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arXiv:1711.10662v1 [] 29 Nov 2017

Undefined 1 (2010) 1–5
IOS Press

An Adaptive Fuzzy-Based System to
Simulate, Quantify and Compensate Color
Blindness
Jinmi Lee a and Wellington Pinheiro dos Santos b,∗
a

Escola Politécnica de Pernambuco, Universidade de Pernambuco,
Rua Benfica, 455, Madalena, Recife, Pernambuco, 50720-001, Brazil
E-mail: jinmilee@gmail.com
b
Núcleo de Engenharia Biomédica, Universidade Federal de Pernambuco,
Av. Prof. Morais Rego, 1235, Cidade Universitária, Recife, Pernambuco, 50670-901, Brazil
E-mail: wellington.santos@ieee.org

Abstract. About 8% of the male population of the world are affected by a determined type of color vision disturbance, which
varies from the partial to complete reduction of the ability to distinguish certain colors. A considerable amount of color blind
people are able to live all life long without knowing they have color vision disabilities and abnormalities. Nowadays the evolution of information technology and computer science, specifically image processing techniques and computer graphics, can be
fundamental to aid at the development of adaptive color blindness correction tools. This paper presents a software tool based
on Fuzzy Logic to evaluate the type and the degree of color blindness a person suffer from. In order to model several degrees
of color blindness, herein this work we modified the classical linear transform-based simulation method by the use of fuzzy
parameters. We also proposed four new methods to correct color blindness based on a fuzzy approach: Methods A and B, with
and without histogram equalization. All the methods are based on combinations of linear transforms and histogram operations.
In order to evaluate the results we implemented a web-based survey to get the best results according to optimize to distinguish
different elements in an image. Results obtained from 40 volunteers proved that the Method B with histogram equalization got
the best results for about 47% of volunteers.
Keywords: Color blindness correction, color blindness simulation, linear color systems, color transformations, digital image
processing

1. Introduction
Millions of years of evolution have made the human
visual system one of the most important sensory faculties. Nevertheless, about 8% of the male population
has some sort of color vision disturbance. This condition is characterized by the partial or complete reduction of the ability to distinguish some colors [1]. It is
a relatively common fact that people with color blindness use to live several years without realizing that
they have a color vision deficiency. The reason for this
* Corresponding

author. E-mail: wellington.santos@ieee.org

fact is that the disorder can appear in different intensities. The increasing user interaction with graphical interfaces has been evidencing several problems related
to color discrimination, which often restrics the use of
these web-based applications [8].
The increasing evolution of information technology
and computer science, as well as digital image processing on the improvement of visual information for human interpretation, have improved the visual quality of
digital images for people with certain degrees of disturbance in color perception. However, most applications intended to lessen the color blindness effects do

0000-0000/10/$00.00 c 2010 – IOS Press and the authors. All rights reserved

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J. Lee and W. P. dos Santos / An Adaptive Fuzzy-Based System to Simulate, Quantify and Compensate Color Blindness

not take in account that such disorders could occur in
many degrees, depending on each person [10].
The classical methods to simulate color blindness
are based on mathematical color models to represent
extreme cases of color blindness, i.e. the absence of
one of the three photoreceptors of the human eye (red,
green, and blue, i.e. low, medium, and high frequencies) [32]. Real cases of color blindness are characterized by some degree of anomaly at the absorbance
spectrum of red, green, and blue spectral bands. Such
a degree of chromatic deviation can be measured by
software tools designed to collect parameters that can
simulate real color blindness using fuzzy membership
functions.
One of the targets of this paper is to perform a study
on the chromatic abnormalities of the human visual
system and to develop computational tools for adaptability of human-machine interfaces, providing the inclusion of individuals with color blindness and creating more accessible solutions.
In order to reach this target, we developed a simulation tool of color blindness from the application of
linear transformation matrices that model the nonexistence or disability of the cone cells responsible for
sensitivity to low, medium and high frequency spectral
bands. We also developed a software tool to test color
blindness and assess the degree of color blindness, using a fuzzy-based approach. The last tool was developed to improve the visual quality of digital images
for people with color blindness. This integrated solution includes tests for the diagnosis of the color disturbance type to the image preview with the adjustments
that aims to reduce the color blindness effects.
In order to contribute for the evaluation of future
color blindness correction tools, another purpose of
this paper is to present a fuzzy-based method to simulate real color blindness. The development of color
blindness simulators is very important both for the development and design of GUIs (Graphical User Interfaces) and for supporting the development of new
mathematical methods of correction of color blindness. We developed a tool which simulates color blindness from linear transformation matrices which model
either the nonexistence or the disability of the cone
cells responsible for the sensitivities to low, medium
and high frequencies. Those matrices are adapted according to the fuzzy parameters obtained by a previous tool, briefly cited above, which evaluates color
blindness and assesses its severity degree, using an approach based on Fuzzy Logic.

