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Precise Omnidirectional Camera Calibration

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Precise Omnidirectional Camera Calibration ... Projection model handles noncentral omnidirectional cameras ... viewpoint cameras. Omnidirectional projections ... – PowerPoint PPT presentation

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Title: Precise Omnidirectional Camera Calibration


1
Precise Omnidirectional Camera Calibration
  • Dennis Strelow, Jeffrey Mishler, David Koes, and
    Sanjiv Singh

2
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

3
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

4
Omnidirectional cameras
5
Omnidirectional projections (1)
  • The mirror point m determines the projection

6
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

7
Omnidirectional projections (3)
  • If the camera and mirror are not aligned, then
    two constraints determine m

8
Equiangular Cameras (1)
9
Equiangular cameras (2)
  • Relative rotation, translation between axes
    distorts projections

10
Calibration (1)
11
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 ?)

12
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?

13
Experiments (2)
  • Three lab sequences
  • Mirror and camera axes
  • 1. Closely aligned
  • 2. Moderate misalignment
  • 3. Severe misalignment

14
Experiments (3)
15
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

16
Experiments (5) residuals
  • Difference between observed target image location
    and reprojected location (pixels)

17
Experiments (6) values
  • Sequences differ mainly in tx
  • Standard deviations are small

18
Experiments (7) apex reproj.
  • Difference between observed screw center and
    reprojected mirror apex

19
Experiments (8) SFM
  • Shape-from-motion average reprojection errors
    (pixels) and depth errors (cm)

20
Experiments (9) epipolar error
  • Average distance in pixels from epipolar line to
    correct match
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