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USC
CS574: Computer Vision, Fall 2010
Copyright 2010, by R. Nevatia
1
Lecture 13: October 6, 10
• HW3 due today
• Exam 1, Oct 13, class time
– Close book, material covered listed in Oct 4 class slides
• Last Class
– Structure from motion
• Number of needed matches
• Affine/Projective ambiguities
• Two camera case
• Today’s objective
– Structure from motion sequences
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CS574: Computer Vision, Fall 2010
Copyright 2010, by R. Nevatia
2
Affine Cameras
• Affine projection matrix
–
is 2 x4 matrix which can be written as
– Note:
p
ij
and
P
j
are both nonhomegeneous coordinates
–
A
i
is an arbitrary 2x3 matrix of rank 2,
b
i
is arbitrary 2 vector
– Some examples (from section 2.3)
•G
i
v
e
n
m
views and
n
points, 8
m
+3
n
unknowns, 2
mn
equations, we
can solve given large enough
m
and
n.
USC
CS574: Computer Vision, Fall 2010
Copyright 2010, by R. Nevatia
3
Affine Ambiguity
• Solution is ambiguous up to an affine transformation
• Removing 12 unknowns due to affine ambiguity, for 2
images, we need only 4 points for affine reconstruction
2
mn >=
8
m
+3
n
– 12, for m =2, n = 4
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CS574: Computer Vision, Fall 2010
Copyright 2010, by R. Nevatia
4
Affine
Structure from Two Images
using inhomogeneous coordinates;
A is 2x3, b is a 2 vector
M=
(
A
b
)
, M’=
(
A’
b
’
)
Choose:
Any affine transformation of M and M’ will also work,
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This note was uploaded on 11/23/2010 for the course CS 574 taught by Professor Ramnevatia during the Fall '10 term at USC.
 Fall '10
 RAMNEVATIA

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