2. Materials and Methods
In the eyes, specifically in the retina, there is a zone
where we can find the sensory cells specialized to
capture the light stimuli: the photoreceptors known as
rods and cones [8]. The rods have a scotopic characteristic, i.e they have a high sensitivity to achromatic
light. Since the cones have the photopic characteristic, they are less sensitive to light, but are able to discriminate between different wavelengths [8]. There are
three different types of cones in human eyes, each containing one type of photosensitive pigment. One type
detects the spectrum of low frequencies of light (red
color), while another one detects the medium frequencies spectrum (green color). The third type of cones
detects the high frequencies spectral band (blue color).
All these cones working together allow color vision
[8,32].
The eye cones can be classified according to their
sensitivity to different wavelengths. Those which are
sensitive to the red spectral band are stimulated by long
wavelengths; those ones sensitive to green are stimulated by wavelengths considered average, while cones
that are sensitive to blue color are stimulated by short
wavelengths. The vision of different types of colors
becomes possible when those three types of cones are
stimulated at the same time [8].
Several statistical studies show that about 8% of
males and 0.4% of females have some form of disability related to the perception of colors [8]. Deficiencies
for the colors are also called dyschromatopsias, or simply color blindness [32,8].
Most people have trichromatic vision. However, regarding to color vision disorders such as color blindness, it is possible to classify them in [8]:
Anomalous trichromacy: anomaly in the proportions
of red, green and blue. There are three types of
anomalous trichomatic classified:
1. Protanomaly: less sensitive to red.
2. Deuteranomaly: less sensitive to green.
3. Tritanomaly: less sensitive to colors in the
range of blue-yellow.
Dichromatism: it can be considered as special absolute cases of anomalous dichromatism, i.e. the total lack of sensitivity to red, green or blue. Due to
the absence of one kind of cone, it is presented in
the form of:
1. Protanopia: absence of red retinal photoreceptors.

J. Lee and W. P. dos Santos / An Adaptive Fuzzy-Based System to Simulate, Quantify and Compensate Color Blindness

2. Deuteranopia: absence of green retinal photoreceptors.
3. Tritanopia: absence of blue retinal photoreceptors.
Monochromatism: Total inability to perceive color.
This type of color blindness makes one see the
world in gray levels. It is a very rare deficiency
called achromatic vision.
Considering monochromatism as monospectral vision, it is not possible to realce image features depending on color. Furthermore, dichromatism can be
perceived as extremes cases of anomalous trichromacy. Therefore, herein this paper we focused only on
anomalous trichromacy and dichromatism.
In order to simplify notation and avoid transcribing the full name of the deficiencies of the chromatic
visual system, throughout this article we decided to
adopt the terms protan, deuteran and tritan to the deficiency of sensitivity to the frequencies of red (low frequencies), green (medium frequencies) and blue (high
frequencies), respectively.
About twenty methods of diagnosis and classification of color disorders are most often used. Among
them are: pseudoisochromatic plates or color discrimination tests, color arrangement tests or color hue test,
equalization, appointment or designation, etc. Pseudoisochromatic plates are used in the discrimination
tests. These various types of available plates are combined in various tests, among which the Ishihara test,
that is quite popular, being the most known and used
worldwide [8].
Although this test does not provide a quantitative
assessment of the problem and does not identify deficiencies of the tritan type, studies show that the Ishihara test remains the most effective test for rapid identification of congenital deficiencies in color vision [8].
Once visual information depends on image color
distribution, it also depends on the frequency response
of the visual system. Consequently, the lack of information can constitute a considerable problem for people with color blindness. Thus, it is possible to say
that color blindness constitutes an obstacle to the effective use of computers, which nowadays uses more
and more graphics in its interface and its visual communication.
There is a growing commitment to create computational tools focused on the accessibility of people with
color visual disturbances. The color blindness simulators are already quite common and avoid serious problems of accessibility, aiding to comprehend the percep-

