Title: Basic Principles of Surface Reflectance
1- Basic Principles of Surface Reflectance
- Lecture 3
Thanks to Shree Nayar, Ravi Ramamoorthi, Pat
Hanrahan
2Computer 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.
3Surface Appearance
sensor
source
normal
surface element
Image intensities f ( normal, surface
reflectance, illumination ) Surface Reflection
depends on both the viewing and illumination
direction.
4BRDF 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
5Important Properties of BRDFs
source
z
incident direction
viewing direction
normal
y
surface element
x
- Rotational Symmetry
-
- Appearance 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) -
- Appearance does not change when source and
viewing directions are swapped.
6Derivation of the Scene Radiance Equation
From the definition of BRDF
7Derivation 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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9Differential Solid Angle and Spherical Polar
Coordinates
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11Mechanisms of Surface 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
12Mechanisms 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
13Diffuse 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
source intensity
- Commonly used in Vision and Graphics!
14Diffuse Reflection and Lambertian BRDF
15White-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?
16Diffuse 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)
17Specular 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
18BRDFs of Glossy Surfaces
- Delta Function too harsh a BRDF model
- (valid only for polished mirrors and metals).
- Many glossy surfaces show broader highlights in
addition to specular reflection. - Example Models Phong Model (no physical basis,
but sort of works (empirical)) - Torrance Sparrow model (physically based)
Next Class
19Phong Model An Empirical Approximation
- An illustration of the angular falloff of
highlights - Very commonly used in Computer Graphics
20Phong Examples
- These spheres illustrate the Phong model as
lighting - direction and nshiny are varied
21All components of Surface Reflection
22A Simple Reflection Model - Dichromatic Reflection
Observed Image Color a x Body Color b x
Specular Reflection Color
Klinker-Shafer-Kanade 1988
R
Color of Source (Specular reflection)
Does not specify any specific model
for Diffuse/specular reflection
G
Color of Surface (Diffuse/Body Reflection)
B
23Separating Diffuse and Specular Reflections
Observed Image Color a x Body Color b x
Specular Reflection Color
R
Color of Source (Specular reflection)
G
Color of Surface (Diffuse/Body Reflection)
B
24Dror, Adelson, Wilsky