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CS 395/495-25: Spring 2004

CS 395/495-25: Spring 2004. IBMR: Measuring Lights, Materials, Lenses and more Jack Tumblin jet@cs.northwestern.edu. Recall: An Image Is…. Light + 3D Scene: Illumination, shape, movement, surface BRDF,… . 2D Image: A map of light intensities . A ‘Camera’:

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CS 395/495-25: Spring 2004

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  1. CS 395/495-25: Spring 2004 IBMR: Measuring Lights, Materials, Lenses and more Jack Tumblin jet@cs.northwestern.edu

  2. Recall: An Image Is… Light + 3D Scene: Illumination, shape, movement, surface BRDF,… 2D Image: A map of light intensities A ‘Camera’: ?What are ALL the possibilities? Position(x,y)

  3. An Planar Projection Image Is… Light + 3D Scene: Illumination, shape, movement, surface BRDF,… 2D Image: Collection of rays through a point Image Plane I(x,y) Position(x,y) Angle(,) ‘Center of Projection’ (P3 or P2 Origin)

  4. Image Making: Pinhole  Thin Lens • Interactive Thin Lens Demo (search ‘physlet optical bench’) http://www.swgc.mun.ca/physics/physlets/opticalbench.html • From this geometry (for next time) Can you derive Thin Lens Law?

  5. Incident Light Measurement • Flux W = power, Watts, # photons/sec • Uniform, point-source light: flux on a patch of surface falls with distance2 E = Watts/r2 r

  6. 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...

  7. Foreshortening Effect: cos() • Larger Incident angle ispreads 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

  8. 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) 

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

  10. Lighting Invariants Cam Why doesn’t 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 (?!?!)

  11. Lighting Invariants Cam Why doesn’t surface intensity change with distance? 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: • Point source fits in one pixel: 1/r2 • Viewed surface area grows by r2, cancels 1/r2 flux falloff Light ‘intensity’: 1/r2 Surface ‘intensity’: constant (?!?!)

  12. Lighting Invariants Radiance Images are LINEAR: ·(Radiance caused by (Light 1)) + ·(Radiance caused by (Light 2)) = Radiance caused by (· Light 1 +·Light 2) = + http://www.sgi.com/grafica/synth/index.html

  13. Lighting Invariants Light is Linear: ·(Radiance caused by (Light 1)) + ·(Radiance caused by (Light 2)) = Radiance caused by (· Light 1 +·Light 2) Allows ‘negative’ light! = - http://www.sgi.com/grafica/synth/index.html

  14. 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

  15. Point-wise Light Reflection: BRDF Le i Ei  dA i 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

  16. Point-wise Light Reflection: BRDF Le i Ei  dA i 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/sr) /(Watts/area)

  17. 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/sr) / = 1/sr (Watts/area)

  18. Point-wise Light Reflection: BRDF Le i Ei  dA i 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 surface’smicroscopic structure... • Still only an approximation: ignores subsurface scattering...

  19. Scattering Difficulties: Le i Ei  dA i For many surfaces, single-point BRDFs do not exist Example: Leaf Structure Angles Depend on refractive index, scattering, cell wall structures, etc. Depends on total area of cell wall interfaces

  20. Subsurface Scattering Models Classical: Kubelka-Monk(1930s, for paint; many proprietary variants), CG approach: Hanrahan & Krueger(1990s) More Recent: ‘dipole model’ (2001, Jensen) Marble BRDF Marble BSSRDF

  21. Subsurface Scattering Models Classical: Kubelka-Monk(1930s, for paint; many proprietary variants), CG approach: Hanrahan & Krueger(1990s) More Recent: ‘dipole model’ (2001, Jensen) Skin BRDF (measured) Skin BSSRDF (approximated)

  22. BSSRDF Model Approximates scattering result as embedded point sources below a BRDF surface: BSSRDF: “A Practical Model for Subsurface Light Transport” Henrik Wann Jensen, Steve Marschner, Marc Levoy, Pat Hanrahan, SIGGRAPH’01 (online)

  23. BSSRDF Model • Embedded point sources below a BRDF surface • Ray-based, tested, Physically-Measurable Model • ?Useful as a predictive model for IBMR data? Wann Jensen et al., 2001

  24. Summary: Light Measurement • Flux W = power, Watts, # photons/sec • Irradiance E = Watts/area = dW/dA • Radiance L = (Watts/area)/sr = (dW/dA)/sr • BRDF: Measure EMITTED radiance that results from INCOMING irradiance from just one direction:BRDF = Fr = Le / Ei = (Watts/area) / (Watts/areasr)

