Title: Computer Vision
1Computer Vision
- Spring 2010 15-385,-685
- Instructor S. Narasimhan
- PH A18B
- T-R 1030am 1150am
- Lecture 13
2Mechanisms 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
3Example 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
4Diffuse Reflection and Lambertian BRDF
5Diffuse 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!
6White-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?
7Diffuse 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)
8Specular 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
9Combing 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
10Diffuse and Specular Reflection
diffuse
specular
diffusespecular
11- Photometric Stereo
- Lecture 9
12Image Intensity and 3D Geometry
- Shading as a cue for shape reconstruction
- What is the relation between intensity and shape?
- Reflectance Map
13Surface Normal
surface normal
14Surface Normal
15Gradient Space
16Reflectance Map
- Relates image irradiance I(x,y) to surface
orientation (p,q) for given source direction and
surface reflectance - Lambertian case
17Reflectance Map
18Reflectance Map
iso-brightness contour
Note is maximum when
19Reflectance Map
- Glossy surfaces (Torrance-Sparrow reflectance
model)
diffuse term
specular term
20Shape 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
21Solution
- Take more images
- Photometric stereo
- Add more constraints
- Shape-from-shading (next class)
22Photometric Stereo
23Photometric Stereo
Lambertian case
Image irradiance
- We can write this in matrix form
24Solving the Equations
25More than Three Light Sources
- Get better results by using more lights
26Color 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
27Computing light source directions
- Trick place a chrome sphere in the scene
- the location of the highlight tells you the
source direction
28Specular Reflection - Recap
- For a perfect mirror, light is reflected about N
- We see a highlight when
- Then is given as follows
29Computing 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
30Limitations
- 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
31Trick for Handling Shadows
- Weight each equation by the pixel brightness
- Gives weighted least-squares matrix equation
32Results Lambertian Sphere
Input Images
Needles are projections of surface normals on
image plane
Estimated Albedo
Estimated Surface Normals
33Lambertain Mask
34Results Albedo and Surface Normal
35Results Lambertian Toy
I.2
Input Images
Estimated Surface Normals
Estimated Albedo
36Depth 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
37Results Shape of Mask
38Results
- Estimate light source directions
- Compute surface normals
- Compute albedo values
- Estimate depth from surface normals
- Relight the object (with original texture and
uniform albedo)
39Original Images
40Results - Albedo
No Shading Information
41Results - Shape
Shallow reconstruction (effect of
interreflections)
Accurate reconstruction (after removing
interreflections)
42Next Class
- Shape from Shading
- Reading Horn, Chapter 11.