INDIVIDUAL DIFFERENCES IN COLOUR VISION

The first specific theory of colour vision was enunciated by Thomas Young in 1801. It included physical and physiological terms, and was based on the impossibility of there existing in the retina an infinity of particles that could vibrate in resonance with each possible undulation associated with light. It had to be assumed that the number of types of these particles is finite, corresponding to the three main colours – red, yellow, and blue. Each sensitive filament of the nerve could be divided into three portions, one sensitive to red, another to yellow, and a third to blue [1]. This theory is known as the Three Receptor or Trichromatic Theory. Because of its clear limitations, it was not widely accepted. It was Helmholtz who later developed Young's ideas in his 1896 Handbuch der Physiologischen Optik [2], in the second volume of which he wrote:

“The eye is equipped with three different sets of nerve fibres. Stimulation of the first excites the sensation of red, stimulation of the second excites the sensation of green, and stimulation of the third excites the sensation of violet.

“Homogeneous light excites these three types of fibres in various degrees depending on their wavelength. But this does not mean that every colour of the spectrum does not stimulate the three types of fibres, some weakly and others strongly. On the contrary, to explain a series of phenomena it is necessary to assume that this is precisely what occurs.”

At the end of the nineteenth century, a German physiologist, Ewald Hering [3], developed a theory of colour vision based on the subjective appearance of colours rather than on physical experiments. The trichromatic theory was inadequate to explain the appearance of colours. It could not reasonably explain why red and green lights are perceived as yellow when mixed, or why this yellow mixed with blue produces a perfect white [4]. Most defenders of the trichromatic theory were physicists who, at that time, disdained consideration of the appearance of colour as being of little scientific interest. Hering, however, asked himself why we never perceive a reddish green or a greenish red, but we do perceive greenish blues, etc. Hering speculated that the answer could lie in a process of opponent colours. He suggested that the visual system might be capable of generating signals of two opposing types depending on the wavelength. This idea was not favourably received by either physicists or physiologists. More than half a century had to pass until several experiments supported Hering's Opponent Process Theory of colours.

The trichromatic theory and the opponent process theory of colours competed with each other for some time, until the conflict was resolved in around 1920 when the physiologist G.E. Müller [5] and the physicist Edwin Schrödinger [6] developed the Zone Theory to show that the previous two theories were not really incompatible. According to the zone theory, trichromatic separation of the type proposed by Young-Helmholtz occurs initially in one zone, followed by the opponent colour process of the Hering type in another zone. The zone theory postulates three stages of processing:

1.An initial photochemical stage.

2.An intermediate chemical stage.

3.A final stage corresponding to the excitation of the fibres of the optic nerve.

Both Hering's opponent process theory of colour and Müller's zone theory were entirely qualitative in their formulation. This resulted in prolonging the dominance of the

Similarly, before the physiological confirmation of the existence of opponent processes, in 1955 Hurvich & Jameson [9] provided Hering's theory of opponent processes with the quantitative basis that allowed it to be directly compared with the mixture function supported trichromatic theory. In Hurvich & Jameson's initial formulation of the opponent process theory, the chromatic response functions represent the differential effect of light on four substances B, G, Y, and R, whose spectral sensitivities are expressed as linear combinations of the mixture functions.

By assumption, the chromatic and achromatic response curves can be derived from these sensitivity curves, and expressed as linear combinations of the standard observer colour matching functions [8]:

To corroborate this theory, it was necessary to determine the spectral sensitivity of the human visual system. The response of a linear system to any stimulus can be determined if one knows its response to spectral stimuli of constant energy, or if one determines the energy of spectral stimuli that give rise to the same response [10]. The response to constant energy spectral stimuli is a function of the wavelength which is known as the spectral sensitivity. The inverse of the energy of spectral stimuli that give rise to the same response is also a function of wavelength and is known as the action-spectrum. When the system is linear, the spectral sensitivity and the action-spectrum are proportional, and both curves carry the same information. In the particular case of human vision, since one wishes to characterize the response without damaging the system, it is not possible to measure the spectral sensitivity of its components directly. Instead one opts for characterizing by means of the action-spectrum of the light-sensitive elements of the human retina – the cones and rods – obtaining their fundamental response curve.

