GAMES101 Lecture 20 - Color and Perception

GAMES101_Lecture_20.pdf

I. Light Field/Lumigraph

Refer to Lecture19.md.

II. Color and Perception

Physical Basis of Color

The Fundamental Components of Light

Sunlight can be subdivided into a rainbow with a prism.

• The resulting light cannot be further divided.

   

The Spectrum

https://commons.wikimedia.org/wiki/File:EM_spectrum.svg#/media/File:EM_spectrum.svg under CC BY-SA 3.0 via Commons

Spectral Power Distribution (SPD)

• The amount of light present at each wavelength

• Units:

  • Radiometric units/nanometer (e.g., $\text{watts / nm}$$\text{watts / nm}$)

  • Or unitless

• Often use relative units scaled to maximum wavelength for comparison (when absolute magnitude is not important)

• Linearity of Spectral Power Distributions: They can be directly added.

  

Biological Basis of Color

Color is a phenomenon of human perception, not a property of light.

Anatomy of Human Eye

https://en.wikipedia.org/wiki/Human_eye#/media/File:Schematic_diagram_of_the_human_eye_en.svg under CC BY-SA 3.0

Light arrives at the retina and stimulates nerves, causing impulses.

• Retinal Photoreceptor Cells: Rods and Cones

  

  • Rod Cells: Primary receptors in very low light (scotopic conditions), perceive only shades of gray, no color

    • ~120 million rods in eye

  • Cone Cells: Primary receptors in typical light levels (photopic), provide sensation of color

    • ~6-7 millions cones in eye

    • Three types of cones, each with different spectral sensitivity

      • S, M and L type, corresponding to peak response at short, medium and long wavelengths

        

      • Distributions vary significantly among individuals:

        

        Distribution of cone cells at edge of fovea in 12 different humans with normal color vision

Metamerism

Spectral Response of Human Cone Cells

Integrate with respect to lambda on SPD

• Humans perceive only 3 numbers, from SML receptors

Metamerism

Definition: Metamers are two different spectra ($\mathrm{\infty }$$\infty$-dim) that project to the same $(S,M,L)$$(S, M, L)$ ($3$$3$-dim) response.

• These will appear to have the same color to a human

• Critical to color reproduction: No need to reproduce the full spectrum of a real-world scene in order to reproduce color

Tristimulus Theory of Color: Color Reproduction & Matching

Additive Color

• Given a set of primary lights, each with its own spectral distribution (e.g. RGB):

  $$s_R(\lambda ),s_G(\lambda ),s_B(\lambda )$$

• Adjust the brightness of these lights and add them together:

  $$R{s}_R(\lambda )+G{s}_G(\lambda )+B{s}_B(\lambda )$$

CIE RGB Color Matching Experiment

• The target is to find out $R,G,B$$R, G, B$ values to reproduce light at a specific wavelength for human perceptors.

  

  How much of each CIE RGB primary light must be combined to match a given monochromatic light?

  Having the above color-matching function allows us to compute the $R,G,B$$R, G, B$ values:

  $$R_{\text{CIE RGB}}={\int }_{\lambda }s(\lambda )\overline{r}(\lambda )\mathrm{d}\lambda$$
  $$G_{\text{CIE RGB}}={\int }_{\lambda }s(\lambda )\overline{g}(\lambda )\mathrm{d}\lambda$$
  $$B_{\text{CIE RGB}}={\int }_{\lambda }s(\lambda )\overline{b}(\lambda )\mathrm{d}\lambda$$

Color Spaces

Standardized RGB (sRGB)

• Makes a particular monitor RGB standard

• Other color devices simulate that monitor by calibration

• Widely adopted today

• Gamut is limited

CIE XYZ - A Universal Color Space

Imaginary set of standard color primaries $X,Y,Z$$X, Y, Z$

• Primary colors with these matching functions do not exist (i.e., artificial matching functions)

• Y is luminance (brightness regardless of color)

Designed such that:

• Matching functions are strictly positive

• Span all observable colors

Separating Luminance, Chromaticity

• Luminance: $Y$$Y$

• Chromaticity: $x,y,z$$x, y, z$, defined as

  $$x=\frac{X}{X+Y+Z}$$
  $$y=\frac{Y}{X+Y+Z}$$
  $$z=\frac{Z}{X+Y+Z}$$

  

  CIE Chromaticity Diagram

  • Mapping $x$$x$ and $y$$y$ to a figure at a fixed brightness $Y$$Y$

    • Since $x+y+z=1$$x + y + z = 1$, there are two dimensions only.

  • The Spectral Locus: The curved boundary

    • Corresponds to monochromatic light (each point represents a pure color of a single wavelength)

    

     

Gamut

Perceptually Organized Color Spaces

HSV Color Space (Hue-Saturation-Value)

• Hue

  • The kind of color, regardless of attributes

  • Colorimetric correlate: dominant wavelength

  • Artist's correlate: the chosen pigment color

• Saturation

  • The colorfulness

  • Colorimetric correlate: purity

  • Artist's correlate: fraction of paint from the colored tube

• Lightness/Brightness or Value

  • The overall amount of light

  • Colorimetric correlate: luminance

  • Artist's correlate: tints are lighter, shades are darker

CIELAB Space (A.K.A $L^{\ast }{a}^{\ast }{b}^{\ast }$$L^\ast a^\ast b^\ast$) & Opponent Color Theory

• $L^{\ast }$$L^\ast$: lightness, or brightness

• $a^{\ast }$$a^\ast$ and $b^{\ast }$$b^\ast$ are color-opponent pairs

  • $a^{\ast }$$a^\ast$ is red-green

  • $b^{\ast }$$b^\ast$ is blue-yellow

Opponent Color Theory

• The brain seems to encode color using three axes:

  • white - black

  • red - green

  • yellow - blue

• The white-black axis is lightness, the others determine hue and saturation

• Afterimage: You may see opponent colors after the sudden disappearance of an image.

Everything is Relative

• A and B has the same color.

CMYK: A Subtractive Color Space

The more you mix, the darker it will be.

• Cyan, Magenta, Yellow and Key

  

• Separate black for cost-saving purposes