1. CS 395/495-25: Spring 2003 IBMR: Week 9A Image-Based Physics: Measuring Light & Materials Jack Tumblin jet@cs.northwestern.edu

2. Reminders 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 encouraged.MidTerm graded: novel solutions encouraged. ProjC due Friday, May 16: many rec’d...ProjC due Friday, May 16: many rec’d... ProjD posted, due Friday May 30ProjD posted, due Friday May 30 Take-Home Final Exam: Assign on Thurs June 5, due June 11Take-Home Final Exam: Assign on Thurs June 5, due June 11

3. IBMR: Rendering from Light Rays How can we measure ‘rays’ of light? Light Sources? Scattered rays? etc. Shape,Position,Movement, BRDF,Texture,Scattering EmittedLight Reflected,Scattered, Light … Cameras capture subset of these rays.

4. Visible Light Measurement ‘Visible Light’ = what our eyes can perceive;‘Visible Light’ = what our eyes can perceive; –narrow-band electromagnetic energy:  400-700 nm (nm = 10 -9 meter)  400-700 nm (nm = 10 -9 meter) <1 octave; (honey bees: 3-4 ‘octaves’ ?chords?) Not uniformly visible vs. wavelength :Not uniformly visible vs. wavelength : –Equiluminant Curve  defines ‘luminance’ vs. wavelength –eyes sense spectral CHANGES well, but not wavelength –Metamerism http://www.yorku.ca/eye/photopik.htm

5. Visible Light Measurement Measurement of Light—easy. Perception?—hard.Measurement of Light—easy. 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... (MacAdam’s ellipses...) Many Standard Texts, tutorials on colorMany Standard Texts, tutorials on color –Good: http://www.colourware.co.uk/cpfaq.htm http://www.colourware.co.uk/cpfaq.htm –Good: http://www.yorku.ca/eye/toc.htm http://www.yorku.ca/eye/toc.htm –Watt & Watt pg 277-281

6. Incident Light Measurement Flux W = power, Watts, # photons/secFlux W = power, Watts, # photons/sec Uniform, point-source light: flux falls with distance 2Uniform, point-source light: flux falls with distance 2 E = Watts/r 2 r

7. Light Measurement Flux W = power, Watts, # photons/secFlux W = power, Watts, # photons/sec Irradiance E: flux arriving per unit area, (regardless of direction)Irradiance E: flux arriving per unit area, (regardless of direction) E = Watts/area = dW/dA But direction makes a big difference when computing E...

8. Foreshortening Effect: cos(  ) Larger Incident angle  i spreads same flux over larger areaLarger Incident angle  i spreads same flux over larger area flux per unit area becomes W cos(  i ) / areaflux per unit area becomes W cos(  i ) / area Foreshortening geometry imposes an angular term cos(  i ) on energy transferForeshortening geometry imposes an angular term cos(  i ) on energy transfer circular ‘bundle’ of incident rays, flux W W iiii

9. Irradiance 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: cos(  i )Weight flux by its direction: cos(  i ) Add all light sources: or more precisely, integrate over entire hemisphere 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) 

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

11. Lighting Invariants Why doesn’t surface intensity change with distance? We know point source flux drops with distance: 1/r 2We know point source flux drops with distance: 1/r 2 We know surface is made of infinitesimal point sources...We know surface is made of infinitesimal point sources... Cam ‘intensity’: 1/r 2 ‘intensity’: constant (?!?!)

12. Lighting Invariants Why doesn’t surface intensity change with distance? Because camera pixels measure Radiance, not flux! Because camera pixels measure Radiance, not flux! –pixel value  flux *cos(  ) / sr –‘good lens’ design: cos(  ) term vanishes. Vignetting=residual error. Pixel’s size in sr fixed:Pixel’s size in sr fixed: –Point source fits in one pixel: 1/r 2 –Viewed surface area grows by r 2, cancels 1/r 2 flux falloff Cam ‘intensity’: 1/r 2 ‘intensity’: constant (?!?!)

