CS 395/495-25: Spring 2003CS 395/495-25: Spring 2003

IBMR: Week 9A IBMR: Week 9A

Image-Based Physics:Image-Based Physics:

Measuring Light & MaterialsMeasuring Light & Materials

Jack TumblinJack Tumblin

jet@cs.northwestern.edujet@cs.northwestern.edu

RemindersReminders

• ProjA graded: Good Job! 90,95, 110ProjA graded: Good Job! 90,95, 110

• ProjB graded: Good! minor H confusions.ProjB graded: Good! minor H confusions.

• MidTerm graded: novel solutions MidTerm graded: novel solutions encouraged.encouraged.

• ProjC due Friday, May 16: many rec’d...ProjC due Friday, May 16: many rec’d...

• ProjD posted, due Friday May 30 ProjD posted, due Friday May 30

• Take-Home Final Exam: Take-Home Final Exam: Assign on Thurs June 5, due June 11Assign on Thurs June 5, due June 11

IBMR: Rendering from Light RaysIBMR: Rendering from Light Rays

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

Shape, Shape, Position,Position,Movement,Movement,

BRDF,BRDF,Texture,Texture,ScatteringScattering

Emitted Emitted LightLight

Reflected,Reflected,Scattered,Scattered,Light …Light … Cameras capture Cameras capture

subset of these subset of these rays.rays.

Visible Light MeasurementVisible Light Measurement

• ‘‘Visible Light’ = what our eyes can perceive;Visible Light’ = what our eyes can perceive;– narrow-band electromagnetic energy:narrow-band electromagnetic energy:

400-700 nm400-700 nm (nm = 10 (nm = 10-9 -9 meter)meter)

<1 octave; (honey bees: 3-4 ‘octaves’ ?chords?)<1 octave; (honey bees: 3-4 ‘octaves’ ?chords?)

• Not uniformly visible vs. wavelength Not uniformly visible vs. wavelength : : – Equiluminant CurveEquiluminant Curve

defines ‘luminance’ defines ‘luminance’ vs. wavelengthvs. wavelength

– eyes sense spectraleyes sense spectralCHANGES well, butCHANGES well, butnot wavelengthnot wavelength

– MetamerismMetamerism

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

Visible Light MeasurementVisible Light Measurement

• Measurement of Light—easy. Perception?—hardMeasurement of Light—easy. Perception?—hard..– ‘‘Color’ ==crudely perceived wavelength spectrumColor’ ==crudely perceived wavelength spectrum– 3 sensed dimensions from spectra.3 sensed dimensions from spectra.– CIE-standard X,Y,Z color spectra: linear coord. system CIE-standard X,Y,Z color spectra: linear coord. system

for spectra that spans all perceivable colors X,Y,Zfor spectra that spans all perceivable colors X,Y,Z– Projective! Projective! luminance = Z luminance = Z

chromaticity = (x,y) = (X/Z, Y/Z)chromaticity = (x,y) = (X/Z, Y/Z)– NOT perceptually uniform... (MacAdam’s ellipses...)NOT perceptually uniform... (MacAdam’s ellipses...)

• Many Standard Texts, tutorials on colorMany Standard Texts, tutorials on color– Good: Good: http://www.colourware.co.uk/cpfaq.htmhttp://www.colourware.co.uk/cpfaq.htm– Good: Good: http://www.yorku.ca/eye/toc.htmhttp://www.yorku.ca/eye/toc.htm – Watt & Watt pg 277-281Watt & Watt pg 277-281

Incident Light MeasurementIncident Light Measurement

• Flux Flux WW = power, Watts, # photons/sec = power, Watts, # photons/sec

• Uniform, point-source light: Uniform, point-source light: flux falls with distanceflux falls with distance22

E = Watts/rE = Watts/r22

rr

Light MeasurementLight Measurement

• Flux Flux WW = power, Watts, # photons/sec = power, Watts, # photons/sec

• Irradiance Irradiance EE: flux arriving : flux arriving per unit areaper unit area,,(regardless of direction)(regardless of direction)

E = Watts/area = dW/dAE = Watts/area = dW/dA

But direction makes a But direction makes a big difference when big difference when

computing E...computing E...

