Chromatic adaptation of the eye

An object may be viewed under various conditions. For example, it may be illuminated by the sunlight, the light of a fire, or a harsh electric light. In all of these situations, human vision perceives that the object has the same color: an apple always appears red, whether viewed at night or during the day. On the other hand, a camera with no adjustment for light may register the apple as having many different shades. This feature of the visual system is called chromatic adaptation, or color constancy; when the correction occurs in a camera it is referred to as white balance.

Chromatic adaptation is one aspect of vision that may fool someone into observing a color-based optical illusion. Though the human visual system generally does maintain constant perceived color under different lighting, there are situations where the brightness of a stimulus will appear reversed relative to its "background" when viewed at night. For example, the bright yellow petals of flowers will appear dark compared to the green leaves in very dim light.

The opposite is true during the day. This is known as the Purkinje effect, and arises because in very low light, human vision is approximately monochromatic and limited to the region near a wavelength of 550nm (green).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.