987 0.5965

The commonly used grayscale conversion quality metrics such as CCPR, CCFR, and
E-score depend on the color difference parameter τ. Computer simulations show that by
changing the parameter τ, we pick a different decolorization method.

To verify this statement, we compare different decolorization methods on a couple of
images from Ĉad́ık’s dataset [12].

We calculate the E-score quality metric for different values of threshold. We use three
state-of-the-art methods (Lu et al. [5], Sowmya et al. [13], Liu et al. [10]) and the Luminosity
method for comparison. The results are listed in Table 1. Obviously, the best method differs
depending on the threshold value. For example, we can pick three different best methods by
changing parameter τ in the case of the second image. The visual results of decolorization
on these images are shown in Fig. 4.

In the previous work, the quantitative evaluation of color-to-gray conversion was per-
formed using E-score for fixed values of threshold [4, 5]) or the average of several threshold
values [10]. Therefore, there is a need for more independent metrics to investigate the con-
version process for each image.

We introduce a new quality metric called Threshold-Independent Slope (TIS), which
shows the decreasing speed of the E-score as the threshold value grows. We calculate the
E-score metric for different τ values (τ = 1, 2, ..15) and choose the slope of the linear regres-
sion of this data as a new metric. The main advantage of the new metric is that it is not
dependent on the τ parameter.

Linear Regression can be solved using several linear models. A simple linear model
function is defined as

y = α + βx, (4)

which describes a line with a slope β and y-intercept α. One of the easiest ways to estimate
the slope is to use the Least Squares method:

β̂ls = arg min
β

||y − βx||22. (5)



22 A New Image Decolorization Evaluation Quality Metric

Fig. 2. Simple linear function estimation using the Least Squares method,

Ridge regression, and Lasso regression.

Another method for coefficient estimation of (4) is Ridge regression [14]. It is most
suitable when data contains a higher number of predictor variables than the number of
observations. The ridge regression estimator solves the regression problem using l2 penalized
least squares:

β̂ridge = arg min
β

||y − βx||22 + λ||β||
2
2, (6)

where λ > 0 is a tuning parameter that controls the strength of the penalty term. Similar
to ridge regression, Lasso regression can be used for slope estimation [15]. The lasso
estimator uses l1 penalized least squares for solving the following optimization problem with
λ tuning parameter:

β̂lasso = arg min
β

||y − βx||22 + λ||β||1. (7)

Fig. 2 compares these three regression models on a sample image from Ĉad́ık’s
dataset [12]. Each of these models is used to calculate the TIS metric. To find the best
model for our case, we calculate the fitting scores of each model on every image from the
dataset. The Least Squares method has the best average fitting score: thus, we use it for
further evaluations. Therefore, our TIS metric is defined as

TIS = max(1 − |αβ|, 0), (8)

where α and β are coefficients of a simple linear function (4) estimated with the Least
Squares method (5). TIS ranges in [0, 1], and higher values mean a lower decreasing speed
of the E-score metric when the threshold is increased.

Fig. 3 shows the decolorization result on a sample image with four different levels of
visibility. The value of our TIS metric grows with better visibility and contrast in the result.
Therefore, the TIS is also a monotonic metric.



H. Ayunts and S. Agaian 23

Fig. 3. The TIS metric grows with a contrast and visibility increase.

4. Computer Simulation

This section evaluates four decolorization methods using our TIS metric and the existing
quality metrics. We also show the usefulness of our metric in picking the best parameters
for grayscale conversion.

Evaluation of decolorization methods. We chose one traditional conversion method:
the Luminosity method (denoted as LUM in tables) is the most popular conversion used
in many image processing algorithms and electronic devices. In many cases, it fails to
preserve the contrast because the conversion considers only current pixel information. We
also chose three state-of-the-art contrast preserving decolorization methods for evaluation.
These methods are suggested by Lu et al. [5], Liu et al. [10], and Sowmya et al. [13] (we use
PDM, SPD, and SVD acronyms in the tables, respectively). These methods consider global
pixel information and color differences in the image for better conversion.

Fig. 4. Visual results of different decolorization algorithms

(from left to right: source image, PDM, LUM, SPD, SVD)

TIS 0.53565 0.72862 0.82799 0.87882



24 A New Image Decolorization Evaluation Quality Metric

Fig. 5. Visual results of different decolorization algorithms

(from left to right: source image, PDM, LUM, SPD, SVD)

Figs. 4 and 5 show the visual results of four decolorization methods on several images.
The simple Luminosity method usually fails to preserve the color contrast, while the other
three methods produce better visual outputs.

