Bi-directional Reflectance Distribution Function ... - Semantic Scholar
Bi-directional Reflectance Distribution Function (BRDF) Ruigang Yang CS 684
CS684
1
What is BRDF
CS684
2
BRDF
Depends on
Incoming light direction Viewing direction Wave Length Position
BRDFλ (θ i , φi , θ o , φo , u , v) CS684
3
Shift-Invariant BRDF BRDFλ (θ i , φi ,θ o , φo )
ApproximationÆ Texture map In CG, λ=R, G, or B
CS684
4
Spherical Coordinates Cartesian Æ Spherical
Spherical Æ Cartesian
CS684
5
Differential Solid Angles
CS684
6
Solid Angle
CS684
7
CS684
8
BRDF
The ratio of the quantity of reflected light in direction wo, to the amount of light that reaches the surface from direction wi.
Wo
Wi
CS684
9
Definition of BRDF
First attempt:
Φ det fr = Φ src
Source Φsrc ωi
Detector Φdet ωo
CS684
10
Definition of BRDF
Should fr vary with ωi?
Source Φsrc ωi
YES
Detector Φdet ωo
CS684
11
Definition of BRDF
Should fr vary with ωo?
Source Φsrc ωi
YES
Detector Φdet ωo
CS684
12
Definition of BRDF
What about surface area? fr must be independent of surface area Source Φsrc ωi
Detector Φdet ωo
dA CS684
13
Definition of BRDF
Radiance
Φ det (ω det ⋅ dA ) L fr = = Φ src dA E Irradiance
Source Φsrc ωi
Detector Φdet ωo
CS684
14
Radiance
W/m2/sr
CS684
15
Irradiance
W/m2
CS684
16
Digression
CS684
17
CS684
18
CS684
19
Properties of the BRDF
Unit: 1/sr Energy conservation
Helmholtz reciprocity
Not always obeyed by “BRDF” models in graphics CS684
20
Isotropy
A BRDF is isotropic if it stays the same when the surface is rotated around normal
Æ3D function
BRDF = (θ i , θ o , φi − φo ) CS684
21
Anisotropy
Depend on surface rotation
D. McAllister, 2002 CS684
22
CS684
23
CS684
24
CS684
25
CS684
26
CS684
27
BRDF Representation
Physically based vs. empirical model
Phong: for glossy reflection Torrance-Sparrow BRDF: assume surface consisting of tiny “microfacets”, with mirroreflection off each
CS684
28
Measuring BRDFs
A full BRDF is 4-dimensional Simpler measurements often useful Start with the simplest, and get more complex
CS684
29
Measuring Reflectance
0º/45º Diffuse Measurement
45º/45º Specular Measurement CS684
30
BRDF Measurements
Next step up in complexity: measure BRDF in plane of incidence (1- or 2-D)
CS684
31
Gonioreflectometers
Three degrees of freedom spread among light source, detector, and/or sample
CS684
32
Gonioreflectometers
Three degrees of freedom spread among light source, detector, and/or sample
CS684
33
Gonioreflectometers
Can add fourth degree of freedom to measure anisotropic BRDFs
CS684
34
Spatial Gonioreflectometer
Six degrees of freedom
D. McAllister, 2002 CS684
35
Issues in BRDF Measurement
Light source: angular size, brightness, stability, speckle Detector: angular size, sensitivity, noise, resolution (if spatially varying) Positioning: accuracy, drift Acquisition time
CS684
36
Image-Based BRDF Measurement
Reduce acquisition time by obtaining larger (e.g. 2-D) slices of BRDF at once Requires mapping of angles of light to camera pixels
CS684
37
Ward’s BRDF Measurement Setup
Collect reflected light with hemispherical (should be ellipsoidal) mirror [SIGGRAPH 92]
CS684
38
Ward’s BRDF Measurement Setup
Result: each image captures light at all exitant angles
CS684
39
Marschner’s Image-Based BRDF Measurement
For uniform BRDF, capture 2-D slice corresponding to variations in normals
CS684
40
Marschner’s Image-Based BRDF Measurement
Any object with known geometry
CS684
41
BRDF Measurement is Hard!