Because the laws of colorimetry are a reflection of the physiological processes underlying colour matching, the properties on which colorimetry is based such as trivariance and linearity can be attributed to these processes. Thus, trivariance or trichromacy implies the existence of three independent physiological mechanisms that have different sensitivities in different parts of the visual spectrum, and linearity implies that each of these mechanisms performs a linear operation on the spectral distribution of luminous stimuli [11]. These three mechanisms do not necessarily have to be three kinds of receptors. It is only necessary that they are three independent physiological responses, each sensitive to a different part of the spectrum. Nonetheless, a three-receptor based theory has been widely accepted since it seems the most straightforward way to explain trichromatism.

Physiological knowledge of the human visual system has confirmed the existence of three types of cones responsible for colour vision. The spectral sensitivity of these three types of photoreceptor can be derived from colour matching data. This is of great importance both

and analogously in the other two receptors.

If we ask an observer to match monochromatic stimuli u(λ) of constant quantum flux based on these primaries, we shall be able to express the result by means of the expression:

where r (λ), g(λ),b (λ) will be the colour matching functions of this observer.

Since each monochromatic stimulus u(λ) will produce an effective stimulus S1(λ) in photoreceptor S1, the equation of the match of the corresponding physiological tristimuli over

Because S1(λ) represents the spectral sensitivity function of receptor S1, the above equation states that the fundamental S1(λ) is a linear combination of the colour matching functions r(λ), g(λ), and b(λ), with the argument being generalizable to receptors S2 and S3:

The above matrix equation states that the fundamentals of colour vision are linear combinations of the CMFs [11]. If one could determine the matrix S1R…S3B , the fundamentals of any observer could be determined by means of his or her colorimetric matches.

One method of determining the coefficients of this matrix, used by most scientists because of its simplicity, is to make use of the fact that there exist observers called dichromats. These do not require the mixture of three primary stimuli to match foveally any chromatic stimulus, but just two. Such observers seem to have a reduced form of normal colour vision.

In the eyes of a normal observer, the dichromat confuses a series of colours. Maxwell [13] in 1857 was the first to note that the colours which each type of dichromat confuses (which really are the metameric colours for that type of dichromat) lie on a straight line when their chromaticity coordinates are plotted on a trichromatic chromaticity diagram. Maxwell concluded from this observation that these dichromats had a reduced form of a normal observer's colour perception.

For each of the three types of dichromats that exist – protanope, deuteranope, and tritanope – two colour matching functions are sufficient to specify their colour matching. Moreover, the dichromat matching functions must be linear combinations of the colour matching functions of normal observers. For example, in the (X,Y,Z) system, the two colour matching functions of the protanope observer can be written as follows [14]:

Substituting this expression into the previous one, one has the dichromat colour matching functions expressed in terms of the fundamentals:

Now from the König hypothesis, if the fundamental absent in the protanope is S1, the corresponding coefficients in the above equation must be zero:

The above condition is satisfied by taking the coefficients n11 = C1XcP, n21 = C1YcP, and n31 = C1ZcP, where C1 is an arbitrary constant. The argument is analogous for deuteranopes and tritanopes.

This model of reduced colour vision for the case of dichromats can be used for the detection and classification of colour vision deficiencies by isomeric mixing [16] instead of the traditional metameric matching employed in anomaloscopes.

Finally, the equation that defines the basic transformation between the tristimulus XYZ values and the fundamentals with the current LMS notation is as follows:

where (Xcp , Ycp , Zcp) , (Xcd , Ycd , Zcd) , (Xct , Yct , Zct) are the components of the points of confusion of protanopes, deuteranopes, and tritanopes.

If the chromaticity coordinates of these points are known, and given that the coordinates and components are proportional, the equation can be written as:

where kcp , kcd , kct are arbitrary scaling constants.