The objective of this research was to
investigate the current state of human
color vision modeling and to also address its problems and possibilities.
Some existing color vision models were
examined from a computational point
of view, and the behavior of the models was compared with a human observer in experiments that evaluate the
properties of color vision. Also, some
dissertations | No 20 | Tuija Jetsu | Modeling color vision
Tuija Jetsu
Modeling color vision
Tuija Jetsu
Modeling color vision
changes in the anatomical properties of
the human vision system, like the cone
ratio on the retina, were taken into account in a part of the experiments. The
results described in this dissertation
strengthen the idea that color vision as
a concept is complicated, and that the
modeling of it well is a demanding task.
Publications of the University of Eastern Finland
Dissertations in Forestry and Natural Sciences
Publications of the University of Eastern Finland
Dissertations in Forestry and Natural Sciences
isbn 978-952-61-0257-3
issn 1798-5668
TUIJA JETSU
Modeling color vision
Publications of the University of Eastern Finland
Dissertations in Forestry and Natural Sciences
No 20
Academic Dissertation
To be presented by permission of the Faculty of Science and Forestry
for public examination in the Louhela Auditorium in Science Park, Joensuu,
on December 7, 2010, at 12 o’clock noon.
School of Computing
Kopijyvä Oy
Joensuu, 2010
Editors: Prof. Pertti Pasanen, PhD Sinikka Parkkinen, Prof. Kai Peiponen
Distribution:
University of Eastern Finland Library / Sales of publications
P.O. Box 107, FI-80101 Joensuu, Finland
tel. +358-50-3058396
http://www.uef.fi/kirjasto
ISBN: 978-952-61-0257-3, ISSN: 1798-5668 (printed)
ISBN: 978-952-61-0258-0, ISSN: 1798-5676 (PDF)
ISSNL: 1798-5668
Author’s address:
University of Eastern Finland
School of Computing
P.O.Box 111
80101 JOENSUU
FINLAND
email: [email protected]
Supervisors:
Professor Jussi Parkkinen, Ph.D.
University of Eastern Finland
School of Computing
P.O.Box 111
80101 Joensuu
FINLAND
email: [email protected]
Professor Timo Jääskeläinen, Ph.D.
University of Eastern Finland
Department of Physics and Mathematics
P.O.Box 111
80101 JOENSUU
FINLAND
email: [email protected]
Reviewers:
Associate Professor Sérgio Nascimento, Ph.D.
University of Minho
Department of Physics
Campus de Gualtar
4710-057 BRAGA
PORTUGAL
email: [email protected]
Professor Olli Nevalainen, Ph.D.
University of Turku
Department of Information Technology
20014 TURUN YLIOPISTO
FINLAND
email: [email protected]
Opponent:
Senior Research Fellow Alessandro Rizzi, Ph.D.
University of Milan
Department of Information Technology
via Bramante, 65
26013 CREMA
ITALY
email: [email protected]
ABSTRACT
The objective of this research was to investigate the current state of
human color vision modeling and to also address its problems and
possibilities. All the following results strengthen the idea that color
vision as a concept is complicated, and that the modeling of it well
is a demanding task.
First, some existing color vision models were examined from
a computational point of view. No model was able to replicate
the performance of human color vision fully in every experiment,
and our experiments showed that there are large differences in the
properties of these models. At least some kind of nonlinearity had
to be implemented in order to be able to compensate for the differences between different brightness levels. The nonlinear models
also performed significantly better in a color classification task. The
errors made by the nonlinear models were similar to the ones human observers also often make, meaning that if the color was not
classified into the correct class, it was usually classified into one of
the neighboring classes.
Another part of our experiments indicated that if the changes in
cone ratio would not be compensated for at all in the later stages
of the human visual system, the resulting color space would be
very different for each individual. A small part of the research
was related to the Retinex model and color constancy. Finally, we
conducted a color naming experiment by focal colors of different
sizes and durations, and measured the reaction time for each stimulus. The results of the color naming experiment showed that the
connections between different colored stimuli and the actual color
sensation can vary a lot depending on the parameters related to the
stimuli.
UDC: 004.942, 159.937.51, 519.876.5, 591.185.6, 612.843.31
Keywords (INSPEC Thesaurus): colour vision; visual perception; colour;
visible spectra; vision defects; eye; modelling; computers; computer vision
Preface
I would like to start by thanking my supervisors, Prof. Jussi Parkkinen and Prof. Timo Jääskeläinen, for pointing me to the appropriate
direction in the course of my studies and providing me the chance
to be a part of Joensuu Color Group. I was given quite a free hand
to find my own way, and I definitely learned a lot during these past
years.
Next I want to thank all the former and current members of
Joensuu Color Group for the cooperation in all scientific and notso-scientific matters. I had the great pleasure of sharing ideas and
a wide range of different moments with you. The same applies also
to students, staff and alumni of the Biological and Physiological Engineering Laboratory at Toyohashi University of Technology, Japan:
thank you for welcoming me to your group for six months and introducing the various aspects of Japanese culture to me. I also want
to thank Prof. Shigeki Nakauchi separately for the invitation to
Japan and all the help during my stay. Kimiyoshi Miyata, Masayuki
Ukishima, Mitsuyoshi Tashiro, Ryouhei Suzuki, Naoko Takekawa
and the Arai family also deserve thanks for sharing their pieces of
the Land of the Rising Sun with me. Arigatou gozaimashita!
I appreciate the valuable comments that the reviewers of this
thesis, Prof. Olli Nevalainen and Prof. Sergio Nascimento, have
kindly provided. Also my peer reviewers, Ville and Ilja, have given
me important feedback, and the language review done by Prof.
Gregory Watson has helped my work remarkably. The financial
support from Tekniikan edistämissäätiö and Finnish Concordia Fund
for parts of my post-graduate studies is also gratefully acknowledged.
I am most indebted to my family and friends for providing indispensable counterbalance to the world of science during all the
years I spent with my studies. It has been good to know that I
could turn to you whenever necessary, no matter how far or near
from each other we have been.
And last, but definitely not least, I am grateful to my dearest Ilja
for being always there for me. Thank you for your endless love and
support.
Joensuu November 4, 2010
Tuija Jetsu
"If we knew what it was we were doing,
it would not be called research, would it?"
– Albert Einstein
LIST OF PUBLICATIONS
This dissertation consists of an overview part and the following
selection of the author’s publications:
P1 Jetsu, T., Heikkinen, V., Pogosova, A., Jaaskelainen, T., and
Parkkinen, J., "Comparison of color vision models based on
spectral color representation", Color Research and Application,
Vol. 34, Number 5, pp. 341-350 (2009).
P2 Jetsu, T., Heikkinen, V., Pogosova, A., Jaaskelainen, T. and
Parkkinen, J., "Cone ratio in color vision models", in the Proceedings of the IEEE 14th International Conference on Image Analysis and Processing Workshops (ICIAP 2007), pp. 179-182, Modena, Italy, September 11-13, 2007.
P3 Pogosova, A., Jetsu, T., Heikkinen, V., Hauta-Kasari, M., Jaaskelainen, T. and Parkkinen, J., "Spectral images and the Retinex
model", in the Proceedings of the 9th International Symposium on
Multispectral Colour Science and Application (MCS07), pp. 80-87,
Taipei, Taiwan, May 30-June 1, 2007.
P4 Jetsu, T., Essiarab, Y., Heikkinen, V., Jaaskelainen, T. and Parkkinen, J., "Color classification using color vision models", to be
published in Color Research and Application. Available online
since November 9, 2010. DOI: 10.1002/col.20632
P5 Jetsu, T., Komine, H., Nakauchi, S., and Parkkinen, J., "The
effect of stimulus color, size and duration in color naming
reaction times", in the Proceedings of the 11th Congress of the
International Colour Association (AIC) 2009 (AIC2009), Sydney,
Australia, September 27-October 2, 2009.
Throughout the overview, these papers will be referred to as [P1][P5].
AUTHOR’S CONTRIBUTION
The contributions of the author of this dissertation for the publications [P1]-[P5] can be summarized as follows.
In publications [P1], [P2] and [P4] the author was responsible
for the implementation or revision of the necessary functions and
execution of the computations (excluding the implementation of
original Bumbaca & Smith and Ingling & Tsou functions and the
original classification algorithm for [P4] , which were done by Yugo
Imazumi, Anahit Pogosova and Yasser Essiarab, respectively) and
analysis of the results. The author of this dissertation was also the
main writer of these three articles.
In publication[P3], the author was co-supervising the M.Sc. candidate working with the topic, had implemented the original function used for color space conversions, proofread the manuscript and
gave the conference presentation.
In publication [P5], the author planned and executed the psychophysical experiments, analyzed the results and was the main
writer of the article.
Contents
1
INTRODUCTION
1.1 Purpose and Organization of this Dissertation . . . .
1
4
2
MECHANISMS BEHIND COLOR VISION
2.1 The Eye . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 The Brain . . . . . . . . . . . . . . . . . . . . . . . . . .
7
11
14
3
COLOR VISION DEFICIENCIES
3.1 Color Vision Tests . . . . . . . . . . . . . . . . . . . . .
3.2 Differences between Individuals . . . . . . . . . . . .
19
22
24
4
MODELING COLOR VISION
4.1 Theories . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Models . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
29
31
5
SUMMARY OF THE RESULTS
39
6
CONCLUSIONS
43
REFERENCES
45
1 Introduction
Colors are a significant part of our everyday life. They play a major
role, for example, in warning signs, marketing, quality control and
medical applications. In applications where important decisions
must be made based on color, it is necessary to be aware of all the
facts that affect color perception. Color sensation is always a sum
of at least three factors: the object under inspection, the light source
under which the object is examined, and the observer him/herself.
Also, the surroundings of the object under consideration may affect
the perceived color dramatically. Even though a lot of applications
based on accurate color measurements and machine vision have
been developed for different purposes (e.g. [1, 22, 26, 50, 55, 60, 61, 67,
76]), in many cases quality judgements are still made by a human
employee. People can be trained to make judgements of uniform
quality at a certain level, but, nonetheless, the color vision of an
individual is always a subjective characteristic. This study aims at
examining some parts of this sophisticated system in more detail,
especially from a computational point of view.
Human color vision is a very complex system: even though
there are differences in the anatomical and physiological properties between individuals [34, 66], most people are able to recognize
and name the colors on a general level in the same way. Those
individuals who make an exception to this common behavior are
often suffering from some form of color vision deficiency. An example that is not directly related to color vision, but illustrates well
the complexity of the visual processing in the brain, is a case of
a patient who completely lacked activity in the visual cortex, but
was still able to successfully navigate along a long corridor without bumping into any obstacles [16]. A similar case has also been
reported with monkeys [39]. There is also a known case of a patient that has been able to consciously see colors being otherwise
virtually blind [95].
Dissertations in Forestry and Natural Sciences No 20
1
Tuija Jetsu: Modeling Color Vision
Human color vision is fundamentally trichromatic [49]. This
means that on the retina, there are cones that are sensitive to three
different wavelength regions. There are, however, a lot of individuals who have some kind of malfunction in one cone type. A common title for all these abnormalities is color vision deficiency (CVD).
Color vision deficient people usually have problems either with
long or middle wavelength cones. Long wavelength cones receive
most of the information from the red end of the visible spectrum,
and cones sensitive to middle wavelengths have their peak sensitivity in the green region. A complete lack or malfunction of either of these cone types leads to a condition that is in colloquial
language often called red-green color blindness. Such dichromatic or
anomalous trichromatic color vision is actually rather common among
most mammals [45]. An individual with this kind of condition has
problems in differentiating between certain hues of red and green.
It is also possible, however very rare, that the short wavelength
cones of an individual are malfunctioning, which causes problems
mainly with the separation of certain blue and yellow hues [4, 49].
The genetics and the evolution of primate color vision has been
researched a lot (e.g. [43–45, 66, 68, 70, 73, 93]). It is known, for example, that Old World primates have normally three types of cone
photopigments and the set of their visual pigments is more or less