Foreshortening Effect: cos(Foreshortening Effect: cos())

• Larger Incident angle Larger Incident angle ii

spreads same flux over larger areaspreads same flux over larger area

• flux per unit area becomes flux per unit area becomes W cos( W cos( ii) / ) / areaarea

• Foreshortening geometry imposes Foreshortening geometry imposes an angular term cos(an angular term cos(ii) on energy transfer) on energy transfer

circular ‘bundle’ circular ‘bundle’ of incident rays, of incident rays,

flux Wflux W

WW ii

Irradiance EIrradiance E

• To find irradiance at a point on a surface,To find irradiance at a point on a surface,• Find flux from each (point?) light source,Find flux from each (point?) light source,• Weight flux by its direction:Weight flux by its direction: cos( cos(ii) ) • Add all light sources: or more precisely, Add all light sources: or more precisely,

integrate over entire hemisphere integrate over entire hemisphere Defines Radiance L:Defines Radiance L:

L = (watts / area) / srL = (watts / area) / sr(sr = steradians; solid angle; (sr = steradians; solid angle;

= surface area on unit sphere)= surface area on unit sphere)

Radiance LRadiance L

• But for distributed (non-point) light sources? But for distributed (non-point) light sources? integrate flux over the entire hemisphere integrate flux over the entire hemisphere ..

But are units of what we integrate?But are units of what we integrate?

Radiance LRadiance L

L = (watts / area) / srL = (watts / area) / sr(sr = steradians; solid angle; (sr = steradians; solid angle;

= surface area on unit sphere)= surface area on unit sphere)

Lighting InvariantsLighting Invariants

Why doesn’t surface intensity change with distance?Why doesn’t surface intensity change with distance?

• We know point source flux drops with distance: 1/rWe know point source flux drops with distance: 1/r22 • We know surface is made of infinitesimal point sources...We know surface is made of infinitesimal point sources...

CamCam‘‘intensity’: 1/rintensity’: 1/r22

‘‘intensity’: constant (?!?!) intensity’: constant (?!?!)

Lighting InvariantsLighting Invariants

Why doesn’t surface intensity change with distance?Why doesn’t surface intensity change with distance?

Because camera pixels measure Because camera pixels measure RadianceRadiance, not flux!, not flux!– pixel value pixel value flux *cos( flux *cos() / sr) / sr– ‘‘good lens’ design: cos(good lens’ design: cos() term vanishes. Vignetting=residual error.) term vanishes. Vignetting=residual error.

• Pixel’s size in sr fixed:Pixel’s size in sr fixed:– Point source fits in one pixel: 1/rPoint source fits in one pixel: 1/r22

– Viewed surface area grows by rViewed surface area grows by r22, , cancels 1/rcancels 1/r22 flux falloff flux falloff

CamCam‘‘intensity’: 1/rintensity’: 1/r22

‘‘intensity’: constant (?!?!) intensity’: constant (?!?!)

Point-wise Light ReflectionPoint-wise Light Reflection

• Given:Given:– Infinitesimal surface patch Infinitesimal surface patch dAdA, , – illuminated by irradiance amount illuminated by irradiance amount EE

– from just one direction from just one direction ((ii,,ii))

• How should we measure the returned light?How should we measure the returned light?• Ans: Ans: by emittedby emitted

RADIANCERADIANCEmeasured for allmeasured for alloutgoing directions:outgoing directions:(measured on surface of (measured on surface of ))

dAdAii

ii

Point-wise Light Reflection: BRDFPoint-wise Light Reflection: BRDF

BBidirectional idirectional RReflectance eflectance DDistribution istribution FFunction unction

FFrr((ii,,II,,ee,,ee)) = = LLee((ee,,ee) / E) / Eii((ii,,ii))

• Still a ratio (outgoing/incoming) light, butStill a ratio (outgoing/incoming) light, but• BRDF: BRDF: Ratio of Ratio of

outgoing outgoing RADIANCERADIANCE in one direction: in one direction: LLee((ee,,ee))that results from that results from incoming incoming IRRADIANCEIRRADIANCE in one direction: in one direction: EEii((ii,,ii))

• Units are tricky:Units are tricky:

BRDF = FBRDF = Frr = L = Le e // EEii

dAdAii

ii

LLeeEEii

Point-wise Light Reflection: BRDFPoint-wise Light Reflection: BRDF

BBidirectional idirectional RReflectance eflectance DDistribution istribution FFunction unction

FFrr((ii,,II,,ee,,ee)) = = LLee((ee,,ee) / E) / Eii((ii,,ii))

• Still a ratio (outgoing/incoming) light, butStill a ratio (outgoing/incoming) light, but• BRDF: Ratio of BRDF: Ratio of

outgoing RADIANCE in one direction: Loutgoing RADIANCE in one direction: Lee((ee,,ee))that results from that results from incoming IRRADIANCE in one direction: Eincoming IRRADIANCE in one direction: E ii((ii,,ii))

• Units are tricky:Units are tricky:

BRDF = FBRDF = Frr = L = Le e // EEii = ( Watts/area) / = ( Watts/area) /

((Watts/area) /sr))((Watts/area) /sr))

dAdAii

ii

LLeeEEii

Point-wise Light Reflection: BRDFPoint-wise Light Reflection: BRDF

BBidirectional idirectional RReflectance eflectance DDistribution istribution FFunction unction

FFrr((ii,,II,,ee,,ee)) = = LLee((ee,,ee) / E) / Eii((ii,,ii))

• Still a ratio (outgoing/incoming) light, butStill a ratio (outgoing/incoming) light, but• BRDF: Ratio of BRDF: Ratio of

outgoing RADIANCE in one direction: Loutgoing RADIANCE in one direction: Lee((ee,,ee))that results from that results from incoming IRRADIANCE in one direction: Eincoming IRRADIANCE in one direction: E ii((ii,,ii))

• Units are tricky:Units are tricky:

BRDF = FBRDF = Frr = L = Le e // EEii = ( Watts/area) / = ( Watts/area) / = 1/sr = 1/sr

((Watts/area) /sr))((Watts/area) /sr))

Point-wise Light Reflection: BRDFPoint-wise Light Reflection: BRDF

BBidirectional idirectional RReflectance eflectance DDistribution istribution FFunction unction FFrr((ii,,II,,ee,,ee)) = = LLee((ee,,ee) / E) / Eii((ii,,ii), and (1/sr)units), and (1/sr)units

• ‘‘Bidirectional’ because value is SAME if we Bidirectional’ because value is SAME if we swap in,out directions: swap in,out directions: ((ee,,ee)) ((ii,,ii))

Important Property! aka ‘Helmholtz Reciprocity’Important Property! aka ‘Helmholtz Reciprocity’

• BRDF Results from surface’sBRDF Results from surface’smicroscopic structure...microscopic structure...

• Still only an approximation:Still only an approximation: ignores subsurface scattering... ignores subsurface scattering...

dAdAii

ii

LLeeEEii

‘‘Scene’ causes Light FieldScene’ causes Light Field

What measures light rays in, out of scene? What measures light rays in, out of scene?

Measure Light LEAVING a Scene?Measure Light LEAVING a Scene?

Towards a camera?...Towards a camera?...

Measure Light LEAVING a Scene?Measure Light LEAVING a Scene?

Towards a camera: Towards a camera: Radiance. Radiance.

Light Field ImagesLight Field Imagesmeasure Radiancemeasure Radiance L(x,y)L(x,y)

Measure light ENTERING a scene?Measure light ENTERING a scene?

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

Measure light ENTERING a scene?Measure light ENTERING a scene?

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

‘‘Light Map’ Images Light Map’ Images (texture map light source)(texture map light source)

describes Irradiancedescribes Irradiance E(x,y)E(x,y)

Measure light ENTERING a scene?Measure light ENTERING a scene?

leaving a video projector lens?leaving a video projector lens?

RadianceRadiance LL‘‘Reversed’ Camera:Reversed’ Camera:emits Radianceemits Radiance L(x,y)L(x,y)

Measure light ENTERING a scene?Measure light ENTERING a scene?

from a video projector?—Leaving Lens: from a video projector?—Leaving Lens: Radiance Radiance LL

IrradianceIrradiance EE

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