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tual limitations of a color blind individual [32]. Nevertheless, these simulators are designed just for dichromatism [32].
There exist also applications designed to improve
the visual quality of images. However, in most applications, it is assumed that the user already knows his
type of disorder and does not consider that the disorder
may occur in varying degrees. The difference of using
an adaptive filter is related to the diagnosis and the use
of an approach that considers the uncertainty associated with the problem, where Fuzzy Logic appears as
a natural candidate to solve the adaptation to the user
according to his degree of color blindness.
It is quite common for people with color blindness
not to realize that they have visual disturbances, and
many - when they discover the problem - do not know
how to classify it. However, it is very important to improve efficiently the quality of life of those people, the
knowledge of information as the type of color blindness and in what degree it is.
In order to fill this information gap, a test tool called
DaltonTest was developed. The goal of this tool is to
classify the color blindness, showing the degree of the
disability and its possible forms of presentation.
In DaltonTest tool, the user is submitted to the
Ishihara test (see figure 1), that has been customized
through the use of weights. Different weights were assigned to the Ishihara test questions, so that the inaccurate responses received fewer points than the precise
answers. This simple change makes it possible to evaluate approximately the user’s blindness degree.
Figure 2 shows an example of the data structure
adopted to describe and store a question of the Ishihara test used in the DaltonTest tool. The test, when
completed, presents an estimated diagnosis of the user
color blindness, containing three factors: the degree of
color blindness, the degree of protanomaly, and the degree of deuteranomaly. These degrees are in fact degrees of membership to fuzzy sets associated to types
of color blindness, protanomaly, and deuteranomaly,
calculated from the fuzzyfication of determined scores.
Such result is then used by the correction tool, providing a fuzzy characteristic for the application.
The developed tool DaltonSim allows the simulation
of the most common cases of anomalous trichomatic:
protanomaly and the deuteranomaly.
The simulation algorithm of colorblindness is based
on the color model LMS (Longwave, Middlewave,
Shortwave), once this color model is the most adequate
to model the behaviour of light reception: notice eye
cones are organized in receptor groups of short, mid-

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J. Lee and W. P. dos Santos / An Adaptive Fuzzy-Based System to Simulate, Quantify and Compensate Color Blindness

follows [32]:

 
 
Lp
0 2.0234 −2.5258
L
 Mp  =  0 1
 M  ,
0
Sp
0 0
1
S

(3)

and for deuteranopia [32]:
(a)

(c)



 
 
Ld
1 0 0
L
 Md  =  0.4942 0 1.2483   M  .
Sd
0 0 1
S

(4)

Finally, there must be a transformation of the LMS
color model to RGB. This transformation is obtained
using the inverse matrix of the first step matrix [32].
(b)



(d)

Fig. 1. Examples of Ishihara plates: (a) demonstration plate; (b) hidden plate; (c) masked plate; and (d) diagnosis plate.


 
R
L
 G  = TLM S−RGB  M  ,
B
S

(5)


 
L
R
M  ,
 G  = T −1
RGB−LM S
S
B

(6)



 
 
0.0809 −0.1305 0.1167
L
R
 G  =  −0.0102 0.0540 −0.1136   M  . (7)
B
−0.0004 −0.0041 0.6935
S


Fig. 2. Example of XML code describing the data structure of the
DaltonTest tool

dle, and high frequencies [32]. Conversion of the RGB
components into components of the LMS model is the
first step of the algorithm. The conversion is achieved
by the application of a matrix, and, therefore, a linear
conversion [8]:



 
L
R
 M  = TRGB−LM S  G  ,
S
B

(1)



 
 
L
17.8824 43.5161 4.1194
R
 M  =  3.4557 27.1554 3.8671   G  . (2)
S
0.0300 0.1843 1.4671
B
The second step is reducing the normal domain of
colors to the domain of a color blind individual. The
linear transformation for protanopia is expressed as

