CS 39549525: Spring 2003

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CS 395/495-25 Spring 2003

• IBMR Week 9A
• Image-Based Physics
• Measuring Light Materials
• Jack Tumblin
• jet_at_cs.northwestern.edu

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Reminders

• ProjA graded Good Job! 90,95, 110
• ProjB graded Good! minor H confusions.
• MidTerm graded novel solutions encouraged.
• ProjC due Friday, May 16 many recd...
• ProjD posted, due Friday May 30
• Take-Home Final Exam Assign on Thurs June 5,
  due June 11

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IBMR Rendering from Light Rays

• How can we measure rays of light? Light
  Sources? Scattered rays? etc.

Shape, Position, Movement,
Emitted Light
Reflected, Scattered, Light
BRDF, Texture, Scattering
Cameras capture subset of these rays.
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Visible Light Measurement

• Visible Light what our eyes can perceive
• narrow-band electromagnetic energy
• ? ? 400-700 nm (nm 10-9 meter)
• lt1 octave (honey bees 3-4 octaves
  ?chords?)
• Not uniformly visible vs. wavelength ?
• Equiluminant Curve??defines luminance vs.
  wavelength
• eyes sense spectralCHANGES well, butnot
  wavelength
• Metamerism

http//www.yorku.ca/eye/photopik.htm
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Visible Light Measurement

• Measurement of Lighteasy. Perception?hard.
• Color crudely perceived wavelength spectrum
• 3 sensed dimensions from spectra.
• CIE-standard X,Y,Z color spectra linear coord.
  system for spectra that spans all perceivable
  colors X,Y,Z
• Projective! luminance Z chromaticity
  (x,y) (X/Z, Y/Z)
• NOT perceptually uniform... (MacAdams
  ellipses...)
• Many Standard Texts, tutorials on color
• Good http//www.colourware.co.uk/cpfaq.htm
• Good http//www.yorku.ca/eye/toc.htm
• Watt Watt pg 277-281

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Incident Light Measurement

• Flux W power, Watts, photons/sec
• Uniform, point-source light flux falls with
  distance2
• E Watts/r2

r
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Light Measurement

• Flux W power, Watts, photons/sec
• Irradiance E flux arriving per unit
  area,(regardless of direction)
• E Watts/area dW/dA

But direction makes a big difference when
computing E...
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Foreshortening Effect cos(?)

• Larger Incident angle ?i spreads same flux over
  larger area
• flux per unit area becomes W cos( ?i) / area
• Foreshortening geometry imposes an angular term
  cos(?i) on energy transfer

circular bundle of incident rays, flux W
W
?i
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Irradiance E

• To find irradiance at a point on a surface,
• Find flux from each (point?) light source,
• Weight flux by its direction cos(?i)
• Add all light sources or more precisely,
  integrate over entire hemisphere ?
• Defines Radiance L
• L (watts / area) / sr
• (sr steradians solid angle surface area on
  unit sphere)

?
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Radiance L

• But for distributed (non-point) light sources?
  integrate flux over the entire hemisphere ?.
• But are units of what we integrate?
• Radiance L
• L (watts / area) / sr
• (sr steradians solid angle surface area on
  unit sphere)

?
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Lighting Invariants

• Why doesnt surface intensity change with
  distance?
• We know point source flux drops with distance
  1/r2
• We know surface is made of infinitesimal point
  sources...

intensity 1/r2
intensity constant (?!?!)
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Lighting Invariants

• Why doesnt surface intensity change with
  distance?
• Because camera pixels measure Radiance, not
  flux!
• pixel value ? flux cos(?) / sr
• good lens design cos(?) term vanishes.
  Vignettingresidual error.
• Pixels size in sr fixed
• Point source fits in one pixel 1/r2
• Viewed surface area grows by r2, cancels 1/r2
  flux falloff

intensity 1/r2
intensity constant (?!?!)
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Point-wise Light Reflection

• Given
• Infinitesimal surface patch dA,
• illuminated by irradiance amount E
• from just one direction (?i,?i)
• How should we measure the returned light?
• Ans by emittedRADIANCEmeasured for
  alloutgoing directions(measured on surface of
  ?)

?i
?
dA
?i
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Point-wise Light Reflection BRDF

• Bidirectional Reflectance Distribution Function
  Fr(?i,?I,?e,?e) Le(?e,?e) / Ei(?i,?i)
• Still a ratio (outgoing/incoming) light, but
• BRDF Ratio of outgoing RADIANCE in one
  direction Le(?e,?e)that results from incoming
  IRRADIANCE in one direction Ei(?i,?i)
• Units are tricky BRDF Fr Le / Ei

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Point-wise Light Reflection BRDF

• Bidirectional Reflectance Distribution Function
  Fr(?i,?I,?e,?e) Le(?e,?e) / Ei(?i,?i)
• Still a ratio (outgoing/incoming) light, but
• BRDF Ratio of outgoing RADIANCE in one
  direction Le(?e,?e)that results from incoming
  IRRADIANCE in one direction Ei(?i,?i)
• Units are tricky BRDF Fr Le / Ei (
  Watts/area) /
• ((Watts/area) /sr))

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Point-wise Light Reflection BRDF

• Bidirectional Reflectance Distribution Function
  Fr(?i,?I,?e,?e) Le(?e,?e) / Ei(?i,?i)
• Still a ratio (outgoing/incoming) light, but
• BRDF Ratio of outgoing RADIANCE in one
  direction Le(?e,?e)that results from incoming
  IRRADIANCE in one direction Ei(?i,?i)
• Units are tricky BRDF Fr Le / Ei (
  Watts/area) / 1/sr
• ((Watts/area) /sr))

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Point-wise Light Reflection BRDF

• Bidirectional Reflectance Distribution Function
  Fr(?i,?I,?e,?e) Le(?e,?e) / Ei(?i,?i), and
  (1/sr)units
• Bidirectional because value is SAME if we swap
  in,out directions (?e,?e)?? (?i,?i)
• Important Property! aka Helmholtz Reciprocity
• BRDF Results from surfacesmicroscopic
  structure...
• Still only an approximation ignores subsurface
  scattering...

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Scene causes Light Field

• What measures light rays in, out of scene?

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Measure Light LEAVING a Scene?

• Towards a camera?...

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Measure Light LEAVING a Scene?

• Towards a camera Radiance.

Light Field Images measure Radiance L(x,y)
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Measure light ENTERING a scene?

• from a (collection of) point sources at infinity?

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Measure light ENTERING a scene?

• from a (collection of) point sources at infinity?

Light Map Images (texture map light
source) describes Irradiance E(x,y)
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Measure light ENTERING a scene?

• leaving a video projector lens?

Reversed Camera emits Radiance L(x,y)
Radiance L
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Measure light ENTERING a scene?

• from a video projector?Leaving Lens Radiance L

Irradiance E
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END