uniform. At the same time, New World primates are more often dichromats and there is more variance in the photopigments
[43, 63]. Generally speaking, it seems that trichromatic vision is
almost always superior or at least equal in performance when compared to dichromatic. For example, Osorio and Vorobyev [69] have
found that for identification tasks, the dichromat’s eye is almost
as good as a trichromat’s, but for a trichromat it is easier to detect
fruit against leaves. Also, in [68], the authors discuss differences between di- and trichromatic primates, and they state that "it would
be interesting to find a natural situation where dichromat monkeys
or humans enjoy any advantage over trichromats".
In addition to differences in the number of cone types active on
the retina causing some kind of color deficiency, there can be vari-
2
Dissertations in Forestry and Natural Sciences No 20
Introduction
ation in the anatomical structure of individuals with totally normal
color vision. For example, it has been proven with adaptive optics
imaging that there are remarkable differences in the cone mosaics
between individuals with normal color vision [34, 91]. Also, genetic
variations in the sensitivities of the long and middle wavelength
cones are known to exist [66], and it is actually genetically possible
for human beings to simultaneously have on the retina more than
three different cone pigments types [46, 65, 66]. There seem to be
at least some indications that the fourth photopigment could also
yield to a richer color experience [46].
As discussed above, there are a lot of well-known differences
in color vision between individuals. It is also possible that color
vision abilities of certain individuals change during the course of
time [51]. The effect of different environmental variables on color
vision is shown, for example, in a study with monkeys [81], where
the color matching performance of a group of infant monkeys, that
had been kept after birth in a room illuminated only by randomly
changing monochromatic lights almost for one year, was quite different from that of a control group. Some proof of the plasticity
of the neural mechanism behind the color perception has also been
found in experiments with human adults [64]. The chromatic experience of the test subjects was altered using color filters. During the
experiment, there was a shift in color perception, which persisted
1-2 weeks after the filters were no longer used. A more radical example of the adaptivity of the primate visual system was reported
at the end of year 2009, when it was shown that it is possible to cure
the color blindness of adult primates using gene therapy [59]. The
male squirrel monkeys (saimiri sciureus) used as test subjects had
been color blind since birth. When a virus containing a human Lopsin was injected into the photoreceptor layer of color blind monkeys, M-cones that were exposed to the L-opsin shifted their spectral sensitivity to respond to long wavelength light. The treated
monkeys started to behave in tests in a way that indicated that they
had gained trichromatic vision. According to the researchers, this
improvement in color vision has remained stable for more than 2
Dissertations in Forestry and Natural Sciences No 20
3
Tuija Jetsu: Modeling Color Vision
years.
1.1 PURPOSE AND ORGANIZATION OF THIS DISSERTATION
The aspects presented above raise the following questions. How can
the known anatomical and physiological variations affect existing
color vision models? Is it necessary, or even possible, to model the
individual differences of the visual system? Some viewpoints that
affect our color perception and different ways for modeling color
vision are presented in Figure 1.1.
[P5]
Psychophysical
experiments
[P1]-[P4]
Computational
modeling
MODELING
COLOR VISION
Machine vision
Animals
(excl. humans)
Color vision
deficiencies
Color naming
Color classification
Physical properties
of a color vision
system
Learned color
classes
Aging
Lens coloring
Individual cone
ratios and
sensitivities
Eye
movements
Color
constancy
Cultural
differences
Biological structure
of human color
vision system
[P2]
Visual buffer
Shades
Intensity
Surrounds
Figure 1.1: Different aspects of color vision and color vision modeling. The arrows on the
left-hand side of the graph show the connections of publications [P1] - [P5] to different
topics. A detailed presentation of the biological structure of the human color vision system
is shown in Chapter 2 (Figures 2.4 and 2.5).
The objective of this research was to investigate the current state
of human color vision modeling and to also address its problems
and possibilities. The main objective of this dissertation has been to
examine the properties of color vision in different ways:
• Based on existing models [P1], [P2], [P3], [P4]
4
Dissertations in Forestry and Natural Sciences No 20
Introduction
• Based on the latest research of cone distribution in the human
eye [P2]
• Based on psychophysical experiments [P5]
The major contribution of this dissertation is the examination of
some existing color vision models from a computational point of
view, and comparison of the behavior of the models with a human
observer in experiments that evaluate the properties of color vision.
Also, some changes in the anatomical properties of the human vision system, like the cone ratio on the retina, is taken into account
in a part of the experiments. Based on the findings reported in the
publications [P1] - [P5], conclusions are drawn and prospective research possibilities for understanding the properties of color vision
in even more detail are suggested.
The structure of this dissertation is as follows: After the Introduction in Chapter 1, general principles of color theory and color
vision are presented in Chapter 2. Chapter 3 describes the different
types of color vision deficiencies and introduces tools for diagnosing them. In addition, a more detailed discussion about differences
in color vision between individuals is given. Chapter 4 includes a
general description of modeling color vision and details of a couple of known color vision models. Chapter 5 is a summary of the
publications included in this dissertation, and, finally, Chapter 6
contains a discussion and the conclusions.
Dissertations in Forestry and Natural Sciences No 20
5
Tuija Jetsu: Modeling Color Vision
6
Dissertations in Forestry and Natural Sciences No 20
2 Mechanisms behind Color
Vision
Human beings interpret certain wavelengths of electromagnetic radiation as visible light (Figure 2.1). Light reflecting from an object
and traveling through our visual system causes a color sensation
(Figure 2.2). Also, the light illuminating the object can be interpreted to be of a certain color depending on its spectral power distribution.
Figure 2.1: The electromagnetic spectrum
The most accurate representation for color is the color spectrum
S(λ), which represents the intensity of light as a function of wavelength λ. For example, the spectra of natural objects are continuos
functions over a defined wavelength range, but in practical applications the spectrum is presented as a set of discrete values, as in
Equation 2.1.
S(λ) = [S(λ1 ) S(λ2 ) . . . S(λn )]
(2.1)
A spectrum that only contains information on how an object
Dissertations in Forestry and Natural Sciences No 20
7
Tuija Jetsu: Modeling Color Vision
interacts with light is called a reflectance spectrum in the case of
opaque objects and a transmittance spectrum in the case of transparent objects [92]. When the spectral power distribution L(λ) of
a light source and the reflectance or transmittance characteristics of
an object are known, the interaction between the light and the material can be calculated as an element-wise product of two vectors
using Equation 2.2.
Sout (λ) = L(λ) · Sre f l/trans (λ)
(2.2)
Examples of these spectra in the case of an opaque object are
shown in Figure 2.2. In the color vision context, the result of the
aforementioned interaction reaches the human eye and, after being
processed in the color vision system, causes color sensation.
Figure 2.2: Factors affecting color sensation
Even though the n-dimensional color spectrum is the most accurate representation for color, very often in practical applications
the color is represented in a lower-dimensional color space. This reduction in the dimensionality of the color space sometimes causes
a problem, in that multiple colors from the original color space are
mapped onto a single color in the target space. This happens, for
example, if the color spectra of two objects are fundamentally different, but when viewed by a particular observer under a certain
8
Dissertations in Forestry and Natural Sciences No 20
Mechanisms behind Color Vision
illumination the colors look the same. This phenomenon is called
metamerism [92]. Digital devices have their own 3-dimensional color
spaces in which the color is represented as a combination of three
primary colors. Most commonly in use are different RGB color
spaces where each color is expressed as proportions of red, green
and blue primaries. Also, the human color vision is based on information received through receptors sensitive to three different wavelength areas. The mathematical model for calculating the responses
for a detected signal in a certain color space is:
ci =
Z
λ
Sout (λ)si (λ)dλ,
(2.3)
where i ∈ [1, n], n indicating the dimensionality of the target color space, Sout (λ) is the light reflecting from or transmitted
through an object under observation, si (λ) is the i th sensitivity function of the observer, and ci is the value of the i th coordinate in the
target color space. For example, in the case of an RGB camera
n = 3, the sensitivity functions of the camera s1 (λ), s2 (λ), s3 (λ) are
defined by the manufacturer and the responses c1 , c2 , c3 are commonly known as color coordinates R, G, B.
An example of the dimensionality reduction described above in
the case of a human observer is shown in Figure 2.3, where the
light reflecting from an object is processed through the cones in the
eye. In the case of the human observer, the sensitivity functions
si (λ) are usually denoted as l (λ), m(λ), s(λ), and the responses ci
as L, M, S. The sensitivity functions and the responses are related
to the three types of cone cells in the human eye that are sensitive to
long, middle and short wavelengths of the visible light. The event
in Figure 2.3 is only the very first phase in the complicated process
that finally leads to color perception. Kaiser and Boynton in their
book "Human Color Vision" [49] have very thoroughly explained
these facts and also other important properties of color vision that
will be briefly mentioned in this chapter. A good reference for this
topic is also Goldstein’s Sensation and Perception [27].
Dissertations in Forestry and Natural Sciences No 20
9
Tuija Jetsu: Modeling Color Vision
l(λ)
m(λ)
s(λ)
400
450
500
550
Wavelength [nm]
600
650
400
700
(a) Light reflecting from an object (see
also Figure 2.1)
S
450
500
550
Wavelength (nm)
600
650
700
(b) Relative cone sensitivities of an observer
M
L
(c) Responses of cones (b) to stimulus
(a)
Figure 2.3: The first stage of human color vision
10
Dissertations in Forestry and Natural Sciences No 20
Mechanisms behind Color Vision
2.1
THE EYE
When light enters the eye, it first travels through its optical part ending up at the retina at the back of the eye. The general structure of a
human eye is illustrated in Figure 2.4 [38]. The retina is a very complex organ and a part of the central nervous system [27, 49]. On the
retina, there are two types of light-sensitive cells: rods and cones.
Rods are active in low illumination conditions, whereas cones function when more light is available. Cones are mainly responsible
for color vision. There are three types of cone cells in the human
retina, which are sensitive to short, middle and long wavelengths of
the visible spectrum. There are also a number of other types of cells
in the retina that further transfer the signals from photoreceptors to
the optic nerve and lateral geniculate nucleus (LGN). The different
layers in the retina are shown in Figure 2.5 [37].
Figure 2.4: A schematic diagram of the human eye [38]
The distribution of photoreceptor cells varies in different retinal locations as shown in Figure 2.6 [27, 47, 49, 71]. For example,
the central foveal part of the retina, which is mainly responsible for
visual fixation, is completely lacking rods. There are also differ-
Dissertations in Forestry and Natural Sciences No 20
11
Tuija Jetsu: Modeling Color Vision
Figure 2.5: A schematic diagram of the retina [37]
12
Dissertations in Forestry and Natural Sciences No 20
Mechanisms behind Color Vision
180
CONES
160
RODS
140
120
100
OPTIC DISC
RECEPTOR DENSITY (mm-2 x 103)
ences between the cones found in the fovea and the other parts of
the retina: foveal cones are thinner and more closely packed than
anywhere else. The retina is less than half as thick in the fovea as
in the remainder of the eye, but even so the foveal cones are longer
than cones in the other parts of the retina. Further away from the
central fovea, the cones become fatter and rods start to appear. Outside the fovea, the cones are a lot fatter than the rods, which means
that they also occupy more space. At the margin of so-called foveal
pit there are already many more rods than cones per unit area (see
Figure 2.6).
80
60
40
20
0
70
60
TEMPORAL
50
40
30
20
10
0
10
20
30
40
FOVEA
50
60
70
80
90
NASAL
ECCENTRICITY (degrees)
Figure 2.6: The distribution of rods and cones on a human retina (image based on [71])
