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«Publications of the University of Eastern Finland Dissertations in Forestry and Natural Sciences TUIJA JETSU Modeling color vision Publications of ...»

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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

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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.

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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]

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• 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.

5 Dissertations in Forestry and Natural Sciences No 20 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.

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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.

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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.

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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:

(2.3) ci = Sout (λ)si (λ)dλ, λ 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].

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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].

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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

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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).

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80 60 40 20

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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

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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

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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

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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].

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