Color Science, Summaries of Linear Algebra

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Steve Marschner

CS 4620

Cornell University

Color Science

1: Color matching

Color Science

• Light is electromagnetic radiation
  • exists as oscillations of different frequency (or, wavelength) [Lawrence Berkeley Lab / MicroWorlds] What light is

• Salient property is the spectral power distribution (SPD)
  • the amount of light present at each wavelength
  • units: Watts per nanometer (tells you how much power you’ll find in a narrow range of wavelengths)
  • for color, often use “relative units” when overall intensity is not important Measuring light wavelength band (width d λ) amount of light = 180 d λ (relative units) wavelength (nm)

• Build a model for human color perception
• That is, map a Physical light description to a

Perceptual color sensation

Physical Perceptual [Stone 2003] The problem of color science

• We can model the low-level

behavior of the eye by thinking

of it as a light-measuring machine

• its optics are much like a camera
• its detection mechanism is also much like a camera
• Light is measured by the

photoreceptors in the retina

• they respond to visible light
• different types respond to different wavelengths [Greger et al. 1995] The eye as a measurement device

A simple light detector

• Same math carries over to power distributions
  • spectrum entering the detector has its spectral power distribution (SPD), s (λ)
  • (^) detector has its spectral sensitivity or spectral response , r (λ) measured signal input spectrum detector’s sensitivity Light detection math

Cornell CS4620 Fall 2019 • Lecture 23 Steve Marschner • 64 Human eye: retina Light passes through blood vessels & retinal layers before reaching the light-sensitive cells (“rods” & “cones”) slide courtesy Pieter Peers

• S,M,L cones have broadband spectral sensitivity
• S,M,L neural response is integrated w.r.t. λ - we’ll call the response functions r S , r M , r L
• Results in a trichromatic visual system
• S, M, and L are tristimulus values [source unknown] Cone Responses

• Wanted to map a Physical light description to a

Perceptual color sensation

• Basic solution was known and standardized by 1930
  • Though not quite in this form Physical Perceptual [Stone 2003] s Colorimetry: an answer to the problem

• Take a spectrum (which is a function)
• Eye produces three numbers
• This throws away a lot of information!
  • Quite possible to have two different spectra that have the same S, M, L tristimulus values
  • Two such spectra are metamers Basic fact of colorimetry

• The information available to the visual system about a

spectrum is three values

• this amounts to a loss of information analogous to projection on a plane
• Two spectra that

produce the same

response are

metamers

Pseudo-geometric interpretation

• Luminance
  • the overall magnitude of the the visual response to a spectrum (independent of its color) - corresponds to the everyday concept “brightness”
  • determined by product of SPD with the luminous efficiency function V λ that describes the eye’s overall ability to detect light at each wavelength
  • e.g. lamps are optimized to improve their luminous efficiency (tungsten vs. fluorescent vs. sodium vapor) [Stone 2003] Basic colorimetric concepts