ECE 549CS 543: COMPUTER VISON LECTURE 12

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ECE 549/CS 543 COMPUTER VISON LECTURE 12 COLOR
II

• Color Shading Models
• Color Image Interpretation
• A First Look at Multi-View Geometry

• Reading Chapters 6 and 10
• List of potential projects (will be soon) at
• http//www-cvr.ai.uiuc.edu/ponce/fall04/project
  s.pdf
• Homework Photometric stereo (due Tue. Oct. 12)
• http//www-cvr.ai.uiuc.edu/ponce/fall04/hw2/hw2
  .txt

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RGB Color Matching Functions
R645.16nm G526.32nm B444.44nm
Negative weights
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A rather poor reproduction of the RGB
color cube..
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CIE XYZ Color Matching Functions
Note there are no physical XYZ primaries!
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Color Matching Functions

• Problem given a set of primaries, what are the
  weights
• matching a given spectral radiance?

• Experiments

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l
Colour matching functions
L(l) f1(l)P1f2(l)P2f3(l)P3

• To match S use linearity

S(sL f1(l)S(l)dl)P1(sL f2(l)S(l)dl)P2(sL
f3(l)S(l)dl)P3
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CIE XYZ and xy spaces
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Simple Color Models for Images
Geometric terms
C(P) Gd(P) D(P) Gs(P) S(P) others..
Image color
Color terms
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Color Interpretation (Klinker and Shafer, 1987)
Metal
Dielectric material
Assume a single dielectric object with uniform
reflectance is observed.
C(P) Gd(P) D Gs(P) S

• Diffuse component Line through the origin
• Specular component Second line

Dog-leg pattern
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The dog-leg pattern
Dichromatic plane
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B
S
Illuminant color
T
G
Dif
fuse component
R
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Boundary of
specularity
Dif
fuse
region
B
B
G
G
R
R
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(Klinker, Shafer, Kanade, IJCV 4, 1990)
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Acquiring 3D information from multiple images
The INRIA Mobile Robot, 1990.
The Stanford Cart, H. Moravec, 1979.
Courtesy O. Faugeras and H. Moravec.
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Reconstruction / Triangulation
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(Binocular) Fusion
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Epipolar Geometry

• Epipolar Plane

• Baseline

• Epipoles

• Epipolar Lines

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Epipolar Constraint

• Potential matches for p have to lie on the
  corresponding
• epipolar line l.

• Potential matches for p have to lie on the
  corresponding
• epipolar line l.

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Epipolar Constraint Calibrated Case
Essential Matrix (Longuet-Higgins, 1981)
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Properties of the Essential Matrix

• E p is the epipolar line associated with p.
• E p is the epipolar line associated with p.
• E e0 and E e0.
• E is singular.
• E has two equal non-zero singular values
• (Huang and Faugeras, 1989).

T
T
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Epipolar Constraint Small Motions
To First-Order
Pure translation Focus of Expansion
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Epipolar Constraint Uncalibrated Case
Fundamental Matrix (Faugeras and Luong, 1992)
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Properties of the Fundamental Matrix

• F p is the epipolar line associated with p.
• F p is the epipolar line associated with p.
• F e0 and F e0.
• F is singular.

T
T
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The Eight-Point Algorithm (Longuet-Higgins, 1981)