Stereo Ranging with verging
Cameras
Based on the paper by E. Krotkov,
K.Henriksen and R. Kories
The system description
• Two cameras mounted on a platform can translate
horizontally and vertically, and rotate left-right and updown. Motors mounted on each lens adjust the focal
length, focusing distance, and aperture diameter.
Further, the two camera can verge by rotating towards
each other (converging) or away form each other
(diverging). The travel from minimum to maximum
vergence angle is approximately 6degrees, covering
90,000motor steps. Potential advantage of vergence
include increasing the field of view common to two
cameras and constraining the stereo disparity.
Model
• The lens is modeled as pinhole. The lens
centers are separated by a baseline distance b,
and both lenses have focal length f. Each
camera is associated with a reference frame L
and R with origins at the lens center and Z axes
coincident with the optic axes positive in the
direction fo the scene. We define a Cyclopean
reference frame W with origin at the midpoint of
the baseline, Z-axes normal to the base line and
X axis coincident with the baseline.
Vergence mechanism
Reference Frames
The problem
Computing Range
Perspective transformation yields
the image coordinates
Derivation for Z
The distance
Relationship of parameters to
observation
Indirect measurements
Getting f and baseline from
measurements
Constrain on offset
Parameter identification
Parameter Identification
• Second, we acquire disparity data from the
scene viewed with different vergence angles.
We servo the vergence motor to N different
positions. At each we digitize a stereo pair of
images and identify conjugate image points for
each of the M objects. The outcome of this
procedure is MxN conjugate points below and
(uL , vL ), (uR , vR )
• the associate vergence motor positions V.
Parameter identification
• Third we search for the least square
values for baseline and the offset.
Experimental Results
Figure explanation
• We identify conjugate image points for
each of 7 objects.
• There were 9 vergence positions. For
each vergence position 7 different distant
places were measured.
• The outcome is 7 x 9 conjugate points and
associated vergence motor ositions.
Distance versus disparity
Vergence Changes Baseline
Distance
This figure illustrates the case
when the center of rotation is not
the same as the lens center