Photoreceptor cells are connected in the outer plexiform level of
the retina to bipolar and horizontal cells. The bodies of the bipolar
and horizontal cells, as well as amacrine cells, lie in a region of the
retina called the inner nuclear layer. Bipolar and horizontal cells further transmit the signal to interplexiform cells, which are also located
in the inner nuclear layer. The cells in the inner nuclear layer are
connected to ganglion cells in the inner plexiform layer. From ganglion cells nerve fibers conduct the signal to the optic nerve [49, 96].
The retina contains over one hundred million photoreceptor cells,
but there are only one million ganglion cells that send information
to the brain [96]. This is a clear sign of the fact that the visual signal
Dissertations in Forestry and Natural Sciences No 20
13
Tuija Jetsu: Modeling Color Vision
is already processed at least on some level at the retina. An abbreviated description of the connections relevant for color vision at the
retina according to [49] is given in Summary 1.
1. Light is captured by cones
2. Any given cone is in contact with 2-4 horizontal cells
- Horizontal cells tie groups of receptors together
3. Cones are also connected to bipolar cells
- Midget bipolars are chromatically selective
- Diffuse bipolars carry luminosity signals
- Blue cone bipolars synapse with
short wavelength sensitive receptors
4. Bipolar cells synapse with amacrine cells
- Amacrine cells send processes horizontally
in a layer between bipolar and ganglion cells
- The relation of amacrine cells to
color vision is not clear
5. Interplexiform cells send signals from
the inner to the outer plexiform system
- May take part in some sort of ’feedback’ system
6. Ganglion cells connect the retina to the optic nerve
- Two types of ganglion cells: M-cells and P-cells
Summary 1: Signal processing on the retina
2.2 THE BRAIN
After leaving the retinal ganglion cells, the visual signals continue
their way to the brain through optic nerve fibers [27, 49]. The path-
14
Dissertations in Forestry and Natural Sciences No 20
Mechanisms behind Color Vision
way in the brain is shown in Figure 2.7, and Summary 2 gives a
concise description of the different connections. About half of the
optic nerve fibers from each eye cross the midline of the head at
the optic chiasm. After the chiasm, about 80 percent of the optic
nerve connects to the lateral geniculate nucleus (LGN) of the thalamus. There is one lateral geniculate nucleus on each side of the
brain, and each LGN receives input from both eyes. In addition,
the LGN also receives signals from the brain stem and visual cortex. It is not totally clear yet what kinds of roles these other signals
play, but this complex construction shows that various things can
influence the information sent to the LGN. It has been suggested
that the major function of the LGN would not be to modify the response of neurons, but to regulate neural information coming from
the retina to the visual cortex. This regularization can be seen when
we examine the signals arriving at and leaving the LGN: for every
10 nerve impulses that reach the LGN from the retina, only about 4
leave the LGN for the cortex [7, 27].
The LGN consists of six layers that can be divided into two
different parts: the top four layers are called parvocellular pathways and the bottom two layers magnocellular pathways. Distinction between magno- and parvocellular pahways already occurs
at the ganglion cell level, and even though the precise distinction
between these pathways is still under investigation, it has been
suggested that the magnocellular pathways deliver the main part
of all luminance-related signals, whereas the parvocellular layers
are responsible for carrying the signals that result in color perception.Research by Schiller et. al. [75] shows that monkeys with
lesions in the parvocellular layer lost their ability to detect color,
which is a clear indication that the parvocellular layer plays a role
in the color vision process.
Most of the neural fibers connect from the LGN to the primary visual cortex (V1). The visual cortex provides a complex and a greatly
distorted map of the retinal image. V1 also seems to be the place
where the information from the two eyes is brought together [49].
There is a lot of research (e.g. [14,21,28]) that shows that on the cor-
Dissertations in Forestry and Natural Sciences No 20
15
Tuija Jetsu: Modeling Color Vision
tex there are a number of types of opponent cells that are excited
by wavelengths at one end of the visible spectrum and inhibited
by wavelengths at the other end of the spectrum. Opponent cells
can also be found in the LGN [17]. A thorough summary of the
color-coding in the different parts of the human color vision system has been done by Conway [13]. Opponent cells behave in a
way that offers a foundation for the opponent-process theory of
color vision [33].
1. Signals from the retinal ganglion cells
continue to the optic nerve
2. After crossing in the optic chiasma,
ganglion cell signals reach the LGN
- M-cells synapse in layers 1 & 2:
magnocellular layers (luminance signals)
- P-cells synapse in layers 3, 4, 5 & 6:
parvocellular layers (chromatic signals)
3. A LGN neuron also receives information from
brain stem and visual cortex
- opponent cells on the LGN
4. LGN transfers information to the visual cortex
- opponent cells on the cortex
Summary 2: Signal processing in the brain
16
Dissertations in Forestry and Natural Sciences No 20
Mechanisms behind Color Vision
Figure 2.7: The visual pathway of the human vision system
Dissertations in Forestry and Natural Sciences No 20
17
Tuija Jetsu: Modeling Color Vision
18
Dissertations in Forestry and Natural Sciences No 20
3 Color Vision Deficiencies
Even though most people have normal trichromatic color vision,
about 8 % of males and less than 1 % of females have some level of
color vision deficiency (CVD) [11]. The most severe version is a total
lack of one or more types of cone cells in the eye. Dichromacy is a
condition where one of three cone cell types is missing completely.
If two (long- and middle-wavelength) or all types of cone cells are
missing, the defect is called monochromacy, and the color vision of
the subject is limited to black, white and shades of gray. Instead of a
total loss of a certain cone type, it is also possible that the sensitivity
of a cone type has been shifted towards the sensitivity of another
type (anomalous trichromacy).
The most common form of color vision deficiency is red-green
color blindness, which results from the absence of either the long or
middle wavelength sensitive visual photopigments [4]. Red-green
blind subjects, as the name implies, have problems with differentiating between red and green hues. This type of color vision deficiency can be divided into two sub-categories: protan and deutan
defects, depending on the type of cones that are not working properly. A protan defect can more accurately be defined as protanopia if
the long-wavelength cones are completely missing, and protanomaly
if there has been a shift in pigment absorption to shorter wavelengths. A deutan defect can similarly be defined as deuteranopia if
the middle-wavelength cones are completely missing, and deuteranomaly if there has been a shift to longer wavelengths. Because the
red-green color vision deficiency is a typical case of X-linked recessive inheritance, this form of color deficiency is more common with
men than with women. See Table 3.1 for more details.
A considerably rarer case of color vision deficiency is blueyellow or tritan color deficiency. Like protan and deutan defects,
tritan defect can also have forms of tritanopia or tritanomaly, describing either a total or partial loss of short-wavelength cone pig-
Dissertations in Forestry and Natural Sciences No 20
19
Tuija Jetsu: Modeling Color Vision
Table 3.1: Prevalence of different types of color deficiency in men and women [4, 12]
Prevalence
in men (%) in women (%)
Type of deficiency
Protanopia
Protanomalous trichromatism
Deuteranopia
Deuteranomalous trichromatism
Tritanopia
Tritanomalous trichromatism
1
1
1
5
0.0001
0.002
0.01
0.03
0.01
0.35
0.0001
0.002
ment. In the case of tritanomaly, the pigment absorption of shortwavelength cones is not shifted as in protanomaly and deuteranomaly but rather the pigment is partly missing [4, 49]. Tritan defects are inherited autosomally, so the probability of inheriting a
tritan defect is equal for men and women. See Table 3.1 for more
details.
Even though protan and deutan color vision deficiencies are
generally referred to as red-green deficiencies, protan and deutan
subjects only have problems in differentiating certain hues of red
and green. The confused colors lie in a CIE 1931 x,y chromaticity
diagram on so-called confusion lines that converge at a single point,
the confusion point (Figure 3.1) [92]. The same principle holds also
for tritan deficiency.
Color vision deficiencies are also common among other primates, especially among New World Monkeys [43,44]. For example,
in the species of squirrel monkeys (Saimiri sciureus), some females
have trichromatic color vision, whereas males are, in general, redgreen color blind. Until now, color vision deficiency has been considered to be an incurable condition. It was however shown by a
group of researchers at the end of 2009 [59] that by using gene ther-
20
Dissertations in Forestry and Natural Sciences No 20
Color Vision Deficiencies
(a) Protan confusion lines
(b) Deutan confusion lines
Figure 3.1: Examples of confusion lines for protan and deutan color vision deficiencies in
a CIE xy chromaticity diagram
Dissertations in Forestry and Natural Sciences No 20
21
Tuija Jetsu: Modeling Color Vision
apy it is possible to cure color blindness in adult monkeys that had
been color blind since birth. The experiments were conducted using
a group of male squirrel monkeys, which were known to be redgreen color blind. In the experiments, a virus carrying the opsin for
the third cone pigment type was added to the dichromatic retinas
of the monkeys, providing a receptoral basis for trichromatic color
vision. The researchers report that the treated monkeys’ improvement in color vision has remained stable for more than 2 years. This
is a remarkable result that also proves the plasticity of the primate
visual system in the sense that the rest of the visual system is able
to adapt to the addition of the third receptor type.
3.1 COLOR VISION TESTS
There are various kinds of tests for recognizing the different types
of color vision defects. A comprehensive description of different
tests can be found, for example, from the book Diagnosis of Defective Colour Vision by Jennifer Birch [4], which has also been used
as a general reference throughout this chapter. Table 3.2 shows the
suitability of color vision tests for different purposes.
Screening tests are used to discover whether or not a person has a
color vision deficiency. Grading tests aim at defining the severity of
the deficiency. Classifying tests are used to identify the type of the
deficiency (protan, deutan, tritan) and diagnostic tests to differentiate between dichromats and anomalous trichromats. There are also
numerous tests that measure occupational suitability rather than
really define the type of the subject’s color vision deficiency. Commonly used tests in clinical practice include arrangement tests, like
Farnsworth-Munsell 100-Hue test and Farnsworth D15 test [23, 24],
pseudoisochromatic plates (American Optical Society (HRR) plates,
Ishihara plates [32, 42]), anomaloscopes, like Nagel anomaloscope
[90] and lantern tests, like Holmes-Wright lanterns [35].
A spectral anomaloscope (Figure 3.2(b)) is a standard reference
test for determining normal or abnormal red-green color vision
and for diagnosing the exact type of red-green color deficiency. In
22
Dissertations in Forestry and Natural Sciences No 20
Color Vision Deficiencies
Table 3.2: Suitability of color vision tests for different tasks according to J. Birch [4]
Numbering used in the table: 0 (not suitable) - 3 (excellent suitability)
Task A: Precise colour matching (Spectral anomaloscopes)
Task B: Identification of figure (Pseudoisochromatic plates)
Task C: Arrangement of hues in sequence (Hue discrimination)
Task D: Colour naming (Lanterns)
Task A
Task B
Task C
Task D
Screening
(identifying)
3
3
0
1
Classifying (protan,
deutan and tritan)
3
2
2
0
Grading (severity)
3
Depends on
plate series
2
1
Diagnosis (dichromat/
anomalous trichromat)
3
0
0
0
Occupational
suitability
0
0
3
3
Visual task
Function
anomaloscope testing, the subject is shown a circle that consists of
two halves, test and target stimuli. The subject is asked to manipulate the red/green mixture ratio and the yellow luminance of
the test stimulus by using two control wheels until the test stimulus matches the target stimulus in both color and brightness. Four
separate matches are made.
Pseudoisochromatic plates (Figure 3.2(c)) are designed in a way
that individual elements of the plates are spots or patches of color
which vary in size and lightness. The design exploits isochromatic
color confusions so that elements in the plates can be seen by people with normal color vision but cannot be seen by color deficient
Dissertations in Forestry and Natural Sciences No 20
23
Tuija Jetsu: Modeling Color Vision
people. It is possible to design plates so that figures either vanish, appear or transform when the results of normal color vision
subjects and color deficient subjects are compared.
