Measuring Material Appearance: BRDF, BSSRDF, BTF Computer Graphics, Fall 2009 Mohit Gupta

110 Pages·2009·5.05 MB·English

Measuring Material Appearance:
BRDF, BSSRDF, BTF
Computer Graphics, Fall 2009
Mohit Gupta
Thanks to Steve Marschner, Shree Nayar, Ravi Ramamoorthi, Szymon Rusinkiewicz,
Images Courtest Ben-Ezra et al Marc Levoy, Pat Hanrahan, Kristin Dana, Ken Perlin, Debevec, Matusik
A variety of material appearances
Methods Relying on Surface Reflectance
Shape from Shading Texture Modeling
Reflection Separation
Photometric Stereo
Mechanisms of Reflection
source
incident
surface
direction
reflection
body
reflection
surface
Surface Reflection: Body Reflection:
Specular Reflection Diffuse Reflection
Glossy Appearance Matte Appearance
Highlights Non-Homogeneous Medium
Dominant for Metals Clay, paper, etc
Image Intensity = Body Reflection + Surface Reflection
Mechanisms of Reflection
Surface Reflection:
Body Reflection:
Specular Reflection
Diffuse Reflection
Glossy Appearance
Matte Appearance
Highlights
Non-Homogeneous Medium
Dominant for Metals
Clay, paper, etc
Many materials exhibit both Reflections:
Surface Appearance
sensor
source
normal
surface
element
Image intensities = f ( normal, surface reflectance, illumination )
Surface Reflection depends on both the viewing and illumination
directions.
BRDF: Bidirectional Reflectance
Distribution Function
source
z
incident
direction viewing
direction

(,) ( ,)
i i r r
normal
y

surface
element
x
Esurface(,) Irradiance at Surface in direction (,)
i i i i
Lsurface( ,) Radiance of Surface in direction ( ,)
r r r r
Lsurface( ,)
f (,; ,)  r r
BRDF :
i i r r Esurface(,)
i i
Derivation of the Scene Radiance Equation
src
L (,)
i i
surface
L ( , )
r r
From the definition of BRDF:
surface surface
L ( , )  E (,) f (,; , )
r r i i i i r r
Important Properties of BRDFs
source
z
incident
direction viewing
direction

(,) ( ,)
i i r r
normal
y

surface
x
element
• Rotational Symmetry:
BRDF does not change when surface is rotated about the normal.
f (, , )
BRDF is only a function of 3 variables :
i r i r
• Helmholtz Reciprocity: (follows from 2nd Law of Thermodynamics)
BRDF does not change when source and viewing directions are swapped.
f (,; ,)  f ( ,;,)
i i r r r r i i
Specular Reflection and Mirror BRDF
I
source intensity
specular/mirror
r
direction ( ,)
r r
incident
s
direction n
normal
(,)
i i
viewing
v
( , )
direction
surface v v
element
• Very smooth surface.
v r
• All incident light energy reflected in a SINGLE direction. (only when = )
• Mirror BRDF is simply a double-delta function :
specular albedo
f (,; ,)   (  )( )
i i v v s i v i v
• Surface Radiance : L  I  (  )( )
s i v i v