basic principles of surface reflectance lecture #3
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Basic Principles of Surface Reflectance Lecture #3. Thanks to Shree Nayar, Ravi Ramamoorthi, Pat Hanrahan. Shape from Shading. Photometric Stereo. Reflection Separation. Texture Modeling. Methods Relying on Surface Reflectance. Camera. Physical Models. Computer. - PowerPoint PPT PresentationTRANSCRIPT
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Basic Principles of Surface Reflectance
Lecture #3
Thanks to Shree Nayar, Ravi Ramamoorthi, Pat Hanrahan
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Methods Relying on Surface Reflectance
Shape from Shading
Photometric Stereo Reflection Separation
Texture Modeling
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Computer Vision: Building Machines that See
Lighting
Scene
Camera
Computer
Physical Models
We need to understand the relation between the lighting, surface reflectance and medium and the image of the scene.
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Surface Appearance
Image intensities = f ( normal, surface reflectance, illumination )
Surface Reflection depends on both the viewing and illumination direction.
source sensor
surfaceelement
normal
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BRDF: Bidirectional Reflectance Distribution Function
x
y
z
source
viewingdirection
surfaceelement
normal
incidentdirection
),( ii ),( rr
),( iisurfaceE
),( rrsurfaceL
Irradiance at Surface in direction ),( ii Radiance of Surface in direction ),( rr
BRDF :),(
),(),;,(
iisurface
rrsurface
rrii E
Lf
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Important Properties of BRDFs
x
y
z
source
viewingdirection
surfaceelement
normal
incidentdirection
),( ii ),( rr
BRDF is only a function of 3 variables :
),;,(),;,( iirrrrii ff
• Rotational Symmetry:
BRDF does not change when surface is rotated about the normal.
),,( ririf
• Helmholtz Reciprocity: (follows from 2nd Law of Thermodynamics)
BRDF does not change when source and viewing directions are swapped.
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Derivation of the Scene Radiance Equation
),( iisrcL
),( rrsurfaceL
),;,(),(),( rriiiisurface
rrsurface fEL
From the definition of BRDF:
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Derivation of the Scene Radiance Equation – Important!
),;,(),(),( rriiiisurface
rrsurface fEL
iirriiiisrc
rrsurface dfLL cos),;,(),(),(
From the definition of BRDF:
Write Surface Irradiance in terms of Source Radiance:
Integrate over entire hemisphere of possible source directions:
2
cos),;,(),(),( iirriiiisrc
rrsurface dfLL
2/
0
sincos),;,(),(),( iiiirriiiisrc
rrsurface ddfLL
Convert from solid angle to theta-phi representation:
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Differential Solid Angle and Spherical Polar Coordinates
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Mechanisms of Reflection
source
surfacereflection
surface
incidentdirection
bodyreflection
Body Reflection:
Diffuse ReflectionMatte AppearanceNon-Homogeneous MediumClay, paper, etc
Surface Reflection:
Specular ReflectionGlossy AppearanceHighlightsDominant for Metals
Image Intensity = Body Reflection + Surface Reflection
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Mechanisms of Surface Reflection
Body Reflection:
Diffuse ReflectionMatte AppearanceNon-Homogeneous MediumClay, paper, etc
Surface Reflection:
Specular ReflectionGlossy AppearanceHighlightsDominant for Metals
Many materials exhibit both Reflections:
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Diffuse Reflection and Lambertian BRDF
viewingdirection
surfaceelement
normalincidentdirection
in
v
s
d
rriif ),;,(• Lambertian BRDF is simply a constant :albedo
• Surface appears equally bright from ALL directions! (independent of )
• Surface Radiance :
v
• Commonly used in Vision and Graphics!
snIIL di
d .cos
source intensity
source intensity I
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Diffuse Reflection and Lambertian BRDF
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White-out Conditions from an Overcast Sky
CAN’T perceive the shape of the snow covered terrain!
CAN perceive shape in regions lit by the street lamp!!
WHY?
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Diffuse Reflection from Uniform Sky
• Assume Lambertian Surface with Albedo = 1 (no absorption)
• Assume Sky radiance is constant
• Substituting in above Equation:
Radiance of any patch is the same as Sky radiance !! (white-out condition)
2/
0
sincos),;,(),(),( iiiirriiiisrc
rrsurface ddfLL
skyii
src LL ),(
1
),;,( rriif
skyrr
surface LL ),(
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Specular Reflection and Mirror BRDF
source intensity I
viewingdirectionsurface
element
normal
incidentdirection n
v
s
rspecular/mirror direction
),( ii ),( vv
),( rr
• Mirror BRDF is simply a double-delta function :
• Very smooth surface.
• All incident light energy reflected in a SINGLE direction. (only when = )
• Surface Radiance : )()( vivisIL
v r
)()(),;,( vivisvviif specular albedo
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Specular Reflections in Nature
Compare sizes of objects and their reflections!
The reflections when seen from a lower viewpoint are always longer than when viewedfrom a higher view point.
It's surprising how long the reflections are when viewed sitting on the river bank.
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Specular Reflections in Nature
The reflections of bright objects have better perceived contrast.
Intensity of reflected light is a fraction of the direct light – [Fresnel term (derivation in a later class)]
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Papers to Read
http://grail.cs.washington.edu/projects/sam/
Shape and Materials by Example: A Photometric Stereo Approach
http://www.eecs.harvard.edu/~zickler/helmholtz.html
Helmholtz Stereopsis
http://www.eecs.harvard.edu/~zickler/dichromaticediting.html
http://www.eecs.harvard.edu/~zickler/projects/colorsubspaces.html
Color Subspaces as Photometric Invariants
Specularity Removal and Dichromatic Editing