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Computer Vision

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Title: Computer Vision


1
Computer Vision
  • Spring 2010 15-385,-685
  • Instructor S. Narasimhan
  • PH A18B
  • T-R 1030am 1150am
  • Lecture 13

2
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
3
Example Surfaces
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
4
Diffuse Reflection and Lambertian BRDF
5
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!

6
White-out Snow and Overcast Skies
CANT perceive the shape of the snow covered
terrain!
CAN perceive shape in regions lit by the
street lamp!! WHY?
7
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)
8
Specular Reflection and Mirror BRDF
source intensity I
specular/mirror direction
incident direction
normal
viewing direction
surface element
  • Valid for very smooth surfaces.
  • All incident light energy reflected in a SINGLE
    direction (only when ).
  • Mirror BRDF is simply a double-delta function

specular albedo
  • Surface Radiance

9
Combing Specular and Diffuse 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
10
Diffuse and Specular Reflection
diffuse
specular
diffusespecular
11
  • Photometric Stereo
  • Lecture 9

12
Image Intensity and 3D Geometry
  • Shading as a cue for shape reconstruction
  • What is the relation between intensity and shape?
  • Reflectance Map

13
Surface Normal
surface normal
14
Surface Normal
15
Gradient Space
16
Reflectance Map
  • Relates image irradiance I(x,y) to surface
    orientation (p,q) for given source direction and
    surface reflectance
  • Lambertian case

17
Reflectance Map
  • Lambertian case

18
Reflectance Map
  • Lambertian case

iso-brightness contour
Note is maximum when
19
Reflectance Map
  • Glossy surfaces (Torrance-Sparrow reflectance
    model)

diffuse term
specular term
20
Shape from a Single Image?
  • Given a single image of an object with known
    surface reflectance taken under a known light
    source, can we recover the shape of the object?
  • Given R(p,q) ( (pS,qS) and surface reflectance)
    can we determine (p,q) uniquely for each image
    point?

NO
21
Solution
  • Take more images
  • Photometric stereo
  • Add more constraints
  • Shape-from-shading (next class)

22
Photometric Stereo
23
Photometric Stereo
Lambertian case
Image irradiance
  • We can write this in matrix form

24
Solving the Equations
25
More than Three Light Sources
  • Get better results by using more lights

26
Color Images
  • The case of RGB images
  • get three sets of equations, one per color
    channel
  • Simple solution first solve for using one
    channel
  • Then substitute known into above equations to
    get
  • Or combine three channels and solve for

27
Computing light source directions
  • Trick place a chrome sphere in the scene
  • the location of the highlight tells you the
    source direction

28
Specular Reflection - Recap
  • For a perfect mirror, light is reflected about N
  • We see a highlight when
  • Then is given as follows

29
Computing the Light Source Direction
Chrome sphere that has a highlight at position h
in the image
N
h
H
rN
c
C
sphere in 3D
image plane
  • Can compute N by studying this figure
  • Hints
  • use this equation
  • can measure c, h, and r in the image

30
Limitations
  • Big problems
  • Doesnt work for shiny things, semi-translucent
    things
  • Shadows, inter-reflections
  • Smaller problems
  • Camera and lights have to be distant
  • Calibration requirements
  • measure light source directions, intensities
  • camera response function

31
Trick for Handling Shadows
  • Weight each equation by the pixel brightness
  • Gives weighted least-squares matrix equation
  • Solve for as before

32
Results Lambertian Sphere
Input Images
Needles are projections of surface normals on
image plane
Estimated Albedo
Estimated Surface Normals
33
Lambertain Mask
34
Results Albedo and Surface Normal
35
Results Lambertian Toy
I.2
Input Images
Estimated Surface Normals
Estimated Albedo
36
Depth from Normals
  • Get a similar equation for V2
  • Each normal gives us two linear constraints on z
  • compute z values by solving a matrix equation

37
Results Shape of Mask
38
Results
  1. Estimate light source directions
  2. Compute surface normals
  3. Compute albedo values
  4. Estimate depth from surface normals
  5. Relight the object (with original texture and
    uniform albedo)

39
Original Images
40
Results - Albedo
No Shading Information
41
Results - Shape
Shallow reconstruction (effect of
interreflections)
Accurate reconstruction (after removing
interreflections)
42
Next Class
  • Shape from Shading
  • Reading Horn, Chapter 11.
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