ECE 549CS 543: COMPUTER VISON LECTURE 5

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ECE 549/CS 543 COMPUTER VISON LECTURE 5 CAMERA
CALIBRATION

• Intrinsic and extrinsic camera parameters
• The calibration problem
• Least-squares techniques
• MATLAB tutorial

Reading Chapters 2 and 3 Slides
http//www-cvr.ai.uiuc.edu/ponce/fall04/lect5.ppt
Programming assignment 1, due Tue. Sep. 22
http//www-cvr.ai.uiuc.edu/ponce/fall04/hw1/hw1.
pdf

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Data courtesy of T. Papadopoulo and RealViz
A Mosaic
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The Intrinsic Parameters of a Camera
Units
k,l pixel/m
f m
a,b
pixel
Physical Image Coordinates
Normalized Image Coordinates
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The Intrinsic Parameters of a Camera
Calibration Matrix
The Perspective Projection Equation
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The Extrinsic Parameters of a Camera
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Explicit Form of the Projection Matrix
Note
M is only defined up to scale in this setting!!
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Theorem (Faugeras, 1993)
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Calibration Problem
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Linear Systems
Square system
A
x
b

• unique solution
• Gaussian elimination

Rectangular system ??

• underconstrained
• infinity of solutions

A
x
b

• overconstrained
• no solution

Minimize Ax-b
2
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How do you solve overconstrained linear equations
??
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Homogeneous Linear Systems
Square system
A
x
0

• unique solution 0
• unless Det(A)0

Rectangular system ??

• 0 is always a solution

A
x
0

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Minimize Ax under the constraint x 1
2
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How do you solve overconstrained homogeneous
linear equations ??
The solution is e .
1
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Example Line Fitting
Problem minimize with respect to (a,b,d).

• Minimize E with respect to d

n

• Minimize E with respect to a,b

where

• Done !!