We use Ĉad́ık’s dataset [12] for performance evaluation. It contains 24 PNG images and
mainly consists of synthetically generated images and some colorful real-life photos. Most of
these images are challenging for traditional color-to-gray conversion methods. That’s why
Ĉad́ık’s dataset is the most popular in this field and can be beneficial for the evaluation of
decolorization methods.

Table 2: Average TIS and E-score for different thresholds on Ĉad́ık’s dataset.

Method τ = 3 τ = 5 τ = 7 τ = 9 τ = 15 τ = 25 TIS

PDM 0.98222 0.97009 0.95866 0.94697 0.90971 0.84409 0.91635

LUM 0.96340 0.93755 0.91399 0.89556 0.83167 0.71761 0.84992

SPD 0.98241 0.97060 0.95922 0.94810 0.90966 0.83835 0.91560

SVD 0.98045 0.96651 0.95334 0.94040 0.89324 0.81638 0.90121

The quantitative evaluation of four decolorization methods using the E-score metric for
different thresholds and our new TIS metric on Ĉad́ık’s dataset are presented in Table 2. It
presents the performance of each metric (average value) of all images from Ĉad́ık’s dataset.
It also shows that the presented TIS metric is more stable and picks only the best method
for this dataset. So it can be helpful in both individual and large-scale evaluations of the
grayscale conversion methods.

Picking the best parameter for the simple grayscale conversion. Image decol-
orization quality metrics can not only be useful in method evaluation, but they can also



H. Ayunts and S. Agaian 25

help pick the best parameters for an algorithm. For example, in simple grayscale conversion,
coefficients can be changed to get a “better” conversion.

Fig. 6. Comparison of the “best” linear conversion with the luminosity method

(from left to right: source image, luminosity, the best conversion).

We pick the best parameters of the linear grayscale conversion by maximizing the value
of the quality metric for each image individually. Fig. 6 shows the results corresponding to
the highest values of the TIS for two images (a = 0.02, b = 0, c = 0.98 for the first image,
and a = 0, b = 0.06, c = 0.94 for the second one).

5. Perceptual Validation

This section validates our TIS metric using the preference scores.
We invited 20 users to participate in a survey to show the effectiveness and importance

of our metric. After a small introduction to decolorization, they were asked to rate the
color-to-gray conversion for ten random images from the Ĉad́ık’s dataset on a scale of one
to three. To facilitate the scoring process, we use the three-scale modification of the Mean
Opinion Score (MOS). One means the conversion is bad, and it failed to preserve the contrast.
Score two corresponds to mediocre conversion. Finally, three is for the best conversion with
contrast preservation and the most visually pleasing result.

To validate our metric, we use the Kendall rank correlation coefficient [16]. It is defined
as

R =
#{concordant pair} − #{disconcordant pair}

1
2
n(n − 1)

, (9)

where n = 4 denotes the number of methods. Let si be the score for the result produced by
the ith method, and pi be the preference score for the same result. If two pairs (si, sj) and
(pi, pj) are with the same order (i.e., (si − sj)(pi − pj) > 0), the pair (i, j) is concordant.



26 A New Image Decolorization Evaluation Quality Metric

Otherwise, it is discordant. R ranges in [−1, 1]. We get R > 0 if the two rankings agree with
each other and R < 0 otherwise.

We calculate the Kendall rank correlation coefficient (R) for the existing metrics and our
TIS metric. The TIS metric has a high correlation with the user preference scores and can
easily replace the existing quality metrics for quantitative evaluations of decolorization. The
ranks for several images presented in the survey are listed in Table 3.

Table 3: Kendall rank correlation coefficient for the E-score metric with different thresholds,
and our TIS metric

Image τ = 5 τ = 7 τ = 9 τ = 15 τ = 25 TIS

0.333 0.333 0.333 0.667 0.667 0.667

0.333 0.333 0.333 1 1 1

0.667 0.333 0.333 0.333 0 0.333

6. Conclusion

This paper proposes a new TIS image quality metric for accurately evaluating image decol-
orization methods. The TIS quality metric is a blind, robust, monotonic, non-parametric
metric and correlates with subjective preference scores. The quantitative and qualitative
computer simulations on the Ĉad́ık’s dataset demonstrate that the proposed metric outper-
forms the current state-of-the-art metrics. The TIS metric is also helpful in picking the best
parameters of the grayscale algorithm.