In order to modify these dichromatism models, we
generate other matrices by including several fuzzy parameters, in order to get a mathematical model useful to deal with anomalous trichromatism. Therefore,
our fuzzy-based model considers not only the extreme
cases of protanopia and deuteranopia, but also hybrid cases where each case of color reception, including color “normality”, is represented by a given degree of membership to fuzzy sets designed to model
these cases [15,35,6,33,11,5,34,20,31,23,30,18,24,21,
1,28,27,4,26,16,29,12,2,3,13,22,17,25,7,7,14].
The fuzzy parameter were designed to generate a
linear dichromatism model to get LMS models able
to vary from nondichromatic matrices represented by
identity matrices to the absolute dichromatic simulation matrices given by expressions 3 and 4. Consequently, for the fuzzy degree of protanomaly αp , if
αp = 0 we have the identity matrix, whilst in case we
have αp = 1, we get the transform matrix described
by expression 3. The analysis is similar for the deuteranopia simulation matrix. Our proposal deals with the

J. Lee and W. P. dos Santos / An Adaptive Fuzzy-Based System to Simulate, Quantify and Compensate Color Blindness

(a)

(a)

(a)

Fig. 3. Result of dichromate simulation. (a) Original image, normal
vision. (b) Image simulating protan type color blindness. (c) Image
simulating type deuteran color blindness.

generation of intermediate simulation matrices able to
model nonabsolute cases of dichromatism. Therefore,
considering the components already converted into the
LMS model, the linear transformation for protanomaly
is proposed as following:


 
 
Lp
(1 − αp ) 2.0234αp −2.5258αp
L
 Mp  = 
 M  ,
0
1
0
Sp
S
0
0
1
(8)
where αp is equal to the degree of protan; and for
deuteranomaly:

5

individuals. Figure 3 shows some results from the simulation tool. Notice the presence of green color, since
the absence of cones that detect green, in this case the
type deuteran color blindness, does not prevent the perception of this spectral range, as there is a compensation due to the presence of other cones, as evidenced
in the mathematical model of the anomaly deuteran.
However, there is no perception of the real green [32].
Herein this work we also implemented a software
tool called DaltonCor, intended to improve the visual
quality of the color blind individuals, whereas its deficiency may be presented in different degrees. Two
methods (A and B) were developed for the DaltonCor tool. Method A is based on the generation of a
compensated image generated by the linear combination of the original image and the corrected versions for protan and deuteran cases. The weights are
based on fuzzy rules. Method B is based on a linear
transform matrix based on the fuzzy degrees of protan
and deuteran color blindness, without using additional
fuzzy rules. Both methods try to compensate for the
lack of sensitivity to a particular color with new values
for the normal color perception.
2.1. Method A











Ld
1
0
0
L
 Md  =  0.4942αd (1 − αd ) 1.2483αd   M  ,
Sd
0
0
1
S
(9)
where αd is equal to the degree of deuteran.
Based on both linear transformations, we propose a
hybrid model of protanomaly and deuteranomaly:


 
 
Lh
(1 − αp ) 2.0234αp −2.5258αp
L
 Mh  =  0.4942αd (1 − αd ) 1.2483αd   M  .
Sh
0
0
1
S
(10)
The degrees of protanomaly αp and deuteranomaly
αd are parameters obtained from the testing tool DaltonTest. Therefore, it is possible to simulate real cases
of color blindness.
The DaltonSim has a very simple interface, and the
result from the simulation is the visualization of the
original images alongside the simulated images.
The simulation has shown to be essential to understand the problems of accessibility of the color blind

The Method A was divided into three modules: Filter, Fuzzy and Control. This last one, in addition to link
the other two modules, communicates with the graphical interface and feeds it with information. The solution developed in the filter module is based on color
perception in cases of absolute color blindness. First,
let us focus on the protan color blindness:
Consider f = (fr , fg , fb ) the original image followed by its three bands of color r, g and b. Its correction is performed by following two steps. The first one
(equation 11) is to assign new values to the bands not
affected by color blindness. To protans, these bands of
color are fg and fb , as following:
f 0 = (fr , fg0 , fb0 ),



fg0 = 12 (fr + fg )
.
fb0 = 12 (fr + fb )

(11)

In order to increase the visual quality of the image, the second step (equation 12) is intended to improve the contrast. The chosen technique was the standard histogram equalization presented by Gonzalez
and Woods (2002) [10]. Considering γ the contrast optimizer (histogram equalizer), we have the following