Arrangement, i.e. hue discrimination, tests (Figure 3.2(a)) are usually meant to be used for identifying people with significant color
deficiency, who are likely to experience practical difficulties in specific occupations. Arrangement tests consist of color samples that
the subject arranges in a natural order according to hue, lightness
or saturation. Based on the errors made during the process, it is
usually possible to define the type and severity of the color deficiency.
Lantern tests (Figure 3.2(d)) are often used when testing people
interested in careers in maritime, military, aviation and transport
services. In these fields, recognition of colored light signals correctly is considered to be important for safety. Colors are either
shown in pairs or singly in order to demonstrate the different kinds
of light signals and the subject has to name the color(s) present. It
should, though, be kept in mind that color naming is not an ideal
method for identifying color deficiency, because when dealing with
only small number of colors, it is possible to get reasonable results
also with lucky guesses.
3.2 DIFFERENCES BETWEEN INDIVIDUALS
A lot of research has been carried out in an attempt to explain
the differences in color vision between individuals (for example
[2, 3, 19, 34, 36, 46, 51–53, 58, 65, 74, 86, 91], just to mention a few more
recent papers). Because color vision deficiency is linked to the Xchromosome, it is genetically possible for women to be carriers of
the color deficiency gene without being color vision deficient themselves. Findings in the field of molecular genetics have revealed
that instead of three retinal visual pigments, for the female it is actually genetically possible to have four different photopigments on
the retina [19,52,65]. The effect of the fourth photopigment on color
vision has not really been noticed in the conventional color vision
24
Dissertations in Forestry and Natural Sciences No 20
Color Vision Deficiencies
(a) Farnsworth-Munsell 100-Hue test
colors (hue arrangement)
(b) The anomaloscope principle (precise color matching)
(c) A vanishing pseudoisochromatic
plate (figure identification)
(d) Test lantern light combinations (color naming)
Figure 3.2: Outlines of different color vision tests
Dissertations in Forestry and Natural Sciences No 20
25
Tuija Jetsu: Modeling Color Vision
tests, and it is yet partly unknown how it really affects color vision.
Jameson et.al. [46] have found that women with four-photopigment genotypes perceive significantly more chromatic appearances than either male or female trichromat controls. Bimler et.al.
[3] have also examined the differences in color experience between
trichromat male and female subjects and concluded that when differentiating between colors, males placed significantly less weight
on a red-green axis, and more on lightness. However, they soundly
state that the differences in behavior can be caused by a number of
reasons, ranging from retinal performance to patterns of socialization. On the other hand, Hood et.al. [36] report that the chromatic
discrimination along a red-green axis was impaired in the case of
carriers of deutan deficiencies but was normal in the case of carriers of protan deficiencies. Also, results from Bimler et.al. [2] support the fact that the color space of heterozygous women would be
compressed in a red-green dimension. Because of a low number
of subjects, they were unable to provide reasonable separate results
for protan and deutan carriers.
In addition to individual differences in sensor photopigments,
there are also large inter-subject variations in the distribution of
cone cells in the retina. The estimates of the relative numbers of
cone cells sensitive to long (L) wavelengths and middle (M) wavelengths depend a lot on the experimental method in use [53]. A
recently developed technique for measuring cone distribution from
a living eye involves high-resolution adaptive-optics imaging combined with retinal densitometry [34, 74, 91]. Also an adaptive-optics
scanning laser ophthalmoscope has been used to measure the packing of the cones on the retina [9, 10]. Kremers et.al. [53] mention in
their summary article of different methods for defining the cone
distribution that the L/M cone ratio in normal eyes has previously
been found to vary between 10:1 and 1:3. Large individual variation is also shown in the results of Roorda and Williams [74,91] and
Hofer et.al. [34], where the ratio of L to M cones varied from 1.1:1
to 16.5:1 within normal subjects. Hofer et.al. also found a protan
carrier with normal color vision who had an even more extreme
26
Dissertations in Forestry and Natural Sciences No 20
Color Vision Deficiencies
L:M ratio (0.37:1). All subjects in these two experiments had nearly
identical S-cone densities. In the case of color vision deficient subjects, it has also been shown by adaptive-optics imaging [6] that in
some cases there is nothing in the place of the deficient cone type,
and in other cases cones have been replaced by another type.
Instead of being congenital, it is also possible that a color vision
defect is acquired at some point in life. Some medical conditions,
like cortical or retinal lesions, glaucoma, diabetes and intracranial
injury or prolonged use of certain therapeutic drugs, can all cause
changes in color vision [4]. Color vision also changes with age, and
the different effects of aging with respect to color vision have been
summarized in [88]. It is known for example that the wavelength
discrimination abilities often decrease when aging, especially in areas related to long and middle wavelengths causing a tritan-like
color deficiency (e.g. [77]). Also, a general loss of sensitivity in color
vision during aging is a known fact [89]. Werner [88] also mentions
in his summary other possible age-related causes for changes in
color vision, like the decreasing transmittance of the optical media
in the eye, neural changes in the receptors (loss of foveal cones or
photopigment density), and the effects of aging upon the higher
neural pathways. However, it should be kept in mind that the
age-related changes in visual functions may be compensated for, to
some extent, by the plasticity of the adult vision system (e.g. [64]).
Dissertations in Forestry and Natural Sciences No 20
27
Tuija Jetsu: Modeling Color Vision
28
Dissertations in Forestry and Natural Sciences No 20
4 Modeling Color Vision
There are at least two different ways to start building a theory or a
model for human color vision [82]. Research in psychophysics and
physiology is based on assumptions that there are certain relations
between color experiences and physiological states and events. Psychophysics investigates which kinds of responses subjects have to
well-defined physical stimuli, and physiology attempts to define
correlations between these responses and the neural structures of
the human visual system. Computational research, on the other
hand, aims to explain different phenomena of color vision, at a
distinctly different level from those of psychophysics and physiology. For example, the computational approach has been used to
explain the approximate color constancy property of human color
vision [56, 57].
Color related tasks that at first sight seem to be rather straightforward for a human being, can be computationally quite demanding. A human observer can, for example easily recognize and categorize colors under various illuminations [31], and also take, with
ease, into account other factors than just color when the task is to
identify an object. Modeling this kind of behavior is a challenging
task, because, for example, the boundaries between different color
classes are generally not linear [8], and categorization results vary
between observers (e.g. [36, 54]).
4.1
THEORIES
The first theories for color vision were already developed over 200
years ago. The principle of trichromatic color vision was originally
presented in 1802 by Thomas Young [94], and the theory, nowadays
known as Young–Helmholtz trichromatic theory, was further developed by Hermann von Helmholtz [83]. The basic idea behind this
theory was that in the eye there are three types of photoreceptors
Dissertations in Forestry and Natural Sciences No 20
29
Tuija Jetsu: Modeling Color Vision
that are sensitive to different wavelengths of visible light. Signals
from these photoreceptors then produced a color perception when
further processed by the brain.
Even though the trichromatic theory is able to explain a part of
the behavior of human color vision, there are still some aspects that
it cannot cover. For example, why in the case of color deficiency
are there always problems with certain pairs of colors, red-green or
blue-yellow instead of some single colors? And why under normal
conditions [15] is there no such color as reddish green or bluish
yellow? Ewald Hering developed a different opponent process theory [33] to explain this kind of phenomena. He stated that instead
of three, there are actually four different primaries that appear in
pairs as red versus green and blue versus yellow. According to
Hering, the color processing system was based on three main components that would respond in two opposite directions to signal red
vs. green, blue vs. yellow and black vs. white [72]. He believed
that this kind of processing already happens in the receptor level.
Zone theories for color vision bring together the trichromatic and
opponent theories. The properties of both theories are combined
into two separate but sequential zones which describe the process
of the visual stimulus arriving at the retina. The first versions of
this type of combined theory was suggested by M¸ller in 1930 [62]
followed by Judd in 1949 [48]. In 1957, Leo Hurvich and Dorothea
Jameson [40] provided quantative data for color opponency and
proposed a precise testable formulation for a theory based on two
sequential stages of color processing [72].
In addition to trichromatic and zone theories, there are also
other theories with different approaches that try to explain the
properties of color vision. One of the well-known theories is the
Retinex theory introduced by Land in 1964 [56] and the further developed by Land and McCann [57]. The Retinex theory attempts
to model color constancy, one of the fundamental features of human
color vision. Color constancy can be defined as an ability to maintain the color of an object even if the illumination conditions and/or
the surrounding colors of the object change. Even though the hu-
30
Dissertations in Forestry and Natural Sciences No 20
Modeling Color Vision
man visual system is not able to preserve color constancy perfectly,
it still outperforms artificial simulations of the visual system.
The term Retinex is a combination of the words retina and cortex. This illustrates Land’s idea about retinal-cortical systems that
independently process the spatial information from a visible scene.
The systems are assumed to be sensitive to short, middle and long
wavelengths, and each system forms a separate image of the world.
According to Land’s theory, images from different systems are compared with each other. The information from the entire visible scene
is used to eliminate the effect of the unknown and not necessarily
uniform illumination, leading to approximation of color constancy.
4.2
MODELS
Models for color vision rest on the assumptions made in theories for
color vision [92]. Usually the assumptions must be somehow simplified in order to make the models useful for practical applications.
For example, when modeling the sensitivities of the human visual
system, a CIE standard observer (Figure 4.1) or a transformation
of it is used. There are also a number of different cone sensitivity
functions available for modeling the first phase of the human vision
system, for example from Smith & Pokorny (extended later by DeMarco, Pokorny and Smith) [20, 78], Vos & Walraven [84, 85, 87] and
Stockman & Sharpe [79, 80].
One quite common limitation of color vision models is that the
processing of the color information is based on a single pixel, which
does not accurately describe the real color vision system. The parameters of models are usually defined based on the results of different psychophysical experiments, for example replicating the behavior of subjects in discrimination or classification (e.g. [5, 30, 41]).
It is also possible to start the modeling from a physiological point
of view ( [18]) or to use a computational approach ( [25, 56]). As we
examine some of the existing color vision models, we can see that
the basic structure of most models follows the well-known color
vision theories described in the previous section.
Dissertations in Forestry and Natural Sciences No 20
31
Tuija Jetsu: Modeling Color Vision
1.8
x(λ)
y(λ)
z(λ)
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
400
500
600
700
Wavelength (nm)
Figure 4.1: CIE 1931 XYZ color matching functions
Ingling and Tsou [41] have formulated a simple one-opponent
stage vector space model for color vision. The calculation of the
opponent stage responses of the Ingling and Tsou model is done in
two steps. The first step is to multiply the incoming signal by Smith
and Pokorny cone fundamentals in order to get cone responses L,
M and S. After that, opponent stage responses r − g, b − y, and
Vλ (red-green, blue-yellow and achromatic channel, respectively)
are calculated simply by summing up cone responses. Ingling and
Tsou present in their model two different formula sets, one for darkand one for light-adapted conditions (threshold and suprathreshold
forms, see Equations 4.1 and 4.2, respectively).
 


