Biomedical Engineering Reference
In-Depth Information
The basis functions can be also considered as color filters through which the light is
observed. The projections, or coordinates, express the total energy passed through
these filters.
16.3.1
Origin of Color Vision
We might ask how many different classes of photoreceptors are needed to sufficiently dis-
criminate between the given color spectra, and we also want to evaluate the discrimina-
tion accuracy. In human visual system, the infinite dimensionality of spectral
representation is greatly reduced to just three by the three types of cones. Once photons
are absorbed by a visual pigment in photoreceptors, the only remaining information is the
photon count; information about the wavelength of each individual photon is lost. This
property is called the principle of univariance (Rushton, 1972), (21). The color of the
objects is assigned by the visual system by comparing the signals from different cones.
From the principle of univariance, it is followed that the sensor with only one class of
photoreceptor will not discriminate among wavelengths. To gain some color vision, we
need at least two classes of photoreceptors. Each of these photoreceptors contains a visual
pigment with different absorption spectrum. Each given monochromatic stimuli would
activate the two receptors differently from any other monochromatic stimuli.
In Figure 16.1 are shown two examples of ideal photosensitivity functions, which corre-
spond to the basis functions of Eq. 16.1. In Figure 16.1a, it is shown that the problem of
equal stimuli for different colors may also exist in two sensitivity cases. Two monochro-
matic stimuli of 450 nm and 650 nm give the same response to both sensors. This same
response to both sensors is also given by one 550-nm stimulus. It means that for this color-
vision system the light with two monochromatic light sources (450 and 650 nm) would
look exactly the same as with one monochromatic light source (550 nm). In the human
visual system, there are three light-sensitive cells (Figure 16.1b). In this system, the former
light would appear purple and the latter one green.
16.3.2
Evaluation of Accuracy and Acuteness
The discrimination accuracy of color vision shows actual ability to discriminate between color
stimuli. This ability can be characterized in several ways (22). The simplest characterization
evaluates the ability to discriminate between monochromatic stimuli. Hallikainen (23) plot-
ted inverse of the normalized Euclidean distance between the lateral geniculate nucleus
(LGN) responses to adjacent pairs of equally spaced equal-energy monochromatic stimuli to
receive an estimate of wavelength discrimination of the human visual system. Figure 16.2
presents a wavelength discrimination curve calculated from the XYZ color coordinates of
equal-energy monochromatic stimuli in the visible spectrum interval spaced in 1-nm steps.
Naturally, the best discrimination is where the slope of color matching functions x , y , and z is
steep. It is convenient to describe wavelength discrimination ability by a single number. The
number can be defined as either the Euclidean distance between the vector of normalized dis-
tances and the unity vector of the same dimension, or the angle between these two vectors.
In either case, smaller number will mean better overall discrimination.
Accuracy of human color vision across the whole color space can be evaluated by
recording minimum perceivable color difference, so-called just-noticeable difference
(JND) (21,24). An observer is presented with two color stimuli; one fixed and the other
alterable. The observer is then asked to adjust the alterable stimuli so that the difference
between visual appearances of the two stimuli would be just noticeable. By repeating this
scheme for various colors, MacAdam (21,25) has evaluated a change of JND across the
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