USC
CS574: Computer Vision, Fall 2010
Copyright 2010, by R. Nevatia
1
Lecture 3: Aug 30, 10
• Course Enrollment
– Those on waiting list will be admitted as slots open
• Must continue to attend class, must hand in assignments
• Lecture slides posted in two formats (single page, 4 pp)
– Preliminary slides posted ahead of class
• Last Class
– Image formation: equations for projection of a point
– Homogeneous coordinates
– Intrinsic camera parameters
• Today’s objective
– Intrinsic and Extrinsic parameters
– Affine Cameras
– Camera Calibration
USC
CS574: Computer Vision, Fall 2010
Copyright 2010, by R. Nevatia
2
Homogeneous Coordinates
• Add an extra coordinate
–(
x,y,z
) => (
x
h
,
y
h
,
z
h
,
w
h
) = (
wx, wy, wz, w
),
w
is any constant
(in the book, w is set to 1)
• Advantage: allows perspective transformation to be
linearized
,
i.e.
expressed as a matrix equation
x
h
′
f’ 0
0
0
x
h
y
h
′
=
0
f’ 0
0
y
h
w
h
′
0
0
1
0
z
h
w
h
x
h
′
= f
′
x
h
, y
h
′
= f
′
y
h
, w
h
′
= z
h
x
′
= x
h
′
/ w
h
′
= f
′
*x/z, y
′
= f
′
* y/z
–
NOTE:
If image plane in front, replace f
′
by –f
′
in the above
equations.
USC
CS574: Computer Vision, Fall 2010
Copyright 2010, by R. Nevatia
3
Rigid Transformations
• Translation
• Rotation
• Combine rotation and translation
• Note:
t
=
B
O
A
, from object to camera coordinates, it may be
more convenient to be given
A
O
B
in which case
t
= -R
A
O
B
USC
CS574: Computer Vision, Fall 2010
Copyright 2010, by R. Nevatia
4
Intrinsic
Camera Parameters
•
Figure 2.8
• Measurement in image coordinate system may be in “pixel” units (u,v),
pixels may not be rectangular, origin of image coordinate system may not
be at the center of
image
(projection of lens center), axis may be
skewed
.
Normalized
image plane is unit distance in front.