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	   CS 99D - Light and shadow lecture #2 - February 15, 2001

				  Marc Levoy
			      Stanford University
				   (c) 2001

		      (with corrections, March 14, 2003)

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			      *** Reflection II ***

Reflection from surfaces II - from physical optics:
	o Augustin Fresnel (1819)
		o equations for reflection and refraction of waves at a surface
		o reflectance depends on angle of incidence
			==> Piece of paper at grazing angle
		o color depends on angle of incidence
			==> Clean penny
		o lustre of metals = color of metal; of glass = color of light
			==> Penny & copper-colored book cover

		o Examples:  (at normal incidence) (Minneart, p. 102)
			o clouds	80%
			o fresh snow	80%	(equality explains "whiteout"!)
			o old snow	40%
			o grass		30%
			o soil		15%
			o rivers	7%
			o ocean		3%

		o reflection vrs. transmission
			-> green glass pieces of varying sizes,
			   Hunter, p. 36 (B&W) or slide from Gary Meyer
			o white paint is titanium dioxide in an acrylic base,
			  both transparent!

	o anisotropic reflectance
		o draw general BRDF
		o can be modeled by parallel cylinders
			-> Westin, Arvo, Torrance, Siggraph '92, p. 261,263
		o explosion in dimensionality

	o interference colors, etc.
		==> mother of pearl, glass pyramid

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				*** Shadow ***

Types of shadows:
	o attached - beyond shadow horizon
	o cast ("projected") - separated from occluder by empty space
	o no visible distinction between these two
		-> chin-to-neck on Leonardo's head,
		   Leonardo on Painting, p. 92

Shadows from point sources:
	o illuminated surfaces form a perspective view taken from point source
	o infinitely distant point sources correspond to a parallel view
	o shadow edges can be computed by tracing rays from point source
	  through occluder vertices onto other surfaces in the scene
		-> illustrations from Lambert (1759),
		   Baxandall, p. 101

Shadows from area sources:
	o Leonardo (p. 103, 105)
		o there are no shadows on a mirror or clear water
			(right)

	o Johann Lambert (1760)
		o geometric analysis of penumbra
			-> Leonardo, p. 111, or
			   Leonardo's notebooks, vol. I, p. 125 (pl. 111)
		o penumbra as convolution of source and occluder

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			    *** Interreflection ***

Interreflections:
	o Leonardo (p. 110)
		o light "reverberates" from surface to surface ("percussions")
			(right)

	o basic features of interreflection
		o most light is reflected, or under table would be black
		o energy is conserved, so reflection must be weaker than source
		o if reflection depicted as stronger, surface seems luminous
		o color bleeding

			==> Demonstrate using colored paper near white wall

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		    *** Perception of light and shadow ***

Tonal cues:
	o absolute gray level - has little effect
	o tone relative to reflectance of known objects in scene
		o e.g. flesh
	o tone relative to assumed or deduced illumination
		o e.g. sun or moon
	o contrast between body color and highlights
		o high->black, low->white
		==> Demonstrate using polished stick of multi-colored marbles

Tonal illusions:
	o reduced/increased contrast at saturation/threshold (Helmholtz)
		o we saw examples of this in the first lecture
	o local contrast effects:
		-> Mach bands, Cornsweet, p. 276, 277,
		   or Solso, p. 64
		-> simultaneous contrast, Cornsweet, p. 279,
		   or Solso, p. 106
		-> Joseph Alber's two "X"'s, Wandell, p. 304+, color plate 2
	o artist should paint local contrasts, not global tone (Helmholtz)
		-> Seurat's La Grande  Jatte (1886), Gardner, , p. 995
		-> application to CG, Cowan, "Rendering with Limited Means"
		o optimize for local contrast, sacrificing global constancy

Shading cues:
	o overview of the field of computer vision
	o shading invariants
		-> Koenderink, Solid Shape

		(p. 297)
		o on a planar curve, curvature vanishes at points of inflection
		o on a surface, parabolic curves are curves of inflection
		o on these curves, one of the two principal curvatures vanish
		o at parabolic curves, the Guass map folds
			-> Show parabolic curve of Gaussian bump, p. 276

		o shading obeys invariants - independent of illumination
		o these invariants allow us to perceive shape from shading
		o they are often structured around the parabolic curves, e.g.
		o highlights will merge and split along parabolic curves
			-> Show highlights on marble ashtray

		(p. 480)
		o academics used to study shading via plaster, then via flesh
		o objects are sometimes painted white to allow study of shading
		o dark white or gray reduces interreflection ("reflexes")
		o uniform illumination reduces cast shadows ("vignetting")
			-> Felix Klein's parabolic lines on the Apollo, p. 489,
			   done in an attempt to derive a theory of beauty!
				(original is in Gardner, p. 163)

Shading illusions:
	o shading versus (assumed) lighting
		-> Ramachandran's eggshell inversions, Solso, p. 167

	o bas-relief ambiguity
		-> Proc. CVPR '97, p. 1060

Shadow cues:
	o cast shadows
		o presence of shadow relates occluder, receiver, and light
		o shape of shadow gives shape of occluder and/or receiver
		o light should come from side, for maximum shadows (Helmholtz)
		o shadows near strong light are complementary color (Helmholtz)

		-> Seurat's La Grande Jatte (1886), Gardner, p. 995

Interreflection cues:
	o contrast between directly and indirectly illuminated surfaces

		==> Demonstrate using reconstruction of Jacobsen's box

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