1.2
−1.6
0
r−g
L
 



 b − y  =  0.048 −0.039 −0.042   M 
0.6
0.4
0
Vλ
S


 


r−g
1.2 −1.6 0.4
L

 


 b − y  =  0.24 0.105 −0.7   M 
Vλ
0.6
0.4
0
S
(4.1)
(4.2)
Bumbaca and Smith [5] have developed a computer vision system,
which would take advantage of the color vision discrimination capabilities of the human color vision. Bumbaca and Smith’s model
starts by multiplying the incoming signal by Smith and Pokorny
32
Dissertations in Forestry and Natural Sciences No 20
Modeling Color Vision
cone fundamentals in order to get cone responses L, M, and S. After that, a logarithm of L, M and S signals is taken in order to simulate the nonlinear response of cones L∗ , M ∗ , and S∗ Equations 4.34.5). Finally, nonlinear cone responses are summed in order to form
achromatic and chromatic channels A, C1 , and C2 (achromatic, redgreen and blue-yellow channel, respectively - see Equation 4.6).
L∗ = log L
(4.3)
M ∗ = log M
(4.4)
S
∗
= log S

 


A
a 0 0
α β
0
L∗


 


 C1  =  0 u1 0   1 −1 0   M ∗ 
S∗
C2
0 0 u2
1 0 −1

(4.5)
(4.6)
Parameters a, u1 and u2 of the Bumbaca and Smith model can
be adjusted, for example, so that the just-noticeable difference in
perception in the AC1 C2 space is a sphere of radius 1. The values
for the parameters in this case are a(= 22.6), u1 (= 41.6) and u2 (=
10.5). α(= 0.7186) and β(= 0.2814) are scaling parameters related
to the model’s abilities to estimate V (λ) curve.
De Valois and De Valois [18] have developed a Multi-Stage Color
Model, which is mainly based on the physiological properties of the
human visual system. The model is based on the assumption that
the cones in the eye have a fixed ratio of 10:5:1 for long-, middle-,
and short-wavelength cones, respectively. De Valois and De Valois introduced in their model two possibilities for receptive field
behavior: discrete and indiscriminate versions. In the discrete version, cells with a L or M cone center are assumedly not affected
by S cones in the surroundings. The indiscriminate version sums
together all kinds of cells in the receptive field surroundings. The
modeling begins by multiplying the incoming signal by Smith and
Pokorny cone fundamentals in order to obtain cone responses L,
Dissertations in Forestry and Natural Sciences No 20
33
Tuija Jetsu: Modeling Color Vision
M and S. After that, cone opponency signals LO , MO , and SO are
calculated by using the receptive field theory (Equation 4.7):
• Subtract surrounding signals from the signal at the center of
receptive field.
• Weight the signal in the center by 16 (sum of assumed ratios).
• Total weight for the surrounding signals is also 16, using ratio
10:5:1 for L, M and S signals, respectively.
Finally, the responses from second stage are summed up to obtain
perceptual opponency signals RG, BY, and A i.e. red-green, blueyellow, and achromatic channels (Equation 4.8). The assumed ratio
10:5:1 is modified at this stage to 10:5:2, thus giving more weight to
short-wavelength signals.


