Stereo Ranging with verging Cameras

1
Stereo Ranging with verging Cameras

• Based on the paper by E. Krotkov, K.Henriksen and
  R. Kories

2
The system description

• Two cameras mounted on a platform can translate
  horizontally and vertically, and rotate
  left-right and up-down. 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.

3
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.

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Vergence mechanism
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Reference Frames
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The problem
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Computing Range
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Perspective transformation yields the image
coordinates
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Derivation for Z
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The distance
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Relationship of parameters to observation
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Indirect measurements
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Getting f and baseline from measurements
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Constrain on offset
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Parameter identification
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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
• the associate vergence motor positions V.

17
Parameter identification

• Third we search for the least square values for
  baseline and the offset.

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Experimental Results
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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.

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Distance versus disparity
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Vergence Changes Baseline Distance
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This figure illustrates the case when the center
of rotation is not the same as the lens center