3-D Computer Vision CSc83029 / Ioannis Stamos 3-D Computer Vision CSc 83029 Radiometry and...
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Transcript of 3-D Computer Vision CSc83029 / Ioannis Stamos 3-D Computer Vision CSc 83029 Radiometry and...
3-D Computer Vision CSc83029 / Ioannis Stamos3-D Computer Vision CSc83029 / Ioannis Stamos
3-D Computer Vision3-D Computer VisionCSc 83029CSc 83029
Radiometry and ReflectanceRadiometry and Reflectance
3-D Computer Vision CSc83029 / Ioannis Stamos3-D Computer Vision CSc83029 / Ioannis Stamos
From 2D to 3DFrom 2D to 3D
DEPTH from TWO or MORE IMAGESDEPTH from TWO or MORE IMAGES StereoStereo Optical Flow -> Factorization Method.Optical Flow -> Factorization Method.
SHAPE from SINGLE IMAGE CUESSHAPE from SINGLE IMAGE CUES SHAPE from SHADINGSHAPE from SHADING SHAPE from TEXTURESHAPE from TEXTURE ……
3-D Computer Vision CSc83029 / Ioannis Stamos3-D Computer Vision CSc83029 / Ioannis Stamos
Shading Encodes ShapeShading Encodes Shape
3-D Computer Vision CSc83029 / Ioannis Stamos3-D Computer Vision CSc83029 / Ioannis Stamos
Radiometry and ReflectanceRadiometry and Reflectance
n
I
Image Intensity I = f ( orientation n,surface reflectance,illumination, imaging system )
L
Surface Element
Note: Image Intensity Understanding is an under-constrained problem!
3-D Computer Vision CSc83029 / Ioannis Stamos3-D Computer Vision CSc83029 / Ioannis Stamos
Solid AngleSolid Angle
δω=(δA cosθ)/R (steradian)
δ
δω
2
Solid AngleSolid Angle
δω=(δA cosθ)/R (steradian)
δ
δω
2
Foreshortened Area
δA’
δω= δA’/R (steradian)2
Solid AngleSolid Angle
δω=(δA cosθ)/R (steradian)
δ
δω
2
Foreshortened Area
UnitSphere
δA’
δω= δA’/R (steradian)2
Solid Angle Sustainedby a hemisphere = 2π
n
Source
Flux
Radiant Intensity of Source: Light flux (power)emitted per unit solid angle:
J=dΦ/dω (watts/steradian)
dω
dA
Surface Irradiance: Flux incident per unit surface area:
E=dΦ/dA (watts/m )Does not depend on where the light is coming from!
2
Flux=dΦ
Surface Radiance(Brightness): Flux emitted per unit foreshortened area,
per unit solid angle:
L= d Φ/(dA cosθr)dω (watts/m . steradian)
Note: L depends on direction θr Surface can radiate into whole hemisphere L is proportional to irradiance E Depends on reflectance properties of surface
dω
dA
2
2
θr
2
3-D Computer Vision CSc83029 / Ioannis Stamos3-D Computer Vision CSc83029 / Ioannis Stamos
Surface Radiance & Image IrradianceSurface Radiance & Image Irradiance
E=δP/δI:Irradiance at point p (Watts/m )δP= (δO * cosθ)* L * ΔΩ , L scene radiance at P.
2
L (Watts/m * steradian)2Trucco & Verri
3-D Computer Vision CSc83029 / Ioannis Stamos3-D Computer Vision CSc83029 / Ioannis Stamos
F=f/d: F-number:How much lightis captured by the camera
Trucco & Verri
3-D Computer Vision CSc83029 / Ioannis Stamos3-D Computer Vision CSc83029 / Ioannis Stamos
Radiometry and ReflectanceRadiometry and Reflectance
n
I
Image Intensity I = f ( orientation n,surface reflectance,illumination, imaging system )
)(cos4
4
2
f
dLE
Scene radiance
L
Image irradiance
1 / F-number of lens
E
Optics
Brightness falloff
LE Assume Image irradiance is proportional to scene radiance
3-D Computer Vision CSc83029 / Ioannis Stamos3-D Computer Vision CSc83029 / Ioannis Stamos
Bi-Directional Reflectance Distribution Function Bi-Directional Reflectance Distribution Function (BRDF)(BRDF)
n ii , rr ,
yx
z
φ
θ
3-D Computer Vision CSc83029 / Ioannis Stamos3-D Computer Vision CSc83029 / Ioannis Stamos
Bi-Directional Reflectance Distribution Function Bi-Directional Reflectance Distribution Function (BRDF)(BRDF)
n ii , rr ,
yx
z
φ
θ
iiE , : Irradiance due to source in direction ii ,
rrL , : Radiance of surface in direction rr ,
ii
rrrrii E
Lf
,
,,,, BRDF:
3-D Computer Vision CSc83029 / Ioannis Stamos3-D Computer Vision CSc83029 / Ioannis Stamos
Bi-Directional Reflectance Distribution Function Bi-Directional Reflectance Distribution Function (BRDF)(BRDF)
n ii , rr ,
yx
z
φ
θ
iiE , : Irradiance due to source in direction ii ,
rrL , : Radiance of surface in direction rr ,
ii
rrrrii E
Lf
,
,,,, BRDF:
irrif ,,For Rotationally Symmetric Reflectance Properties:BDRF: ISOTROPIC SURFACES
*Bird Feathers are often Non-Isotropic.