LO


 MO  =
SO


RG


 BY  =
A



6
−5 −1
L



(4.7)
 −10 11 −1   M 
−10 −5 15
S




+1 −1 +1
10 0 0
LO




 −1 +1 +1   0 5 0   MO 
+1 +1 +1
0 0 2
SO



90 −115 +25
L



=  −130
(4.8)
95
35   M 
−10
−5
15
S
The stages of the Ingling & Tsou, Bumbaca & Smith and De
Valois & De Valois color vision models are presented in a flow chart
shown in Figure 4.2.
The history of Guth’s ATD model includes various versions and
modifications. In ATD95 [29], Guth has summarized all his previous work, and also extended the model further [30]. His ATD
model has two opponent stages, and the model parameters have
been tuned to meet certain conditions defined by experimental results. Calculations in Guth’s ATD model begin by defining the responses for L, M, and S channels from an input signal by using
34
Dissertations in Forestry and Natural Sciences No 20
Modeling Color Vision
Figure 4.2: The processing steps in Ingling & Tsou, Bumbaca & Smith and De Valois &
De Valois color vision models
Dissertations in Forestry and Natural Sciences No 20
35
Tuija Jetsu: Modeling Color Vision
modified Smith & Pokorny Equations 4.9-4.11. With these functions, the sensitivity in longer wavelengths is slightly enhanced, the
responses are made nonlinear and constant noise is added to each
receptor response. Also, gain control for the receptor responses
is introduced (Equation 4.12). The final responses for different
two opponent A1 T1 D1 and A2 T2 D2 are calculated through a twophase process that includes calculations for initial responses (Equations 4.13 and 4.14) and compression of those (Equation 4.15). A2 ,
T2 and D2 at the final stage of the model describe the achromatic,
red-green and blue-yellow channels, respectively.
L = [0.66(0.2435X + 0.8524Y − 0.0516Z )]0.70 + 0.024 (4.9)
M = [1.0(−0.3954X + 1.1642Y + 0.0837Z )]0.70 + 0.036(4.10)
S = [0.43(0.04Y + 0.06225Z )]0.70 + 0.31
Rg = R
σ
,
σ+R
where R ∈ { L, M, S} and σ = 300.

 


A1i
3.57
2.64
0
Lg

 


0   Mg 
 T1i  =  7.18 −6.21
D1i
Sg
−0.70 0.085 1.00

 


A2i
0.09
0
0
A1i

 


