Basic Principles of Surface Reflectance

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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
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Computer Vision Building Machines that See
Lighting
Scene
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
sensor
source
normal
surface element
Image intensities f ( normal, surface
reflectance, illumination ) Surface Reflection
depends on both the viewing and illumination
direction.
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BRDF Bidirectional Reflectance Distribution
Function
source
z
incident direction
viewing direction
normal
y
surface element
x
Irradiance at Surface in direction
Radiance of Surface in direction
BRDF
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Important Properties of BRDFs
source
z
incident direction
viewing direction
normal
y
surface element
x

• Rotational Symmetry
• BRDF does not change when surface is rotated
  about the normal.

BRDF is only a function of 3 variables

• 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
From the definition of BRDF
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Derivation of the Scene Radiance Equation
Important!
From the definition of BRDF
Write Surface Irradiance in terms of Source
Radiance
Integrate over entire hemisphere of possible
source directions
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
incident direction
surface reflection
body reflection
surface
Surface Reflection Specular Reflection Glossy
Appearance Highlights Dominant for Metals
Body Reflection Diffuse Reflection Matte
Appearance Non-Homogeneous Medium Clay, paper,
etc
Image Intensity Body Reflection Surface
Reflection
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Mechanisms of Surface Reflection
Surface Reflection Specular Reflection Glossy
Appearance Highlights Dominant for Metals
Body Reflection Diffuse Reflection Matte
Appearance Non-Homogeneous Medium Clay, paper,
etc
Many materials exhibit both Reflections
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Diffuse Reflection and Lambertian BRDF
source intensity I
incident direction
normal
viewing direction
surface element

• Surface appears equally bright from ALL
  directions! (independent of )

albedo

• Lambertian BRDF is simply a constant

• Surface Radiance

source intensity

• Commonly used in Vision and Graphics!

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Diffuse Reflection and Lambertian BRDF
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White-out Conditions from an Overcast Sky
CANT 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)
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Specular Reflection and Mirror BRDF
source intensity I
specular/mirror direction
incident direction
normal
viewing direction
surface element

• Very smooth surface.
• All incident light energy reflected in a SINGLE
  direction. (only when )

• Mirror BRDF is simply a double-delta function

specular albedo

• Surface Radiance

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Specular Reflections in Nature
It's surprising how long the reflections are when
viewed sitting on the river bank.
Compare sizes of objects and their
reflections! The reflections when seen from a
lower view point are always longer than when
viewed from a higher view point.
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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
Shape and Materials by Example A Photometric
Stereo Approach
http//grail.cs.washington.edu/projects/sam/
http//www.eecs.harvard.edu/zickler/helmholtz.htm
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Specularity Removal and Dichromatic Editing
http//www.eecs.harvard.edu/zickler/dichromaticed
iting.html
Color Subspaces as Photometric Invariants
http//www.eecs.harvard.edu/zickler/projects/colo
rsubspaces.html