Our future work will extend the proposed work to other types of distortion, generate new
decolorization methods, and evaluate them on other databases.

7. Acknowledgment

This work was supported by the professors of the Department of Informatics and Applied
Mathematics of Yerevan State University (S. Sargsyan, E. Danoyan, Yu. Hakopian) and the
Armenian Engineers and Scientists of America.

The authors would like to thank the Picsart employees for participating in the user study.
The authors would also like to thank Sowmya et al. [13] and Lu et al. [4] for sharing source
codes and experiment materials.



H. Ayunts and S. Agaian 27

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Submitted 18.04.2022, accepted 27.05.2022.



2 8 A New Image Decolorization Evaluation Quality Metric

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Ñݳñ³íáñ ¿ ÁÝïñ»É É³í³·áõÛÝ ·áõݳ½»ñÍÙ³Ý Ù»Ãá¹Ý»ñÁ:

´³Ý³ÉÇ µ³é»ñ` ·áõݳíáñ å³ïÏ»ñÝ»ñÇ ÷á˳ϻñåáõÙ ÙáÝáËñáÙ å³ïÏ»ñÝ»ñÇ,
·áõݳ½ñÏáõÙ, ÙáÝáËñáÙ å³ïÏ»ñ, é»·ñ»ëdz, áñ³ÏÇ ã³÷áñáßÇã:



H. Ayunts and S. Agaian 2 9

áûëà ïðåäìåòîì ìíîãèõ èññëåäîâàíèé, âñå åùå îñòàåòñÿ íåñêîëüêî îòêðûòûõ
âîïðîñîâ, êàñàþùèõñÿ íîâûõ ïîêàçàòåëåé êà÷åñòâà ïðåîáðàçîâàíèÿ öâåòíîãî
èçîáðàæåíèÿ â ñåðûé. Íàïðèìåð, êîìïüþòåðíîå ìîäåëèðîâàíèå ïîêàçûâàåò,
÷òî îáû÷íî èñïîëüçóåìûå ïîêàçàòåëè êà÷åñòâà ïðåîáðàçîâàíèè, òàêèå êàê CCPR,
CCFR è E-score, çàâèñÿò îò ïàðàìåòðîâ è ìîãóò âûáèðàòü ðàçëè÷íûå íàèëó÷øèå
ìåòîäû ïóòåì èçìåíåíèÿ ïàðàìåòðîâ.

 ýòîé ñòàòüå ïðåäëàãàåòñÿ íîâàÿ ìåòðèêà êà÷åñòâà äëÿ îöåíêè ìåòîäîâ
îáåñöâå÷èâàíèÿ èçîáðàæåíèÿ. Îíà èñïîëüçóåò èíôîðìàöèþ î çðèòåëüíûõ
ñâîéñòâàõ ÷åëîâåêà è ìåòîä ðåãðåññèè. Ýêñïåðèìåíòàëüíûå ðåçóëüòàòû
òàêæå ïîêàçûâàþò ñèëüíóþ êîððåëÿöèþ ìåæäó ïðåäñòàâëåííîé ìåòðèêîé
êà÷åñòâà îáåñöâå÷èâàíèÿ èçîáðàæåíèÿ è ñðåäíåé îöåíêîé ìíåíèé (MOS), áîëåå
íàäåæíóþ, ÷åì ñóùåñòâóþùèå ìåòðèêè êà÷åñòâà, è ïîìîãàþò âûáðàòü ëó÷øèé
èç ñîâðåìåííûõ ìåòîäîâ îáåñöâå÷èâàíèÿ ñ èñïîëüçîâàíèåì ïðåäñòàâëåííîé
ìåòðèêè è ñóùåñòâóþùèõ ìåòðèê êà÷åñòâà.

Êëþ÷åâûå ñëîâà: ïðåîáðàçîâàíèÿ öâåòíîãî èçîáðàæåíèÿ â ìîíîõðîìíîå,
îáåñöâå÷èâàíèå, ìîíîõðîìíîå èçîáðàæåíèå, ðåãðåññèÿ, ìåòðèêà êà÷åñòâà.


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