0.43 0.76   T1i 
 T2i  =  0
0
0
1.00
D2i
D1i
Rj =
R ji
,
200 + | R ji |
(4.11)
(4.12)
(4.13)
(4.14)
(4.15)
where R ∈ { A, T, D } and j ∈ {1, 2}. A flow chart of Guth’s ATD
model is shown in Figure 4.3.
36
Dissertations in Forestry and Natural Sciences No 20
Modeling Color Vision
Figure 4.3: Guth’s ATD model
Dissertations in Forestry and Natural Sciences No 20
37
Tuija Jetsu: Modeling Color Vision
38
Dissertations in Forestry and Natural Sciences No 20
5 Summary of the Results
It is known that there are already individual differences in the detection phase of the human color vision system, for example in the
spatial configuration or spectral sensitivities of the cone cells in the
eye [34, 66]. The increasing amount of knowledge about human
color vision properties has raised a need to re-evaluate the existing
color vision model. We have started this work with the following
publications. The relationship of each publication to certain aspects
of color vision is shown in Figure 5.1.
?
Color perception
Color naming
General properties of the
human color vision system
[P1] Comparison of
color vision models
based on spectral
color representation
Color classification
Color naming
Color constancy
[P4] Color classification
using color vision models
[P3] Spectral images
and the Retinex model
[P5] The effect of stimulus
color, size and duration
in color naming
reaction times
[P2] Cone ratio
in color vision models
Figure 5.1: Publications
In publication [P1] (Comparison of Color Vision Models Based on
Spectral Color Representation), we re-evaluate four existing color
vision models and consider questions raised by recent break-throughs
in retinal imaging. Many color vision models are based on an as-
Dissertations in Forestry and Natural Sciences No 20
39
Tuija Jetsu: Modeling Color Vision
sumption of the standard observer, and usually there is no consideration regarding how the individual properties of different observers could be taken into account. For example, the retinal mosaic
or the cone sensitivities can vary a lot between observers, which can
be taken into account by starting the color vision process from the
spectral origin.
The main interest in this article was to examine how different
color vision models behave when compared to corresponding human results. The evaluation presented in this paper gives us more
knowledge about the essential properties of the models. The performance of the models in the Farnsworth-Munsell 100 Hue color vision test, the wavelength discrimination power of each model, and
the color spaces spanned by the models were examined. Guth’s
complex nonlinear model was found to be able to approximate the
color vision properties over a wide range of luminances, but also
the lot simpler Ingling and Tsou’s linear model with a single opponent stage was able to give adequate results. However, no model
was able to replicate the performance of human color vision fully
in every experiment, and our experiments show that there are large
differences in the properties of these models.
In publication [P2] (Cone Ratio in Color Vision Models), we considered how the changes of the cone ratio in the retina would affect
color vision models. The basis of our analysis lies in a Multi-Stage
Color Model by de Valois and de Valois (1993), and we show how
changes in cone ratio affect the different stages of this model. The
behavior of the Multi-Stage Color Model was tested with different
cone ratios: 10:5:1, 18:5:1, 3:6:1, 12:1:1 and 1:1:1. The changes in
cone ratio were implemented as changes in the weighting of the responses at the first stage of the model. For the Farnsworth-Munsell
100 Hue color vision test, ratio 3:6:1 best preserved the organization of the test colors in the opponent color space. Ratios 12:1:1 and
1:1:1 differed most from the others. This article shows that if the
changes in cone ratio would not be compensated for at all in the
later stages of the human visual system, the resulting color space
40
Dissertations in Forestry and Natural Sciences No 20
Summary of the Results
would be very different for each individual.
In publication [P3] (Spectral images and the Retinex model), the
color constancy performance of the Retinex algorithm in different
color spaces was reviewed.The Retinex algorithm has earlier been
applied mainly to grayscale or RGB images, but in this paper we
consider different ways of applying the Retinex model to spectral
images. The use of spectral images as the starting point for the
model enables one, for example, more accurate examination of illumination or observer changes. First, we tested how the Retinex
preserves colors when the spectral power distribution of the ambient light changes. To examine this, the algorithm was applied
to images in four different color spaces: spectral, L channel of the
L*a*b*, LMS, and sRGB. The color constancy between different illuminants was best preserved by using the spectral color space,
and the poorest performance was reached by using the sRGB space.
When examining the behavior of the Retinex model in a case where
the surround of an area of a scene changes, the results in RGB and
spectral spaces are similar (contrary to the first experiment) and
closer to the real world color perception than the results in other
color spaces. In general, it was noted that the output of the Retinex
algorithm for all color spaces requires careful selection of the postprocessing method.
In publication [P4] (Color classification using color vision models),
we look at the color vision topic from a classification point of view.
Instead of detecting and analyzing colors exactly in the same way,
we have all just learned to classify colors in a certain way, which
seems to lead almost always to the same result independent of the
individual differences in the color vision system. The color classification abilities of color vision models, considered also in [P1],
were examined by using a simple subspace classification method on
Munsell Matte Collection color samples. The output of the MultiStage Color Model by De Valois and De Valois was a very poor
starting point for color classification, and with the output of Ingling
and Tsou model the color classes were somewhat overlapping. The
Dissertations in Forestry and Natural Sciences No 20
41
Tuija Jetsu: Modeling Color Vision
two nonlinear models, Bumbaca and Smith’s and Guth’s models,
performed significantly better in this classification task. The errors
made by the two latter models were similar to the ones human observers also often make, meaning that if the color was not classified
into the correct class, it was usually classified into one of the neighboring classes.
In publication [P5] (The effect of stimulus color, size and duration in color naming reaction times), we examine the differences
in color naming reaction times between subjects with normal and
deficient color vision. Color deficient people use, in many cases,
color names in a similar manner as people with normal color vision do. This means that the individual differences at the detection
level of a color vision system are somehow compensated for at the
later levels. In order to examine how different parameters affect the
color naming process, we conducted a color naming experiment by
using modified Berlin and Kay (1969) focal colors of different sizes
and durations, and measured the reaction time for each stimulus.
Some differences were found between normal and color vision
deficient subjects. It was found that among the three examined
parameters, color, size and duration, most differences in reaction
times between color vision deficient subjects and subjects with normal color vision were due to the color of the stimuli. Color vision
deficient (protan and deutan) subjects were clearly slower to react
to red and green colors than to blue and yellow, whereas there were
no remarkable differences in the reaction times for different colors
with subjects having normal color vision. There was one deutan
subject who consistently named red colors as green. In addition,
subjects with normal color vision named very small blue stimuli as
green. Also, the size of the stimuli had an effect on the reaction
times for some subjects, and size and duration both affected the
misclassification rate of stimuli.
42
Dissertations in Forestry and Natural Sciences No 20
6 Conclusions
As almost always when modeling natural phenomena, when modeling color vision the following questions also easily arise. Should
the model be universal or specific just for a certain application? At
what level of accuracy should the model be implemented? Is it even
possible to create a universal model?
Understanding the behavior of human color vision requires knowledge from various fields of science. It makes no sense to claim that
the overview presented here would be all-embracing, because there
are countless possibilities for implementing the properties of human color vision. This dissertation and the related articles have
been written with an intention to contemplate the properties of human color vision from a slightly different point of view.
It was found out in [P1] that none of the examined models were
able to replicate the behavior of human color vision perfectly in
all experiments. At least some kind of nonlinearity had to be implemented in order to be able to compensate for the differences
between different brightness levels. Even though the performance
of the Bumbaca and Smith model was the poorest with the tasks
given in [P1], the model performed well in the color classification
task in [P4]. This is a good example of a model that performs well
in a specific task for which it has been originally designed, in this
case the performance being motivated by a computer vision application. Guth’s ATD model performed well in almost all given tasks,
but from the ATD model it is not as easy to separate all the stages
of the biological color vision system as it is, for example, in the
De Valois and De Valois model. As models are based on different
ideas, they also perform differently in given tasks.
Based on the results of [P2], we can speculate that if the only
thing changing anatomically in the color vision system between individuals was the cone ratio on the retina, the personal color space
of each individual would be quite different from others. Of course
Dissertations in Forestry and Natural Sciences No 20
43
Tuija Jetsu: Modeling Color Vision
it is quite a radical simplification of the process if only the cone ratio in the model is changed, and this does not tell the whole truth
of what actually happens in the human color vision. When people have different cone distribution on the retina, the further neural
connections related to color vision are most probably formulated in
a different way, too. The actual spatial arrangement of the cones
was not considered as a part of this dissertation, but it is also one
interesting research topic related to color vision modeling.
Color constancy is one important property of the human color
vision system, but it is not too easy to model, as was seen in [P3].
Also the connections between different colored stimuli and the actual color sensation can vary a lot depending on the parameters
related to the stimuli, as was shown in the experiments in [P5]. The
largest differences in color-related issues are typically seen between
subjects with normal and deficient color vision, but there are also
individual differences within each group.
All these results strengthen the idea that color vision as a concept is complicated, and that the modeling of it well is a demanding
task. The adaptive behavior of the color vision system is important
from the modeling point of view: in order to be able to replicate
the color vision accurately, a model must also have dynamic properties, like possibilities for spatial and temporal processing. It is
very likely that no model can take into account every single aspect
of color vision, but by combining the best properties of each model
it is possible to find a more universal approach.
44
Dissertations in Forestry and Natural Sciences No 20
Bibliography
[1] C. Balas, V. Papadakis, N. Papadakis, A. Papadakis, E. Vazgiouraki, and G. Themelis. A novel hyper-spectral imaging
apparatus for the non-destructive analysis of objects of artistic
and historic value. Journal of Cultural Heritage, 4(Supplement
1):330–337, 2003.
[2] D. Bimler and J. Kirkland. Colour-space distortion in women
who are heterozygous for colour deficiency. Vision Research,
49:536–543, 2009.
[3] D. L. Bimler, J. Kirkland, and K. A. Jameson. Quantifying variations in personal color spaces: Are there sex differences in
color vision? Color Research & Application, 29(2):128–134, 2004.
[4] J. Birch.
Diagnosis of Defective Colour Vision, 2nd Ed.
Butterworth-Heinemann, Boston, 2001.
[5] F. Bumbaca and K. C. Smith. Design and implementation of a
colour vision model for computer vision applications. Computer Vision, Graphics, and Image Processing, 39(2):226 – 245,
1987.
[6] J. Carroll, M. Neitz, H. Hofer, J. Neitz, and D. R. Williams.
Functional photoreceptor loss revealed with adaptive optics:
An alternate cause of color blindness. PNAS, 101(22):8461–
8466, 2004.
[7] V. Casagrande and T. Norton. Lateral geniculate nucleus: A
review of its physiology and function. In J. Cronly-Dillon and
A. G. Leventha, editors, Vision and visual dysfunction: The neural basis of visual function, volume 4, pages 41–84. Macmillan,
London, 1991.
[8] E. J. Chichilnisky and B. A. Wandell. Trichromatic opponent
color classification. Vision Research, 39:3444–3458, 1999.
Dissertations in Forestry and Natural Sciences No 20
45
Tuija Jetsu: Modeling Color Vision
[9] T. Y. Chui, H. Song, and S. A. Burns. Adaptive-optics imaging
of human cone photoreceptor distribution. J. Opt. Soc. Am. A,
25(12):3021–3029, 2008.
[10] T. Y. P. Chui, H. Song, and S. A. Burns. Individual variations
in human cone photoreceptor packing density: variations with
refractive error. Invest. Ophthalmol. Vis. Sci., 49(10):4679–4687,
2008.
[11] B. Cole. Assessment of inherited colour vision defects in clinical practice. Clinical and Experimental Optometry, 90:157–175.,
2007.
[12] B. L. Cole. The handicap of abnormal colour vision. Clinical
and Experimental Optometry, 87(4-5):258–275, 2004.
[13] B. R. Conway. Color vision, cones, and color-coding in the
cortex. Neuroscientist, 15(3):274–290, 2009.