3-D Computer Vision CSc83029 / Ioannis Stamos3-D Computer Vision CSc83029 / Ioannis Stamos
Reflectance ModelsReflectance Models*Reflection: An Electromagnetic Phenomenon
λ
τ
σh
Two Approaches to deriving Reflectance Models:Physical Optics (Wave Optics)Geometrical Optics (Ray Optics)
Geometrical Models are approximation to Physical Models.But easier to use.
3-D Computer Vision CSc83029 / Ioannis Stamos3-D Computer Vision CSc83029 / Ioannis Stamos
Surface Reflection
Body Reflection
Internal scattering
Body Reflection: *Diffuse Reflection *Matte Appearance *Non-Homogeneous Medium
Surface Reflection: *Specular Reflection *Glossy Appearance *Highlights. *Dominant for Metals
Image Intensity: Diffuse Comp + Specular Comp
Lambertian Reflectance ModelLambertian Reflectance Model
f Albedo: intrinsic brightness or color of surface
n
ikE cos
Theta is the angle between source direction and surface normal
s
i
A Lambertian (diffuse) surface scatters light equally in all directions
3-D Computer Vision CSc83029 / Ioannis Stamos3-D Computer Vision CSc83029 / Ioannis Stamos
Lambertian Reflectance ModelLambertian Reflectance Model
i
iirr
kL
EL
EfL
cos
, ,
Surface appears equally bright from all viewing directions
A Lambertian (diffuse) surface scatters light equally in all directions
Albedo: intrinsic brightness or color of surface
Illumination strength
f
n
i
s
ikE cos
3-D Computer Vision CSc83029 / Ioannis Stamos3-D Computer Vision CSc83029 / Ioannis Stamos
Lambertian Reflectance ModelLambertian Reflectance Model
sn
L
kL icos
A Lambertian sphere
ns
Surface normal nDirection of illumination s
Commonly used in Computer Vision and Graphics
Effective albedo
3-D Computer Vision CSc83029 / Ioannis Stamos3-D Computer Vision CSc83029 / Ioannis Stamos
What Information Does Shading What Information Does Shading EncodeEncode
In regions of constant albedo, changesof intensity correspond to changes in thesurface normal of the scene
sn LI
3-D Computer Vision CSc83029 / Ioannis Stamos3-D Computer Vision CSc83029 / Ioannis Stamos
Ideal Specular Model (Mirrors)Ideal Specular Model (Mirrors)
n
))(()( eieikL
Perfect reflector
sr
*Very SMOOTH surface*All incident energy reflected in a single direction
ii , rr ,
ee ,v
Viewer received light only when v=r
3-D Computer Vision CSc83029 / Ioannis Stamos3-D Computer Vision CSc83029 / Ioannis Stamos
Phong Reflectance ModelPhong Reflectance Model
b=0.3, c=0.7, n=2 b=0.7, c=0.3, n=0.5
ni cbL coscos
diffuse specular
v: viewingdirection
αθi
n
s
r
3-D Computer Vision CSc83029 / Ioannis Stamos3-D Computer Vision CSc83029 / Ioannis Stamos
Torrance-Sparrow ModelTorrance-Sparrow ModelSpecular Reflection from Rough Surfaces.Surface Micro-Structure Model
Facet orientationMean orientation α
Micro-facet Orientation Model: (example)
2
2
2
1
2
1)(
a
eap
(Gaussian Model) Isotropic
σ: roughness parameter
3-D Computer Vision CSc83029 / Ioannis Stamos3-D Computer Vision CSc83029 / Ioannis Stamos
Torrance-Sparrow ModelTorrance-Sparrow ModelMasking and Shadowing Effects
shadow shadow
Masked Light
n sr
v
Specular Direction
),,()( vnsGpvn
PL spec
Radiance
Geometric Factor G(Masking-Shadowing)
n’β