Radiometry & Color

Alexei Efros

CS280, Spring 2026

with slides from Hoiem, Malik, Freeman

“Empire of Light”, Magritte

What is in an image?

The image is an array of brightness values (three arrays for RGB images)

A camera creates an image …

The image I(x,y) measures how much light is captured at pixel (x,y)

We want to know

• Where does a point (X,Y,Z) in the world get imaged?
• What is the brightness at the resulting point (x,y)?

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Now let us try to understand brightness at a pixel (x,y) …

The image I(x,y) measures how much light is captured at pixel (x,y). Proportional to the number of photons captured at the sensor element (CCD/CMOS/Rod/cone/..) in a time interval.

Radiance is a directional quantity

Radiant power travelling in a given direction per unit area (measured perpendicular to the direction of travel) per unit solid angle

How does a pixel get its value?

Light emitted

Sensor

Lens

Fraction of light reflects into camera

How does a pixel get its value?

• Major factors
• Illumination strength and direction
• Surface geometry
• Surface material
• Nearby surfaces
• Camera gain/exposure

Image irradiance is proportional to scene radiance in the direction of the camera

BRDF: Bidirectional Reflectance Distribution Function

Slide credit: S. Savarese

• Model of local reflection that tells how bright a surface appears when viewed from one direction when light falls on it from another

Effect of BRDF

Basic models of reflection

• Specular: light bounces off at the incident angle
• E.g., mirror

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• Diffuse: light scatters in all directions
• E.g., brick, cloth, rough wood

incoming light

specular reflection

incoming light

diffuse reflection

Lambertian reflectance model

light source

light source

absorption

diffuse reflection

Diffuse reflection: Lambert’s cosine law

http://en.wikipedia.org/wiki/Lambert%27s_cosine_law

Specular Reflection

• Reflected direction depends on light orientation and surface normal
• E.g., mirrors are fully specular
• Most surfaces can be modeled with a mixture of diffuse and specular components

light source

specular reflection

Flickr, by suzysputnik

Flickr, by piratejohnny

Most surfaces have both specular and diffuse components

• Specularity = spot where specular reflection dominates (typically reflects light source)

​

Photo: northcountryhardwoodfloors.com

Typically, specular component is small

Intensity and Surface Orientation

Slide: Forsyth

Recap

specular reflection

diffuse reflection

absorption

Other possible effects

light source

transparency

light source

refraction

λ

light source

subsurface scattering

So far: light🡪surface🡪camera

• Called a local illumination model
• But much light comes from surrounding surfaces

From Koenderink slides on image texture and the flow of light

Inter-reflection is a major source of light

Inter-reflection affects the apparent color of objects

From Koenderink slides on image texture and the flow of light

Scene surfaces also cause shadows

• Shadow: reduction in intensity due to a blocked source

Shadows

Models of light sources

​

• Distant point source
• One illumination direction
• E.g., sun

​

• Area source
• E.g., white walls, diffuser lamps, sky

​

• Ambient light
• Substitute for dealing with interreflections

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• Global illumination model
• Account for interreflections in modeled scene

Image Formation

f(x,y) = reflectance(x,y) * illumination(x,y)

Reflectance in [0,1], illumination in [0,inf]

Problem: Dynamic Range

1500

1

25,000

400,000

2,000,000,000

The real world is

High dynamic range

Dynamic range and camera response

• Typical scenes have a huge dynamic range

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• Camera response is roughly linear in the mid range (15 to 240) but non-linear at the extremes
• called saturation or undersaturation

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Long Exposure

10^-6

10⁶

10^-6

10⁶

Real world

Picture

^{0 to 255}

High dynamic range

Short Exposure

10^-6

10⁶

10^-6

10⁶

Real world

Picture

^{0 to 255}

High dynamic range

Radiance is a function of wavelength

Spectroradiometer

DIY Spectroradiometer

Electromagnetic Spectrum

http://www.yorku.ca/eye/photopik.htm

Human Luminance Sensitivity Function

Why do we see light of these wavelengths?