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J. Lee and W. P. dos Santos / An Adaptive Fuzzy-Based System to Simulate, Quantify and Compensate Color Blindness

expression:
fp = (fr , fg00 , fb00 ),



fg00 = γ(fg0 )
.
fb00 = γ(fb0 )

(12)

The correction equations for deuterans (13 and 14)
are similar to those presented above:
0

f =

(fr0 , fg , fb0 ),



fr0 = 12 (fr + fg )
.
fb0 = 12 (fg + fb )

(13)

xn =

x0p
.
x0p + x0d + x0n

(20)

The corrected image f ∗ is a weighted average of the
corrected images for protan and deuteran type color
blindness, and the original image, as represented in the
following expression:
f ∗ = xp fp + xd fd + xn f.

fd = (fr00 , fg , fb00 ),



fr00 = γ(fr0 )
.
fb00 = γ(fb0 )

(14)

The Filter Module returns two corrected images,
fp and fd . The Fuzzy Module is responsible for the
filter customization and, based on the outcome from
the test tool, assigns a fuzzy character of this correction. From an experimental approach, the following
fuzzy rules were proposed, based on the output data we
collect from DaltonTest color blindness software test
[20,34,9,19]:
x0p = β ∧ αp ,

(15)

where x0p is equal to the degree of color blindness β
with conjunction the degree of protan αp .
x0d = β ∧ αd ,

(16)

where x0d is equal to the degree of color blindness β
with conjunction the degree of deuteran αd .
x0n = αn ∧ (¬β),

(17)

where x0n is equal to the degree of normality αn and in
conjunction with not color blindness.
From the measurements obtained from the rules
above, it is possible to make a fuzzification process on
these magnitudes to obtain the weights expressed by
the following equations:
xp =

x0p
,
x0p + x0d + x0n

x0p
xd = 0
,
xp + x0d + x0n

(18)

(19)

(21)

2.2. Method B
The Method B is based on linear transformations designed to adaptatively correct the effects of chromatic
disturbance. Differently from method A, this method
is divided into two modules: Correction and Control.
It is important to notice that, in this method, there is no
previous correction for absolute color blindness, as it
occurs in the module Filter of Method A. The module
Control furnishes the graphic interface important information to be described in the following paragraphs.
The solution implemented in module Correction is
inspired by the perception of colors in absolute color
blindness. However, instead of using the absolute degrees of color blindness, we take into account the fuzzy
degrees of protanomaly and deuteranomaly. Therefore,
this method is an adaptative correction method.
Similarly to the method A, the proposal of correction of method B also tries to compensate the lack of
sensitivity for determined colors (in fact, the deficiency
to receive determined spectral bands), increasing their
occurrence in the digital image and modifying the colors acquired with normal perception.
Let f = (fr , fg , fb ) be the original image with its
three color bands: r, g and b. This image is compensated by the use of a transform matrix to correct the
pixel values by changing them using linear combinations. The expressions 22 and 23 represent the corrections for the absolute cases of protan and deuteran
using fuzzy features. These empirical expressions are
based on the following idea: compensating the lack of
color band in color blind vision by equally distributing
the information of this band to the other two bands. For
protans, the corrected image is proposed as following:

fp =

(fr , fg0 , fb0 ),



fg0 =
fb0 =

αp
2 fr
αp
2 fr

2−α

+ 2 p fg
; (22)
2−α
+ 2 p fb

J. Lee and W. P. dos Santos / An Adaptive Fuzzy-Based System to Simulate, Quantify and Compensate Color Blindness

for deuterans, the customization is performed in a similar manner, as can be seen in expression 23:
fd =

(fr0 , fg , fb0 ),



fr0 =
fb0 =

αd
2 fg
αd
2 fg

+
+

2−αd
2 fr
2−αd
2 fb

. (23)

In order to deal with hybrid cases of color blindness
where the individual has anomalous trichromatism for
the red and green spectral bands at the same time, the
new values of bands fr , fg and fb are calculated as
following:
f ∗ = (fr0 , fg0 , fb0 ),

(24)

fr0 =

2 − αd
αd
fg +
fr
2
2

(25)

fg0 =

αp
2 − αp
fr +
fg
2
2

(26)

fb0 =

αp
αd
4 − αp − αd
fr +
fg +
fb
4
4
4

(27)

Based on the new values of the three spectral bands,
r, g and b, it was possible to generate an unique transform matrix to deal with the adaptative correction of
anomalous trichromatism cases, as seen in expression
28:
 0 
 
1 − α2d α2d
0
R
R
 G0  =  α2p 1 − α2p
  G  . (28)
0
αp
α +α
αd
B0
B
1 − p4 d
4
4
The result of the application of the transform matrix
is an image modified based on the given degrees of
protan and deuteran.

