CS/ECE 181b Spring 2006
Midterm Practice Problems
These problems are meant to give a sense of the type of problems that will be on the
midterm.
Answer the following questions clearly and completely to receive full credit.
Provide full
analytical derivations when required. For this exam, we will adopt the following
conventions (READ CAREFULLY):
•
Boldface indicates points (
x
), lines (
l
), vectors (
p
) or matrices (
H
).
•
All the quantities related to the second camera are identified by the superscript
prime
(‘).
•
The notation
H
:
A
→
A’
means a matrix
H
which maps
A
to
A’
.
•
The notation
x
↔
x’
means that
x
and
x’
are corresponding elements (points,
lines, etc.) in the two image planes.
1. How do you approximate the perspective projection of 3D object using parallel
projection?
What criterion must be met for this projection to be valid?
2. The general projective transform
H
maps a point
x
in a plane to another point
x'
in
another plane.
What properties remain invariant under projective transform?
3. Let
P
be the camera projection matrix that maps a 3D point
X
to a point on an image
x
.
P
can be represented as
1
2
3
T
T
T
P
P
P
P
=
where
P
1
,
P
2
, and
P
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 Fall '08
 Staff
 Linear Algebra, Singular value decomposition, Center of Projection

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