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Representations of Visual Appearance Representations of Visual Appearance
COMS 6160 [Spring 2007], Lecture 5
Brief lecture on 4D appearance functions
http://www.cs.columbia.edu/~ravir/6160
Taxonomy of AppearanceTaxonomy of Appearance
Slide courtesy Szymon Rusinkiewicz
General Plenoptic FunctionGeneral Plenoptic Function All knowledge of light in scene [Adelson 91]
Anywhere in space
In any direction
At any time instant
For any wavelength of light
Function of 7 variables, therefore 7D function
We care about taxonomy of scattering functions General Scattering Function is 14D (bet. two plenoptics)
( , , )x y z
( , )q f
( )t
( )l
( , , , , , , ; , , , , , , )i i i i i i i o o o o o o of x y z t x y z tq fl q fl
Common AssumptionsCommon Assumptions
Ignore time dependence (no phosphorescence or time-varying BRDF properties [but see work by Bo and Jinwei])
Ignore wavelength (no fluorescence, assume RGB)
Travel in free space, parameterize on surfaces (no z) Alternative for light fields: 4D space of rays (intersections in 2 planes)
Each of these removes 1D of plenoptic, 2D of scattering
Left with 8D function of greatest importance for class
8D Bi-Directional Surface Scattering Distribution Function (BSSRDF)( , , , ; , , , )i i i i o o o of x y x yq f q f
Taxonomy of 4D Scattering FunctionsTaxonomy of 4D Scattering Functions
Function of two spatial positions, two spherical angles (4 total)
4D appearance functions take 2 of these 4 (6 possibilities)
( , ; , )i i o of x xw wr rr r
Taxonomy of 4D Scattering FunctionsTaxonomy of 4D Scattering Functions
( , ; , )i i o of x xw wr rr r
( , )i of w wr r
BRDF is well studied function [Nicodemus 77]
( , )i if x wr r
Incident Light Field [Unger et al. 03]
( , )o of x wr r
Surface Light Field[Miller 98, Wood et al. 00, Nishino et al. 01, …]
( , )i of x xr r
Heterogeneous Subsurface Scattering[Peers et al. 06]
( , )i of xwrr
Reflectance Fields /Relighting [Debevec 00]
( , )i of x wr r
No easy interpretation
Historical Timeline: Details 4DHistorical Timeline: Details 4D
BRDFs have a long history (70s – 80s), but work on measuring them is accelerating in last 10 years
Light Field Rendering / Lumigraph Levoy and Hanrahan 96 ; Gortler et al. 96
Historical Timeline: Details 4DHistorical Timeline: Details 4D
BRDFs have a long history (70s – 80s), but work on measuring them is accelerating in last 10 years
Light Fields and more general 4D functions Reflectance fields (relighting faces) Debevec et al. 00 Surface Light Fields (Wood et al. 00 ; Nishino et al. 99) Incident Light Fields (Unger et al. 03 ; Goesele et al. 03) Heterogeneous Subsurface Scattering (Peers et al. 06)