Download Trichromatic Theory of Color Vision and more Summaries Linear Algebra in PDF only on Docsity!

Trichromatic Theory of Color

Vision

Jonathan Pillow

Mathematical Tools for Neuroscience (NEU 314)

Fall, 2021

lecture 4

Motivation: James Maxwell’s color-matching experiment

Given any “test” light, you can match it by adjusting the intensities of any three other lights (2 is not enough; 4 is more than enough & produces non-unique matches)

Q : How many numbers would you need to write down to specify the color of a light source? Just one? (“the wavelength”?) eg. “650”?

A : It depends on how you “bin” up the spectrum

• One number for each spectral “bin”: example: 13 bins 0 0 0 0 0 5 10 13 20 15 16 17 12 energy Q : How many numbers would you need to write down to specify the color of a light source? spectral properties (a vector!)

Some terminology for “colored” light: 0 0 0 0 0 5 10 13 20 15 16 17 12 energy the illuminant - light source spectral - referring to the wavelength of light illuminant power spectrum - this curve. amount of energy (or power) at each frequency

energy an illuminant with most power at long wavelengths (i.e., a reddish light source )

energy an illuminant with power at all visible wavelengths (a neutral light source, or “white light”)

Q: How many measurements of this same spectrum does the human eye take (in bright conditions?)

(^420 534 ) absorption spectrum - describes response (or “light absorption”) of a photoreceptor as a function of wavelength photoreceptor response could also call this “sensitivity”

A single photoreceptor doesn’t “see” color; it gives greater response to some frequencies than others single cone absorption spectrum Problem : response from a single cone is ambiguous 10 spikes

Problem is actually much worse: can’t tell a weak signal at the peak sensitivity from a strong signal at an off-peak intensity single cone absorption spectrum spectral power

• All three of these lights give the same response from this cone

+0. 10 spikes cone respone = aborption spectrum x light intensity

single cone absorption spectrum spectral power

+0. Problem of univariance : infinite set of wavelength+intensity combinations can elicit exactly the same response 10 spikes

Written in a linear algebra setting

cone responses cone absorption spectra

S

M

L

illuminant spectrum

400 450 500 550 600 650 700 0

1 wavelength energy cone responses: 40 175 240 Metamers

• Illuminants that are physically distinct but perceptually indistinguishable illuminant #

sensitivity (^) percept