3. Results
3.1. Simulation Results
The fuzzy-based simulation tool presented in this
paper receives as inputs the results obtained by the
customized Ishihara testing tool, DaltonTest. These
parameters allow our simulation tool to generate results in accordance to what is expected from real color

7

blindness cases, which is essential to understand how
people with different degrees of color blindness perceive color variation.
Notice in figure 4 a simulation for different degrees
of the color vision anomalies and the gradual loss of
ability to distinguish different colors.
It is important to notice the similarity of images figure 4(c) is a protanomaly in 50% of cones and figure 4(j) is a hybrid case: 25% protanomaly and 25%
deuteranomaly, which together reduce the compensation due to the presence of other cones, as can be perceived in the new mathematical model we presented
herein this work.
The simulation results with different levels of abnormality proved to be very satisfactory, with exception of hybrid cases with more than 50% of protan and
deuteran.
In order to analyze the results of the correction tool
proposed, 10 images in bitmap 32 bits format were
used. The use of the simulation tool was essential to
understand how the corrections would be perceived
by people with color blindness. We also analyzed all
the correction variations in RGB, LMS, and with and
without histogram equalization. In figure 5, it can be
seen the correction result for an individual 100% color
blind, 0% protan, 100% deuteran and 0% normal.
Notice that in figure 5(b) the red tomatoes and the
green peppers appear nearly equal. However, in figure
5(d) the shades of tomatoes and peppers are very different. Thus it is easy to see the gain of visual information after correcting the image.
3.2. Results for Color Blind People
Although the analysis done by the simulator display
is satisfactory, a group of four people with color blindness volunteered to test the tool. The volunteers were
evaluated with the customized Ishihara test using the
test tool. The test set was composed by a set of 32 bits
bitmap images with size of 300×300 distributed as following: 10 original images without correction and, for
each of these images, 4 corrected images using Method
A with and without histogram equalization, taking into
account RGB and LMS images, composing a total of
44 images. Through the obtained results, the four combinations of correction were analyzed. The results are
presented in Table 1. Althoug these results were not
conclusive due to the small number of volunteers, it
was important as a first feedback from color blind people.

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J. Lee and W. P. dos Santos / An Adaptive Fuzzy-Based System to Simulate, Quantify and Compensate Color Blindness

ORIGINAL

PROTAN

(b)

(a)
DEUTERAN

(f)

(a)

(b)

(c)

(d)

(e)

(f)

(j)

(g)

(k)

(d)

(h)

(l)

(i)

SIMULATED

HYBRID

(c)

(e)

ORIGINALS

(m)

Fig. 4. Results of dichromate simulation: (a) original image, normal
vision; (b), (c), (d) and (e): protan type color blindness, for degrees
of 25%, 50%, 75%, and 100%, respectively; (f), (g), (h) and (i):
deuteran type color blindness, for degrees of 25%, 50%, 75%, and
100%, respectively; (j), (k), (l) and (m): hybrid (protan and deuteran)
type color blindness, for equal degrees of protan and deuteran of
25%, 50%, 75%, and 100%, respectively.

Each corrected image was subjectively evaluated
and judged as much better, better, indifferent, worse
or much worse. Distortion and greater ability to distinguish elements in relation to the original image were
considered as evaluation criteria.
It was observed that, by the correction in RGB domain with histogram equalization, the images became
more understandable, because elements that were perceived with the same color (due to color blindness) re-

Fig. 5. Results from image correction using the methods A and B
in RGB with histogram equalization: (a) original image; (b) simulation for the absolute protan type; (c) corrected image with Method
A; (d) corrected image with Method A simulated for protan color
blindness; (e) corrected image with Method B; (f) corrected image
with Method B simulated for protan color blindness.

ceived different colors. Some images after the correction showed less saturation in their colors and some of
these cases were considered worse. With the correction in RGB without histogram equalization there was
not a big gain in the visual improvement of images, although this type of correction has been found to cause
less negative impact on the distortion of the original
colors.
The correction in LMS, in general, changed overmuch the original colors of the images, although it performed efficiently on images that purposely have hidden elements, like the images used in pseudoisochromatic Ishihara plates.