[14] B. R. Conway and M. S. Livingstone. Spatial and temporal
properties of cone signals in alert macaque primary visual cortex. J. Neurosci., 26(42):10826–10846, 2006.
[15] H. D. Crane and T. P. Piantanida. On seeing reddish green and
yellowish blue. Science, 221:1078–1080, 1983.
[16] B. de Gelder, M. Tamietto, G. van Boxtel, R. Goebel, A. Sahraie,
J. van den Stock, B. M. Stienen, L. Weiskrantz, and A. Pegna.
Intact navigation skills after bilateral loss of striate cortex. Current Biology, 18(24):R1128–R1129, 2008.
[17] R. L. De Valois. Color vision mechanisms in the monkey. The
Journal of General Physiology, 43(6):115–128, 1960.
[18] R. L. De Valois and K. K. De Valois. A multi-stage color model.
Vision Research, 33(8):1053–1065, 1993.
[19] S. S. Deeb and A. G. Motulsky. Molecular genetics of human
color vision. Behavior Genetics, 26:195–207, 1996.
46
Dissertations in Forestry and Natural Sciences No 20
Bibliography
[20] P. DeMarco, J. Pokorny, and V. C. Smith. Full-spectrum
cone sensitivity functions for X-chromosome-linked anomalous trichromats. J. Opt. Soc. Am. A, 9:1465–1476, 1992.
[21] A. M. Derrington, J. Krauskopf, and P. Lennie. Chromatic
mechanisms in lateral geniculate nucleus of macaque. J Physiol., 357:241–265, 1984.
[22] M. Eng, P. Martin, and C. Bhagwandin. The analysis of
metameric blue fibers and their forensic significance. Journal
of Forensic Sciences, 54(4):841–845, 2009.
[23] D. Farnsworth. The Farnsworth-Munsell 100-hue and dichotomous tests for color vision. J. Opt. Soc. Am., 33(10):568–574,
1943.
[24] D. Farnsworth. The Farnsworth dichotomous test for color
blindness panel D-15. Technical report, Psychological Corporation, New York, 1947.
[25] B. Funt, F. Ciurea, and J. McCann. Retinex in Matlab(TM). J.
Electron. Imaging, 13(1):48–57, 2004.
[26] P. Fält, J. Hiltunen, M. Hauta-Kasari, I. Sorri, V. Kalesnykiene,
and H. Uusitalo. Extending diabetic retinopathy imaging from
color to spectra. In Proceedings of the 16th Scandinavian Conference on Image Analysis, pages 149–158, Oslo, Norway, 2009.
Springer-Verlag.
[27] E. B. Goldstein. Sensation & Perception. Brooks/Cole, Pacific
Grove (CA), 5 edition, 1999.
[28] P. Gouras. Cortical mechanisms of colour vision. In P. Gouras,
editor, Vision and visual dysfunction: The perception of colour,
pages 179–197. Macmillan, London, 1991.
[29] S. L. Guth. Further applications of the ATD model for color
vision. Proceedings of SPIE, 2414(1):12–26, 1995. Also in IS&T’s
Recent Progress in Color Science, Karen Braun and Reiner
Dissertations in Forestry and Natural Sciences No 20
47
Tuija Jetsu: Modeling Color Vision
Eschbach, Eds. Society for Imaging Science and Technology,
Springfield, USA, 1997, pp. 177-185.
[30] S. L. Guth. The constancy myth, the vocabulary of color perception, and the ATD04 model. Proceedings of SPIE, 5292:1–14,
2004.
[31] T. Hansen, M. Giesel, and K. R. Gegenfurtner. Investigating
human chromatic discrimination of natural objects. In CGIV
2006 – Third European Conference on Color in Graphics, Imaging
and Vision, pages 119–124, Leeds, UK, 2006.
[32] L. Hardy, G. Rand, and M. Rittler. The H.R.R. polychromatic
plates. J. Opt. Soc. Am., 44:509–523, 1954.
[33] E. Hering. Zur Lehre vom Lichtsinne. Carl Gerolds Sohn, Hamburg, 1878. English translation: Outlines of a theory of the
light sense (translated by Hurvich, L.M. & Jameson, D.). Harvard University Press, Cambridge, Mass., USA, 1964.
[34] H. Hofer, J. Carroll, J. Neitz, M. Neitz, and D. R. Williams. Organization of the human trichromatic cone mosaic. J. Neurosci.,
25(42):9669–9679, 2005.
[35] J. Holmes and W. Wright. A new colour-perception lantern.
Color Research & Application, 7:82–88, 1982.
[36] S. Hood, J. Mollon, L. Purves, and G. Jordan. Color discrimination in carriers of color deficiency. Vision Research, 46(18):2894–
2900, 2006.
[37] http://commons.wikimedia.org (User:Chrkl).
retina diagram (2010).
Basis for the
[38] http://commons.wikimedia.org (User:Rhcastilhos). Eye diagram (2010).
[39] N. K. Humphrey. Vision in a monkey without striate cortex: a
case study. Perception, 3(3):241–255, 1974.
48
Dissertations in Forestry and Natural Sciences No 20
Bibliography
[40] L. Hurvich and D. Jameson. An opponent-process theory of
color vision. Psychol Rev, 64:384–404, 1957.
[41] C. R. Ingling, Jr. and B. H.-P. Tsou. Orthogonal combination
of the three visual channels. Vision Research, 17(9):1075–1082,
1977.
[42] S. Ishihara. The series of plates designed as a test for colourblindness. Kanehara Shuppan Co., Ltd., Tokyo, 1976.
[43] G. H. Jacobs. Primate photopigments and primate color vision.
PNAS, 93(2):577–581, 1996.
[44] G. H. Jacobs. A perspective on color vision in platyrrhine monkeys. Vision Research, 38(21):3307–3313, 1998.
[45] G. H. Jacobs and M. P. Rowe. Evolution of vertebrate colour vision. Clinical and Experimental Optometry, 87(4-5):206–216, 2004.
[46] K. A. Jameson, S. M. Highnote, and L. M. Wasserman. Richer
color experience in observers with multiple photopigment
opsin genes. Psychonomic Bulletin & Review, 8:244–261, 2001.
[47] J. B. Jonas, U. Schneider, and G. O. H. Naumann. Count and
density of human retinal photoreceptors. Graefe’s Archive for
Clinical and Experimental Ophthalmology, 230(6):505–510, 1992.
[48] D. Judd. Response functions for types of vision according to
the Müller theory. Journal of Research of the National Bureau of
Standards, 42:1–16, 1949.
[49] P. K. Kaiser and R. M. Boynton. Human Color Vision (Second
Edition). Optical Society of America, Washington, DC, 1996.
[50] H. Kauppinen. Development of a Color Machine Vision Method for
Wood Surface Inspection. PhD thesis, Oulun Yliopisto, 1999.
[51] K. Knoblauch, F. Vital-Durand, and J. L. Barbur. Variation
of chromatic sensitivity across the life span. Vision Research,
41(1):23–36, 2001.
Dissertations in Forestry and Natural Sciences No 20
49
Tuija Jetsu: Modeling Color Vision
[52] T. W. Kraft, J. Neitz, and M. Neitz. Spectra of human L cones.
Vision Research, 38:3663– 3670, 1998.
[53] J. Kremers, H. P. N. Scholl, H. Knau, T. T. J. M. Berendschot,
T. Usui, and L. T. Sharpe. L/M cone ratios in human trichromats assessed by psychophysics, electroretinography, and retinal densitometry. Journal of the Optical Society of America A,
17:517–526, 2000.
[54] R. G. Kuehni. Variability in unique hue selection: A surprising
phenomenon. Color Research & Application, 29(2):158–162, 2004.
[55] S. Kukkonen, H. Kalviainen, and J. Parkkinen. Color features
for quality control in ceramic tile industry. Opt. Eng., 40(2):170–
177, 2001.
[56] E. H. Land. The Retinex. Am. Scientist, 52:247–264, 1964.
[57] E. H. Land and J. J. McCann. Lightness and Retinex theory. J.
Opt. Soc. Am., 61:1–11, 1971.
[58] M. S. Loop, J. F. Shows, S. C. Mangel, and T. K. Kuyk.
Colour thresholds in dichromats and normals. Vision Research,
43(9):983–992, 2003.
[59] K. Mancuso, W. W. Hauswirth, Q. Li, T. B. Connor, J. A.
Kuchenbecker, M. C. Mauck, J. Neitz, and M. Neitz. Gene therapy for red-green colour blindness in adult primates. Nature,
461:784–787, 2009.
[60] B. Martinkauppi, E. Doronina, J. Piironen, T. Jaaskelainen, and
J. Parkkinen. Novel system for semiautomatic image segmentation of arctic charr. J. Electron. Imaging, 16(3):033012–8, 2007.
[61] P. M. Mehl, Y.-R. Chen, M. S. Kim, and D. E. Chan. Development of hyperspectral imaging technique for the detection
of apple surface defects and contaminations. Journal of Food
Engineering, 61(1):67–81, 2004.
50
Dissertations in Forestry and Natural Sciences No 20
Bibliography
[62] G. Müller. Über die Farbenempfindungen. Zeitschrift für Psychologie und Physiologie der Sinnesorgane, 17/18:1–430/435–647,
1930.
[63] J. Nathans. The evolution and physiology of human color vision: Insights from molecular genetic studies of visual pigments. Neuron, 24(2):299–312, 1999.
[64] J. Neitz, J. Carroll, Y. Yamauchi, M. Neitz, and D. R. Williams.
Color perception is mediated by a plastic neural mechanism
that is adjustable in adults. Neuron, 35(4):783–792, 2002.
[65] J. Neitz, M. Neitz, and G. H. Jacobs. More than three different
cone pigments among people with normal color vision. Vision
Research, 33:117–122, 1993.
[66] M. Neitz and J. Neitz. Molecular genetics of color vision and
color vision defects. Arch Ophthalmol, 118(5):691–700, 2000.
[67] M. Okuyama, N. Yokoyama, D. Nakao, N. Tsumura, and
Y. Miyake. Accurate mapping pigmentations in human skin
by spatio-temporal modulation of light source in the multispectral imaging. In PICS, pages 272–277, 2003.
[68] D. Osorio, A. C. Smith, M. Vorobyev, and H. M. BuchananSmith. Detection of fruit and the selection of primate visual
pigments for color vision. The American Naturalist, 164(6):696–
708, 2004.
[69] D. Osorio and M. Vorobyev. Colour vision as an adaptation
to frugivory in primates. Proceedings. Biological Sciences / The
Royal Society, 263(1370):593–599, 1996. PMID: 8677259.
[70] D. Osorio and M. Vorobyev. A review of the evolution of animal colour vision and visual communication signals. Vision
Research, 48(20):2042–2051, 2008.
[71] G. Osterberg. Topography of the layer of rods and cones in the
human retina. Acta Ophthalmol., Suppl., 13(6):1–102, 1935.
Dissertations in Forestry and Natural Sciences No 20
51
Tuija Jetsu: Modeling Color Vision
[72] S. E. Palmer. Vision Science: Photons to Phenomenology. MIT
Press, Cambridge, 1999.
[73] B. C. Regan, C. Julliot, B. Simmen, F. Vienot, P. CharlesDominique, and J. D. Mollon. Fruits, foliage and the evolution
of primate colour vision. Philosophical Transactions: Biological
Sciences,, 356(1407):229–283, 2001.
[74] A. Roorda and D. R. Williams. The arrangement of the three
cone classes in the living human eye. Nature, 397(6719):520–
522, 1999.
[75] P. H. Schiller, N. K. Logothetis, and E. R. Charles. Functions
of the colour-opponent and broad-band channels of the visual
system. Nature, 343(6253):68–70, 1990.
[76] M. Sharifzaded, P. S. Bernstein, and W. Gellermann. Nonmydriatic fluorescence-based quantitative imaging of human
macular pigment distributions. J. Opt. Soc. Am. A, 23:2373–
2387, 2006.
[77] K. Shinomori, B. E. Schefrin, and J. S. Werner. Age-related
changes in wavelength discrimination. J. Opt. Soc. Am. A,
18:310–318, 2001.
[78] V. C. Smith and J. Pokorny. Spectral sensitivity of the foveal
cone photopigments between 400 and 500 nm. Vision Research,
15(2):161–171, 1975.
[79] A. Stockman and L. T. Sharpe. The spectral sensitivities of
the middle- and long-wavelength-sensitive cones derived from
measurements in observers of known genotype. Vision Research, 40:1711–1737, 2000.
[80] A. Stockman, L. T. Sharpe, and C. Fach. The spectral sensitivity
of the human short-wavelength sensitive cones derived from
thresholds and color matches. Vision Research, 39(17):2901–
2927, 1999.
52
Dissertations in Forestry and Natural Sciences No 20
Bibliography
[81] Y. Sugita. Experience in early infancy is indispensable for color
perception. Current Biology, 14(14):1267–1271, 2004.
[82] E. Thompson. Colour Vision: A Study in Cognitive Science and the
Philosophy of Perception. Routledge Press, London/New York,
1995.
[83] H. von Helmholz. Handbuch der Physiologischen Optik. Voss,
Hamburg, 1867. English translation: Handbook of physiological optics (translated by Southall, J.P.C.). Optical Society of
America, Rochester, N.Y., 1924.
[84] J. J. Vos. Colorimetric and photometric properties of a 2◦ fundamental observer. Color Research & Application, 3(3):125–128,
1978.
[85] J. J. Vos and P. L. Walraven. On the derivation of the foveal
receptor primaries. Vision Research, 11:799–818, 1971.
[86] T. Wachtler, U. Dohrmann, and R. Hertel. Modeling color percepts of dichromats. Vision Research, 44(24):2843–2855, 2004.
[87] P. Walraven. A closer look at the tritanopic convergence point.
Vision Research, 14(12):1339–1343, IN4, 1974.
[88] A. Werner, A. Bayer, G. Schwarz, E. Zrenner, and W. Paulus.
Effects of ageing on postreceptoral short-wavelength gain control: Transient tritanopia increases with age. Vision Research,
50(17):1641–1648, 2010.
[89] J. S. Werner and V. G. Steele. Sensitivity of human foveal
color mechanisms throughout the life span. J. Opt. Soc. Am.
A, 5(12):2122–2130, 1988.
[90] C. H. Williams. Nagel’s anomaloscope for testing color vision.
Trans Am Ophthalmol Soc, 14(1):161–165, 1915.
[91] D. R. Williams and A. Roorda. The trichromatic cone mosaic
in the human eye. In K. R. Gegenfurtner and L. T.Sharpe,
Dissertations in Forestry and Natural Sciences No 20
53
Tuija Jetsu: Modeling Color Vision
editors, Color Vision: From Genes to Perception, pages 113–122.
Cambridge University Press, UK, 1999.
[92] G. Wyszecki and W. S. Stiles. Color science : concepts and methods, quantitative data and formulae (2nd edition). John Wiley &
Sons, Inc., USA, 2000.
[93] S. Yokoyama and F. Radlwimmer. The "five-sites" rule and the
evolution of red and green color vision in mammals. Mol Biol
Evol, 15(5):560–567, 1998.
[94] T. Young. On the theory of light and colours. Philosophical
transactions of the Royal Society of London, 92:12–48, 1802.
[95] S. Zeki, S. Aglioti, D. McKeefry, and G. Berlucchi. The neurological basis of conscious color perception in a blind patient.
PNAS, 96(24):14124–14129, 1999.
[96] H. Zollinger. Color: A Multidisciplinary Approach. Verlag Helvetica Chimica Acta / Wilet-VCH, Zurich / Weinheim, 1999.
54
Dissertations in Forestry and Natural Sciences No 20
The objective of this research was to
investigate the current state of human
color vision modeling and to also address its problems and possibilities.
Some existing color vision models were
examined from a computational point
of view, and the behavior of the models was compared with a human observer in experiments that evaluate the
properties of color vision. Also, some
dissertations | No 20 | Tuija Jetsu | Modeling color vision
Tuija Jetsu
Modeling color vision
Tuija Jetsu
Modeling color vision
changes in the anatomical properties of
the human vision system, like the cone
ratio on the retina, were taken into account in a part of the experiments. The
results described in this dissertation
strengthen the idea that color vision as
a concept is complicated, and that the
modeling of it well is a demanding task.
Publications of the University of Eastern Finland
Dissertations in Forestry and Natural Sciences
Publications of the University of Eastern Finland
Dissertations in Forestry and Natural Sciences
isbn 978-952-61-0257-3
issn 1798-5668