http://www.singinst.org/ourresearch/publications/LOGI.pdf
Levels of Organization in General Intelligence

 

 

The usual statement is that the complexity in a sensory modality
reflects regularities of the environment, but I wish to offer a
slightly different viewpoint. To illustrate this view, I must borrow
and severely simplify the punchline of a truly elegant paper, "The
Perceptual Organization of Colors" by Roger Shepard [Shepard92]. Among
other questions, this paper seeks to answer the question of
trichromancy: Why are there three kinds of cones in the human retina,
and not two, or four? Why is human visual perception organized into a
three-dimensional color space? Historically, it was often theorized
that trichromancy represented an arbitrary compromise between
chromatic resolution and spatial resolution; that is, between the
number of colors perceived and the grain size of visual resolution. As
it turns out, there is a more fundamental reason why three color
channels are needed.

To clarify the question, consider that surfaces possess a potentially
infinite number of spectral reflectance distributions. We will focus
on spectral reflectance distributions, rather than spectral power
distributions, because adaptively relevant objects that emit their own
light are environmentally rare. Hence the physically constant property
of most objects is the spectral reflectance distribution, which
combines with the spectral power distribution of light impinging on
the object to give rise to the spectral power distribution received by
the human eye. The spectral reflectance distribution is defined over
the wavelengths from 400nm to 700nm (the visible range), and since
wavelength is a continuum, the spectral reflectance distribution can
theoretically require an unlimited number of quantities to specify.
Hence, it is not possible to exactly constrain a spectral reflectance
distribution using only three quantities, which is the amount of
information transduced by human cones.

The human eye is not capable of discriminating among all physically
possible reflecting surfaces. However, it is possible that for
"natural" surfaces - surfaces of the kind commonly encountered in the
ancestral environment - reflectance for each pure frequency does not
vary independently of reflectance for all other frequencies. For
example, there might exist some set of basis reflectance functions,
such that the reflectance distributions of almost all natural surfaces
could be expressed as a weighted sum of the basis vectors. If so, one
possible explanation for the trichromancy of human vision would be
that three color channels are just enough to perform adequate
discrimination in a "natural" color space of limited dimensionality.

The ability to discriminate between all natural surfaces would be the
design recommended by the "environmental regularity" philosophy of
sensory modalities. The dimensionality of the internal model would
mirror the dimensionality of the environment.

As it turns out, natural surfaces have spectral reflectance
distributions that vary along roughly five to seven dimensions
[Maloney86]. There thus exist natural surfaces that, although
appearing to trichromatic viewers as "the same color", nonetheless
possess different spectral reflectance distributions.

[Shepard92] instead asks how many color channels are needed to ensure
that the color we perceive is the same color each time the surface is
viewed under different lighting conditions. The amount of ambient
light can also potentially vary along an unlimited number of
dimensions, and the actual light reaching the eye is the product of
the spectral power distribution and the spectral reflectance
distribution. A reddish object in bluish light may reflect the same
number of photons of each wavelength as a bluish object in reddish
light. Similarly, a white object in reddish light may reflect mostly
red photons, while the same white object in bluish light may reflect
mostly blue photons. And yet the human visual system manages to
maintain the property of color constancy; the same object will appear
to be the same color under different lighting conditions.

[Judd64] measured 622 spectral power distributions for natural
lighting, under 622 widely varying natural conditions of weather and
times of day, and found that variations in natural lighting reduce to
three degrees of freedom. Furthermore, these three degrees of freedom
bear a close correspondence to the three dimensions of color opponency
that were proposed for the human visual system based on experimental
examination [Hurvich57]. The three degrees of freedom are:

* The light-dark variation, which depends on the total light reaching
the object.

* The yellow-blue variation, which depends on whether a surface is
illuminated by direct sunlight or is in shade. In shade the surface is
illuminated by the Raleigh-scattered blue light of the sky, but is not
directly illuminated by the sun. The corresponding yellow extreme
occurs when an object is illuminated only by direct sunlight; e.g., if
sunlight enters through a small channel and skylight is cut off.

* The red-green variation, which depends on both the elevation of the
sun (how much atmosphere the sun travels through), and the amount of
atmospheric water vapor. E.g., illumination by a red sunset versus
illumination at midday. Red wavelengths are the wavelengths least
scattered by dust and most absorbed by water.

The three color channels of the human visual system are precisely the
number of channels needed in order to maintain color constancy under
natural lighting conditions20. Three color channels are not enough to
discriminate between all natural surface reflectances, but three color
channels are the exact number required to compensate for ambient
natural lighting and thereby ensure that the same surface is
perceptually the "same color" on any two occasions. This simplifies
the adaptively important task of recognizing a previously experienced
object on future encounters.


Võistlusväljaku tingimustes on võibolla teised muutumissuunad
värvidel, aga idee on sama.