Dimensionality reduction

Recall from Section 4.1 that light energy is a jumble of wavelengths and magnitudes that form the spectral power distribution. Figure 4.6 provided an illustration. As we see objects, the light in the environment is reflected off of surfaces in a wavelength-dependent way according to the spectral distribution function (Figure 4.7). As the light passes through our eyes and is focused onto the retina, each photoreceptor receives a jumble of light energy that contains many wavelengths. Since the power distribution is a function of wavelength, the set of all possible distributions is a function space, which is generally infinite-dimensional. Our limited hardware cannot possibly sense the entire function. Instead, the rod and cone photoreceptors sample it with a bias toward certain target wavelengths, as was shown in Figure 5.3 of Section 5.1. The result is a well-studied principle in engineering called dimensionality reduction. Here, the infinite-dimensional space of power distributions collapses down to a 3D color space. It is no coincidence that human eyes have precisely three types of cones, and that our RGB displays target the same colors as the photoreceptors.

Steven M LaValle 2020-01-06