ECE 549CS 543: COMPUTER VISON LECTURE 7

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ECE 549/CS 543 COMPUTER VISON LECTURE 7 CAMERA
CALIBRATION III

• MATLAB tutorial
• Linear calibration
• Photometry

Reading Chapters 3 and 4 Slides
http//www-cvr.ai.uiuc.edu/ponce/fall04/lect7.ppt
Programming assignment 1, due Tue. Sep. 21
http//www-cvr.ai.uiuc.edu/ponce/fall04/hw1/hw1.
pdf

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Calibration Problem
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Example Line Fitting
Problem minimize with respect to (a,b,d).

• Minimize E with respect to d

• Minimize E with respect to a,b

where

• Done !!

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Linear Camera Calibration
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Once M is known, you still got to recover the
intrinsic and extrinsic parameters !!!
This is a decomposition problem, not an
estimation problem.
r

• Intrinsic parameters
• Extrinsic parameters

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Degenerate Point Configurations
Are there other solutions besides M ??

• Coplanar points (l,m,n )(P,0,0) or (0,P,0) or
  (0,0,P )

• Points lying on the intersection curve of two
  quadric
• surfaces

straight line twisted cubic
Does not happen for 6 or more random points!
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Analytical Photogrammetry
Non-Linear Least-Squares Methods

• Newton
• Gauss-Newton
• Levenberg-Marquardt

Iterative, quadratically convergent in favorable
situations
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Mobile Robot Localization (Devy et al., 1997)
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Image Formation Radiometry
The light source(s)
The sensor characteristics
The surface normal
The surface properties
The optics
What determines the brightness of an image pixel?
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DEFINITION The radiance is the power traveling
at some point in a given direction per unit area
perpendicular to this direction, per unit solid
angle.
d2P L( P, v ) dA dw
d2P L( P, v ) cosq dA dw
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DEFINITION Angles and Solid Angles
(radians)
(steradians)
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DEFINITION Irradiance
The irradiance is the power per unit area
incident on a surface.
d2PdE dALi( P , vi ) cosqidwi dA
dE Li( P , vi ) cosqi dwi
EsH Li (P, vi) cosqi dwi