# Precise Omnidirectional Camera Calibration - PowerPoint PPT Presentation

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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)
• 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