© Stephen E. Palmer, 2002

…because that’s where the

Sun radiates EM energy

Visible Light

The Physics of Light

Any patch of light can be completely described

physically by its spectrum: the number of photons

(per time unit) at each wavelength 400 - 700 nm.

© Stephen E. Palmer, 2002

The Physics of Light

Some examples of the spectra of light sources

© Stephen E. Palmer, 2002

The Physics of Light

Some examples of the reflectance spectra of surfaces

Wavelength (nm)

% Photons Reflected

© Stephen E. Palmer, 2002

Color spaces

• How can we represent color?

http://en.wikipedia.org/wiki/File:RGB_illumination.jpg

Color spaces: RGB vs. CMY(K)

• Light projection vs paint

Source: https://intranet.mcad.edu/kb/cmyk-vs-rgb-what-color-space-should-i-work

Color spaces: RGB

Image from: http://en.wikipedia.org/wiki/File:RGB_color_solid_cube.png

Default color space

R

(G=0,B=0)

G

(R=0,B=0)

B

(R=0,G=0)

RGB cube

• Easy for devices
• But not perceptual
• Where do the grays live?
• Where is hue and saturation?

The Psychophysics of “Color”

There is no simple functional description for the perceived

color of all lights under all viewing conditions, but …...

A helpful constraint:

Consider only physical spectra with normal distributions

© Stephen E. Palmer, 2002

The Psychophysical Correspondence

Mean

Hue

© Stephen E. Palmer, 2002

The Psychophysical Correspondence

Variance

Saturation

© Stephen E. Palmer, 2002

The Psychophysical Correspondence

Area

Brightness

© Stephen E. Palmer, 2002

Color spaces: RGB

Image from: http://en.wikipedia.org/wiki/File:RGB_color_solid_cube.png

Default color space

R

(G=0,B=0)

G

(R=0,B=0)

B

(R=0,G=0)

RGB cube

• Easy for devices
• But not perceptual
• Where do the grays live?
• Where is hue and saturation?

HSV

Hue, Saturation, Value (Intensity)

• RGB cube on its vertex

Decouples the three components (a bit)

Use rgb2hsv() and hsv2rgb() in Matlab

Slide by Steve Seitz

Color spaces: HSV

Intuitive color space

H

(S=1,V=1)

S

(H=1,V=1)

V

(H=1,S=0)

Color spaces: L*a*b*

“Perceptually uniform”* color space

L

(a=0,b=0)

a

(L=65,b=0)

b

(L=65,a=0)

© Stephen E. Palmer, 2002

Color Constancy

The “photometer metaphor” of color perception:

Color perception is determined by the spectrum of light

on each retinal receptor (as measured by a photometer).

© Stephen E. Palmer, 2002

Color Constancy

The “photometer metaphor” of color perception:

Color perception is determined by the spectrum of light

on each retinal receptor (as measured by a photometer).

© Stephen E. Palmer, 2002

Color Constancy

The “photometer metaphor” of color perception:

Color perception is determined by the spectrum of light

on each retinal receptor (as measured by a photometer).

What color is the “The Dress”?

https://en.wikipedia.org/wiki/The_dress

© Stephen E. Palmer, 2002

Color Constancy

Do we have constancy over

all global color transformations?

Color Constancy

© Stephen E. Palmer, 2002

Color Constancy: the ability to perceive the

invariant color of a surface despite ecological

Variations in the conditions of observation.

Another of these hard inverse problems:

Physics of light emission and surface reflection

underdetermine perception of surface color

Camera White Balancing

• Manual
• Automatic (AWB)

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Color Correction

Lightness constancy

Interpret surface in terms of albedo or “true color”, rather than observed intensity

• Humans are good at it
• Computers are not nearly as good

Perception of Intensity

from Ted Adelson

Perception of Intensity

from Ted Adelson

Intrinsic Images