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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 . Color vision also changes with age, and the different effects of aging with respect to color vision have been summarized in . 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. ). Also, a general loss of sensitivity in color vision during aging is a known fact . Werner  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. ).
27 Dissertations in Forestry and Natural Sciences No 20 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 . 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 , 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 , and categorization results vary between observers (e.g. [36, 54]).
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 , and the theory, nowadays known as Young–Helmholtz trichromatic theory, was further developed by Hermann von Helmholtz . The basic idea behind this theory was that in the eye there are three types of photoreceptors 29 Dissertations in Forestry and Natural Sciences No 20 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  is there no such color as reddish green or bluish yellow? Ewald Hering developed a different opponent process theory  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 . 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 MÂ¸ller in 1930  followed by Judd in 1949 . In 1957, Leo Hurvich and Dorothea Jameson  provided quantative data for color opponency and proposed a precise testable formulation for a theory based on two sequential stages of color processing .
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  and the further developed by Land and McCann . 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 huDissertations 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.
Models for color vision rest on the assumptions made in theories for color vision . 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 ( ) 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.
Bumbaca and Smith  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
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 4.3Finally, 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).
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  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,
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.
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 , Guth has summarized all his previous work, and also extended the model further . 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
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.
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.
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
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.