precise omnidirectional camera calibration dennis strelow, jeffrey mishler, david koes, and sanjiv...
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Precise Omnidirectional Camera Calibration
Dennis Strelow, Jeffrey Mishler, David Koes, and Sanjiv Singh
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
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
Omnidirectional cameras
Omnidirectional projections (1)
The mirror point m determines the projection
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
Omnidirectional projections (3)
If the camera and mirror are not aligned, then two constraints determine m
Equiangular Cameras (1)
Equiangular cameras (2)
Relative rotation, translation between axes distorts projections
Calibration (1)
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 ∏)
2 (Rc pi tc) x i
2
i1
n
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?
Experiments (2)
Three lab sequencesMirror and camera axes:
1. Closely aligned 2. Moderate misalignment 3. Severe misalignment
Experiments (3)
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
Experiments (5): residuals
Difference between observed target image location and reprojected location (pixels)
Cal. A Cal. B Cal. C
Seq. 1 1.92 1.91 1.34
Seq. 2 4.01 3.85 1.40
Seq. 3 6.50 6.30 1.36
Experiments (6): values
Sequences differ mainly in tx
Standard deviations are small
tx (cm)
Seq. 1 0.0052 ± 0.0035
Seq. 2 0.21 ± 0.0053
Seq. 3 0.37 ± 0.0056
Experiments (7): apex reproj.
Difference between observed screw center and reprojected mirror apex
Difference
Seq. 1 5.0 pixels
Seq. 2 6.0 pixels
Seq. 3 4.7 pixels
Experiments (8): SFM
Shape-from-motion average reprojection errors (pixels) and depth errors (cm)
Cal. A Cal. B Cal. C
Seq. 1 0.40 / 3.3 0.41 / 3.4 0.37 / 2.0
Seq. 2 1.1 / 9.9 1.1 / 9.6 0.43 / 1.9
Seq. 3 1.9 / 15.9 1.92 / 15.2 0.38 / 1.9
Experiments (9): epipolar error
Average distance in pixels from epipolar line to correct match
Cal. A Cal. B Cal. C
Seq. 1 0.68 0.69 0.64
Seq. 2 1.3 1.4 0.71
Seq. 3 2.1 2.1 0.64
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