J. Lee and W. P. dos Santos / An Adaptive Fuzzy-Based System to Simulate, Quantify and Compensate Color Blindness
With equalization

RGB

LMS

9

Without equalization

Much better

20%

Much better

0%

Better
Indifferent
Worse
Much worse

46%
20%
14%
0%

Better
Indifferent
Worse
Much worse

43%
43%
14%
0%

Much better
Better
Indifferent
Worse
Much worse

20%
17%
20%
7%
36%
Table 1

Much better
Better
Indifferent
Worse
Much worse

7%
33%
3%
7%
50%

Preliminar evaluation by a set of 4 volunteers of 40 images corrected
using Method A based on RGB and LMS, with and without histogram equalization

3.3. Results for People without Color Blindness
Considering that: 1) the amount of people with color
blindness represents a considerably lower percentage
in the world’s population [32,8], 2) the occurrence of
color blindness is not related to factors that might allow a clear separation between color blind individuals
and the rest of the population, it is quite difficult to assemble a good set of test tools to validate the correction of color blindness proposed in this paper. Thus,
we build a test based on the web to collect information of a subjective nature that could be useful to distinguish the methods proposed in this paper according
to a qualitative evaluation.
In order to build the platform test site we used 10 basic images. For each of these 10 images we generated
images for protan and deuteran color blindness using
the simulation method proposed in this work, with degrees of color blindness of 0%, 25%, 50%, 75% and
100%. We also used images with 0% of blindness as
a way of maintaining quality control of results. Thus,
we generated a total amount of 450 images.
The web survey consists of 90 questions with five
randomly arranged choices. Each issue consists in presenting an image, converted to the vision of a colorblind using four simulation methods proposed, with a
certain degree of colorblindness. For each presented
image there are five options, where four of them are
obtained from the application of the correction methods, while the other image is simply a copy of the presented image. The user must choose the option among
five options that best highlights different elements in
the presented image, i.e. the option that optimizes the
contrast between different elements, even if these ele-

Fig. 6. Percentages of responses versus color blindness correction
methods, considering a set of 40 volunteers without color blindness

ments are not clearly distinguished in the original image.
The web survey was administered to a universe of
40 users without color blindness. The absolute results
are present in figure 6. From the results presented, we
can notice that subjective aesthetic criteria influenced
the results: 20.8% of volunteers chose the option “No
improvements”, when the expected number was 11.1%
(10 of the 90 presented images with 0% of color blindness). Figure 7 shows the results without the option
“No improvements”.
The results for protan and deuteran colorblindness
distributed according to the degree of color blindness
are shown in figures 8 and 10, respectively.
Figure 8 shows that Method B with histogram equalization received the greatest number of positive responses from volunteers. Method B without histogram
equalization also had a reasonable amount of positive
responses for all degrees of color blindness, yet its
performance was inferior to that obtained by Method
B with histogram equalization. Method A, with and
without histogram equalization, is shown below the
Method B, for the degrees of color blindness of 25%,
50% and 75%. However, for protans with 100% of
color blindness, Method A with histogram equalization can achieve a similar performance to the performance of Method B without histogram equalization.
For protans with 100% color blindness, Method A
without histogram equalization reaches almost twice

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J. Lee and W. P. dos Santos / An Adaptive Fuzzy-Based System to Simulate, Quantify and Compensate Color Blindness

Fig. 7. Percentages of positive responses (responses different from
“no improvements”) versus color blind correction methods, considering a set of 40 volunteers without color blindness

Fig. 8. Percentages of positive responses (responses different from
“no improvements”) versus the degree of protan color blindness,
considering a set of 40 volunteers without color blindness

the performance obtained for 25% and 50% protans.
However, despite the improvement acquired for protan
cases with 100% of color blindness, Method A without
histogram equalization is still much lower than other
methods.
Figure 9 shows the overall results for protan colorblindness. The results show that, for protan colorblindness, Method B with histogram equalization had the
best performance: 47.3% of positive responses, compared with Method B without histogram equalization,