  25. IBMR Tools • Digital Light Input: • Light meter: measure visible irradiance E (some have plastic ‘dome’ to ensure accurate foreshortening) • Camera: pixels measure Radiance Li ; flux arriving at lens from one (narrow solid) angle • Digital Light Output: • Luminaires: point lights, extended(area) sources • Emissive Surfaces: CRT, LCD surface • Projectors: laser dot,stripe,scan; video display • Light Modifiers (Digital?): • Calibration objects, shadow sources, etc. • Lenses,diffusers, filters, reflectors, collimators... • ?Where are the BRDF displays / printers?

  26. Two Big Missing Pieces • Computer controlled BRDF. • Can we really do without it? • are cameras and projectors enough to ‘import the visible world’ into our computers? • BRDF is not enough: • Subsurface scattering is crucial aspect of photographed images • ? how can we model it? measure it? use it?

  27. More help: • GREAT explanation of BRDF: • www.cs.huji.ac.il/~danix/advanced/RenderingEq.pdf • Some questions about measuring light:

  28. END

  29. IBMR---May 13,2004: Projects? (due Tues May 25!) Let’s discuss them…

  30. Summary: Light Measurement • Flux W = power, Watts, # photons/sec • Irradiance E = Watts/area = dW/dA • Radiance L = (Watts/area)/sr = (dW/dA)/sr • BRDF: Measure EMITTED radiance that results from INCOMING irradiance from just one direction:BRDF = Fr = Le / Ei = (Watts/area) / (Watts/areasr)

  31. IBMR: Measure,Create, Modify Light How can we measure ‘rays’ of light? Light Sources? Scattered rays? etc. Cameras capture subset of these rays. Shape, Position, Movement, Emitted Light Reflected, Scattered, Light … BRDF, Texture, Scattering Digital light sources (Projectors) can produce a subset of these rays.

  32. ‘Scene’ modifies Set of Light Rays What measures light rays in, out of scene?

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

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

  35. Measure light ENTERING a Scene? from a (collection of) point sources at infinity?

  36. Measure light ENTERING a Scene? from a (collection of) point sources at infinity? ‘Light Map’ Images (texture map light source) describes IrradianceE(x,y)

  37. Measure light ENTERING a Scene? leaving a video projector lens? ‘Reversed’ Camera: emits RadianceL(x,y) RadianceL

  38. Measure light ENTERING a Scene? from a video projector?—Leaving Lens: RadianceL IrradianceE

  39. ‘Full 8-D Light Field’ (10-D, actually: time, ) • Cleaner Formulation: • Orthographic camera, • positioned on sphere around object/scene • Orthographic projector, • positioned on spherearound object/scene • (and wavelength and time) F(xc,yc,c,c,xl,yl l,l, , t) camera projector

  40. Summary: Light Measurement • Flux W = power, Watts, # photons/sec • Irradiance E = Watts/area = dW/dA • Radiance L = (Watts/area)/sr = (dW/dA)/sr • BRDF: Measure EMITTED radiance that results from INCOMING irradiance from just one direction:BRDF = Fr = Le / Ei = (Watts/area) / (Watts/areasr) Lenses map radiance to the image plane (x,y): THUS: Pixel x,y must measureRadiance L at x,y. well, not exactly; there are distortions!…

  41. What do Photos Measure? What We Want What We Get

  42. Film Response:(digital cameras, video cards too!)approximately linear, but ONLY on log-log axes.

  43. Two Key parameters: m == scale == exposure  == gamma == ‘contrastyness’

  44. Problem:Map Scene to Display Domain of Human Vision: from ~10-6 to ~10+8 cd/m2 starlight moonlight office light daylight flashbulb 10-6 10-2 1 10 100 10+4 10+8 ?? ?? 0 255 Range of Typical Displays: from ~1 to ~100 cd/m2

  45. High-Contrast Image Capture? • An open problem! (esp. for video...) • Direct (expensive) solution: • Flying Spot Radiometer: brute force instrument, costly, slow, delicate • Novel Image Sensors: line-scan cameras, logarithmic CMOS circuits, cooled detectors, rate-based detectors... • Most widely used idea: multiple exposures • Elegant paper (Debevec1996) describes how: (On class website)

  46. starlight moonlight office light daylight flashbulb Use Overlapped Exposure Values

  47. starlight moonlight office light daylight flashbulb Use Overlapped Exposure Values

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