13. Point-wise Light Reflection Given:Given: –Infinitesimal surface patch dA, –illuminated by irradiance amount E –from just one direction (  i,  i ) How should we measure the returned light?How should we measure the returned light? Ans: by emitted RADIANCE measured for all outgoing directions: (measured on surface of  )Ans: by emitted RADIANCE measured for all outgoing directions: (measured on surface of  )  dA iiii iiii

14. Point-wise Light Reflection: BRDF Bidirectional Reflectance Distribution Function F r (  i,  I,  e,  e ) = L e (  e,  e ) / E i (  i,  i ) Still a ratio (outgoing/incoming) light, butStill a ratio (outgoing/incoming) light, but BRDF: Ratio of outgoing RADIANCE in one direction: L e (  e,  e ) that results from incoming IRRADIANCE in one direction: E i (  i,  i )BRDF: Ratio of outgoing RADIANCE in one direction: L e (  e,  e ) that results from incoming IRRADIANCE in one direction: E i (  i,  i ) Units are tricky: BRDF = F r = L e / E iUnits are tricky: BRDF = F r = L e / E i  dA iiii iiii LeLeLeLe EiEiEiEi

15. Point-wise Light Reflection: BRDF Bidirectional Reflectance Distribution Function F r (  i,  I,  e,  e ) = L e (  e,  e ) / E i (  i,  i ) Still a ratio (outgoing/incoming) light, butStill a ratio (outgoing/incoming) light, but BRDF: Ratio of outgoing RADIANCE in one direction: L e (  e,  e ) that results from incoming IRRADIANCE in one direction: E i (  i,  i )BRDF: Ratio of outgoing RADIANCE in one direction: L e (  e,  e ) that results from incoming IRRADIANCE in one direction: E i (  i,  i ) Units are tricky: BRDF = F r = L e / E i = ( Watts/area) /Units are tricky: BRDF = F r = L e / E i = ( Watts/area) / ((Watts/area) /sr))  dA iiii iiii LeLeLeLe EiEiEiEi

16. Point-wise Light Reflection: BRDF Bidirectional Reflectance Distribution Function F r (  i,  I,  e,  e ) = L e (  e,  e ) / E i (  i,  i ) Still a ratio (outgoing/incoming) light, butStill a ratio (outgoing/incoming) light, but BRDF: Ratio of outgoing RADIANCE in one direction: L e (  e,  e ) that results from incoming IRRADIANCE in one direction: E i (  i,  i )BRDF: Ratio of outgoing RADIANCE in one direction: L e (  e,  e ) that results from incoming IRRADIANCE in one direction: E i (  i,  i ) Units are tricky: BRDF = F r = L e / E i = ( Watts/area) / = 1/srUnits are tricky: BRDF = F r = L e / E i = ( Watts/area) / = 1/sr ((Watts/area) /sr))

17. Point-wise Light Reflection: BRDF Bidirectional Reflectance Distribution Function F r (  i,  I,  e,  e ) = L e (  e,  e ) / E i (  i,  i ), and (1/sr)units ‘Bidirectional’ because value is SAME if we swap in,out directions: (  e,  e )  (  i,  i )‘Bidirectional’ because value is SAME if we swap in,out directions: (  e,  e )  (  i,  i ) Important Property! aka ‘Helmholtz Reciprocity’ BRDF Results from surface’s microscopic structure...BRDF Results from surface’s microscopic structure... Still only an approximation: ignores subsurface scattering...Still only an approximation: ignores subsurface scattering...  dA iiii iiii LeLeLeLe EiEiEiEi

18. ‘Scene’ causes Light Field What measures light rays in, out of scene?

19. Measure Light LEAVING a Scene? Measure Light LEAVING a Scene? Towards a camera?...

20. Measure Light LEAVING a Scene? Measure Light LEAVING a Scene? Towards a camera: Radiance. Light Field Images measure Radiance L(x,y)

21. Measure light ENTERING a scene? from a (collection of) point sources at infinity?

22. 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)

23. Measure light ENTERING a scene? leaving a video projector lens? Radiance L ‘Reversed’ Camera: emits Radiance L(x,y)

24. Measure light ENTERING a scene? from a video projector?—Leaving Lens: Radiance L Irradiance E

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