Fig. 9. Percentages of positive responses (responses different from
“no improvements”) versus color blind correction methods, considering a set of 40 volunteers without color blindness and protan simulated images

with 31.4% of positive responses. Method A was very
inferior to Method B, with 14.1% and 7.2% of positive responses, with and without histogram equalization, respectively. The results also show that the histogram equalization is also an important factor in improved distinction of different elements in the images.
Figure 10 shows the results for deuteran color blindness, considering all degrees of color blindness. Here
again the results obtained with Method B with histogram equalization were superior to those obtained
by other methods. However, the distance to Method
B without histogram equalization increased. The performance of Method A, with and without histogram
equalization, improved slightly to 25%, 50% and 75%
of blindness in relation to protan cases, although it remains well below the Method B with histogram equalization, but the behavior for 100% of color blindness
was similar. Unlike the protan cases, Method B without histogram equalization had the worst performance
among the four methods for 75% of blindness.
Figure 11 illustrates the general results for the cases
of deuteran color blindness. Comparing the results for
deuterans with the results for protans, it is clear to
notice that the performance of Method B with histogram equalization remained virtually the same, at approximately 47%. However, Method A with and without histogram equalization had much better results for
deuterans than for protans. Already Method B with-

J. Lee and W. P. dos Santos / An Adaptive Fuzzy-Based System to Simulate, Quantify and Compensate Color Blindness

Fig. 10. Percentages of positive responses (responses different from
“no improvements”) versus the degree of deuteran color blindness,
considering a set of 40 volunteers without color blindness

Fig. 11. Percentages of positive responses (responses different from
“no improvements”) versus color blind correction methods, considering a set of 40 volunteers without color blindness and deuteran
simulated images

out histogram equalization proved to be far worse for
deuterans than for protans. Therefore it is important to
notice that there is a clear improvement of results due
to the addition of histogram equalization.

4. Discussion and Conclusion
Despite the rapid technological developments and
advancements in the area of digital image processing,

11

it is not easy to find tools that simulate milder, intermediate forms of color vision impairment and reduce the effects of chromatic visual disturbances. As
cited before, the extreme forms of color blindness which are characterized by the complete functional absence of one type of cones - are not as common as the
milder forms with partial or shifted sensitivity. However, many studies assume that if a color scheme is
legible for someone with extreme color vision impairment, it will also be easily legible for those with a
minor affliction, and ignore the possibility of adaptive
and customized correction methods.
This work presents an adaptive tool to simulate color
blindness. The fuzzy parameters designed to make the
simulation flexible are obtained from the testing tool
previously presented.
Therefore, this paper proposed the development of a
set of computational tools to improve the accessibility
and visual quality of life for color blind people. However, one of the greatest difficulties encountered in developing this work is the relative lack in the literature
about other mathematical methods for adaptive compensation of color blindness as the proposed.
As mentioned, color blindness affects only a low
percentage of population. The absence of color blindness cases in a statistically significant amount can be
an obstacle to the development of adaptive tools for
correction of the anomaly, especially when the focus
is on real cases, rather than in extreme cases (dichromatism). Thus good color blindness simulators are of
great importance on generating of synthetic cases of
color vision disturbance in a statistically significant
amount, so that they can be used in the development of
correction tools. The fuzzy-based simulation proved to
be essential to understand the accessibility problems of
people with red and green color disorders in different
degrees.
Tests were conducted with a group of people with
color blindness. This experience was important to evaluate the results obtained from the correction filters, and
to more accurately gauge the difficulties encountered
by the volunteers. The results were very positive, confirming that the proposed correction is able to extract a
higher amount of information from an image.
Moreover, all the tools proved to be intuitive and
easy to use, providing a better user experience, and
consequently their habitual use.
Extensive tests were also conducted with people
without color blindness using color blindness simulators and a web tool based on a survey. These tests were
performed by a group of 40 volunteers. Results indi-

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J. Lee and W. P. dos Santos / An Adaptive Fuzzy-Based System to Simulate, Quantify and Compensate Color Blindness

cated that the Method B with histogram equalization
got better results for both protan and deuteran color
blindness.

[18]

[19]

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