Result of fitting model to Ward’s measurements
CS684
42
CS684
1
What is BRDF
CS684
2
BRDF
Depends on
Incoming light direction Viewing direction Wave Length Position
BRDFλ (θ i , φi , θ o , φo , u , v) CS684
3
Shift-Invariant BRDF BRDFλ (θ i , φi ,θ o , φo )
ApproximationÆ Texture map In CG, λ=R, G, or B
CS684
4
Spherical Coordinates Cartesian Æ Spherical
Spherical Æ Cartesian
CS684
5
Differential Solid Angles
CS684
6
Solid Angle
CS684
7
CS684
8
BRDF
The ratio of the quantity of reflected light in direction wo, to the amount of light that reaches the surface from direction wi.
Wo
Wi
CS684
9
Definition of BRDF
First attempt:
Φ det fr = Φ src
Source Φsrc ωi
Detector Φdet ωo
CS684
10
Definition of BRDF
Should fr vary with ωi?
Source Φsrc ωi
YES
Detector Φdet ωo
CS684
11
Definition of BRDF
Should fr vary with ωo?
Source Φsrc ωi
YES
Detector Φdet ωo
CS684
12
Definition of BRDF
What about surface area? fr must be independent of surface area Source Φsrc ωi
Detector Φdet ωo
dA CS684
13
Definition of BRDF
Radiance
Φ det (ω det ⋅ dA ) L fr = = Φ src dA E Irradiance
Source Φsrc ωi
Detector Φdet ωo
CS684
14
Radiance
W/m2/sr
CS684
15
Irradiance
W/m2
CS684
16
Digression
CS684
17
CS684
18
CS684
19
Properties of the BRDF
Unit: 1/sr Energy conservation
Helmholtz reciprocity
Not always obeyed by “BRDF” models in graphics CS684
20
Isotropy
A BRDF is isotropic if it stays the same when the surface is rotated around normal
Æ3D function
BRDF = (θ i , θ o , φi − φo ) CS684
21
Anisotropy
Depend on surface rotation
D. McAllister, 2002 CS684
22
CS684
23
CS684
24
CS684
25
CS684
26
CS684
27
BRDF Representation
Physically based vs. empirical model
Phong: for glossy reflection Torrance-Sparrow BRDF: assume surface consisting of tiny “microfacets”, with mirroreflection off each
CS684
28
Measuring BRDFs
A full BRDF is 4-dimensional Simpler measurements often useful Start with the simplest, and get more complex
CS684
29
Measuring Reflectance
0º/45º Diffuse Measurement
45º/45º Specular Measurement CS684
30
BRDF Measurements
Next step up in complexity: measure BRDF in plane of incidence (1- or 2-D)
CS684
31
Gonioreflectometers
Three degrees of freedom spread among light source, detector, and/or sample
CS684
32
Gonioreflectometers
Three degrees of freedom spread among light source, detector, and/or sample
CS684
33
Gonioreflectometers
Can add fourth degree of freedom to measure anisotropic BRDFs
CS684
34
Spatial Gonioreflectometer
Six degrees of freedom
D. McAllister, 2002 CS684
35
Issues in BRDF Measurement
Light source: angular size, brightness, stability, speckle Detector: angular size, sensitivity, noise, resolution (if spatially varying) Positioning: accuracy, drift Acquisition time
CS684
36
Image-Based BRDF Measurement
Reduce acquisition time by obtaining larger (e.g. 2-D) slices of BRDF at once Requires mapping of angles of light to camera pixels
CS684
37
Ward’s BRDF Measurement Setup
Collect reflected light with hemispherical (should be ellipsoidal) mirror [SIGGRAPH 92]
CS684
38
Ward’s BRDF Measurement Setup
Result: each image captures light at all exitant angles
CS684
39
Marschner’s Image-Based BRDF Measurement
For uniform BRDF, capture 2-D slice corresponding to variations in normals
CS684
40
Marschner’s Image-Based BRDF Measurement
Any object with known geometry
CS684
41
BRDF Measurement is Hard!
Result of fitting model to Ward’s measurements
CS684
42
