Precise Omnidirectional Camera Calibration

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Precise Omnidirectional Camera Calibration

• Dennis Strelow, Jeffrey Mishler, David Koes, and
  Sanjiv Singh

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Overview (1)

• Projection model for omnidirectional cameras that
  accounts for the full rotation and translation
  between camera and mirror
• Projection model handles noncentral
  omnidirectional cameras
• Calibration algorithm determines relative
  position from one omnidirectional image of known
  3D targets

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Overview (2)

• One image sufficient for accurate calibration of
  transformation
• Full calibration allows shape-from-motion and
  epipolar matching even if camera-mirror
  misalignment is severe
• Full model improves shape-from-motion and
  epipolar geometry results even if the camera and
  mirror are closely aligned

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Omnidirectional cameras
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Omnidirectional projections (1)

• The mirror point m determines the projection

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Omnidirectional projections (2)

• Finding the mirror point is
• one-dimensional (z only) if the mirror and camera
  are assumed aligned
• closed form for aligned single viewpoint cameras

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Omnidirectional projections (3)

• If the camera and mirror are not aligned, then
  two constraints determine m

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Equiangular Cameras (1)
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Equiangular cameras (2)

• Relative rotation, translation between axes
  distorts projections

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Calibration (1)
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Calibration (2)

• Least squares error to be minimized
• Known 2D projections xi, 3D points pi
• Unknown Camera position Rc, tc mirror-to-camera
  transformation (implicit in ?)

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Experiments (1)

• Basic questions about calibration
• 1. Does the calibration produce the correct
  mirror-to-camera transformation?
• 2. Is the model correct, e.g., is it possible to
  perform SFM with misaligned a mirror?
• 3. Is the full model worthwhile if the mirror is
  nearly aligned?

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Experiments (2)

• Three lab sequences
• Mirror and camera axes
• 1. Closely aligned
• 2. Moderate misalignment
• 3. Severe misalignment

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Experiments (3)
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Experiments (4)

• Performed shape-from-motion on each sequence
  using each of three calibrations
• A. Calibrate nothing
• B. Calibrate mirror-camera distance
• C. Calibrate rotation and translation
• Calibration B is interesting because computing
  the projection in this case is a one-dimensional
  problem

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Experiments (5) residuals

• Difference between observed target image location
  and reprojected location (pixels)

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Experiments (6) values

• Sequences differ mainly in tx
• Standard deviations are small

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Experiments (7) apex reproj.

• Difference between observed screw center and
  reprojected mirror apex

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Experiments (8) SFM

• Shape-from-motion average reprojection errors
  (pixels) and depth errors (cm)

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Experiments (9) epipolar error

• Average distance in pixels from epipolar line to
  correct match