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)