# Elements & Enzymes present in the eye

A humanly perceived color may be modeled as three numbers: the extents to which each of the 3 types of cones is stimulated. Thus a humanly perceived color may be thought of as a point in 3-dimensional Euclidean space. We call this space R3color.Since each wavelength w stimulates each of the 3 types of cone cells to a known extent, these extents may be represented by 3 functions r(w), g(w), b(w) corresponding to the response of the so-called “red”, “green”, and “blue” cone cells, respectively.

Finally, since a beam of colored light can be composed of many different wavelengths, to determine the extent to which a physical color C in Hcolor stimulates each cone cell, we must calculate the integral (with respect to w), over the interval [Wmin,Wmax], of C(w)*r(w) (for red), of C(w)*g(w) (for green), and of C(w)*b(w) (for blue). The triple of resulting numbers associates to each physical color C (which is a region in Hcolor) to a particular perceived color (which is a single point in R3color). This association is easily seen to be linear. It may also easily be seen that many different regions in the “physical” space Hcolor can all result in the same single perceived color in R3color, so a perceived color is not unique to one physical color.

Thus human color perception is determined by a specific, non-unique linear mapping from the infinite-dimensional Hilbert space Hcolor to the 3-dimensional Euclidean space R3color.

Technically, the image of the (mathematical) cone over the simplex whose vertices are the spectral colors, by this linear mapping, is also a (mathematical) cone in R3color. Moving directly away from the vertex of this cone represents maintaining the same chromaticity while increasing its intensity. Taking a cross-section of this cone yields a 2D chromaticity space. Both the 3D cone and its projection or cross-section are convex sets; that is, any mixture of spectral colors is also a color.

The CIE 1931 color space chromaticity diagram. The outer curved boundary is the spectral (or monochromatic) locus, with wavelengths shown in nanometers. Note that the colors depicted depend on the color space of the device on which you are viewing the image, and therefore may not be a strictly accurate representation of the color at a particular position.In practice, it would be quite difficult to measure an individual’s cones’ three responses to various physical color stimuli. So instead, three specific benchmark test lights are typically used; let us call them R, G, and B. In order to calibrate human perceptual space, scientists allowed human subjects to try to match any physical color by turning dials to create specific combinations of intensities (IR, IG, IB) for the R, G, and B lights, resp., until a match was found. This needed only to be done for physical colors that are spectral (since a linear combination of spectral colors will be matched by the same linear combination of their (IR, IG, IB) matches). Note that in practice, often at least one of R, G, B would have to be added with some intensity to the physical test color, and that combination matched by a linear combination of the remaining 2 lights. Across different individuals (without color blindness), the matchings turned out to be nearly identical.