USC
CS574: Computer Vision, Fall 2010
Copyright 2010, by R. Nevatia
1
Lecture 4: Sept 1, 10
• Course Enrollment
• HW1 to be posted later today, Due Sept 13
• Make up class today: 5-6:20PM, OHE 120
• Last Class
– Intrinsic and extrinsic parameters
– Affine cameras
• Today’s objective
– Camera calibration
– Photometry
– Color perception
USC
CS574: Computer Vision, Fall 2010
Copyright 2010, by R. Nevatia
2
Homogeneous Coords in 3-D
• Point X:
normal coords (x,y,z); homogeneous (x, y, z,1)
T
• Plane
Π
: ax + by + cz + d =0 is defined by (a, b, c, d)
T
• Point X is on plane
iff
Π
T
X
= 0
• 3 points define a plane (
X
1
T
,
X
2
T
,
X
3
T
)
T
Π
= 0
– Note: this equation is correct, the outer transpose is simply intended to
indicate that the components
X
1
T
,
X
2
T
and
X
3
T
are arranged in a column,
not a row.
• 3 planes define a point (
Π
1
T
,
Π
2
T
,
Π
3
T
)
T
X
= 0
USC
CS574: Computer Vision, Fall 2010
Copyright 2010, by R. Nevatia
3
Affine Cameras
• In many cases, perspective projection can be approximated by
simpler camera models
– Typically when the objects are far from the camera relative to their size
• Projection matrix can be simplified by having only two rows:
affine transformation
– M becomes a 2 x 4 (3-D point expressed as homogeneous, 2-D as non-
homogeneous): examples to come
– Smaller number of parameters makes it easier to estimate them.
– Images of affine cameras have simpler properties,
e.g.
parallelism may be
preserved under certain models
• Some specific affine cameras
– Orthographic camera
– Weak perspective camera
– Para-perspective camera
USC
CS574: Computer Vision, Fall 2010
Copyright 2010, by R. Nevatia
4
Weak Perspective
• All points at nearly same distance, but not necessarily very far