Robust Plane-Based Calibration for Linear Cameras
ROBUST PLANE-BASED
CALIBRATION FOR
LINEAR CAMERAS
Simon Donné, ICIP 2017, 18/09/2017
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RESEARCH GROUP IMAGE PROCESSING AND INTERPRETATION
PRESENTATION OVERVIEW
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Linear cameras and applications
̶
Existing work
̶
Proposed approach
̶
Experiments and results
̶
Conclusion
2
LINEAR CAMERAS
Single sensor line
Camera moving orthogonally to the sensor line
(parallel to the image plane)
3
LINEAR CAMERAS
Applications: satellite cameras
-
smaller (lighter) cameras
-
‘free’ ‘linear’ movement
4
LINEAR CAMERAS
Applications: hyperspectral cameras
-
2D sensor grid:
-
wavelength (diffraction)
-
width
-
height through movement
5
LINEAR CAMERAS
6
EXISTING WORK
7
EXISTING WORK
8
EXISTING WORK
9
PROPOSED APPROACH
10
PROPOSED APPROACH
11
RESULTS AND EXPERIMENTS
The result is not only a more robust method (applicable
in our real experiments with a horizontal robot arm)
But also a more accurate estimate!
12
RESULTS AND EXPERIMENTS
Synthetic datasets:
13
RESULTS AND EXPERIMENTS
Real experiments: those elements were always zero!
Absolute error on 200 mm offsets: 1,19mm
14
CONCLUSION
We formulate a more stable and robust estimation for the
rotation matrix from the homography that does not entail
dividing by elements of the rotation matrices.
The result is a more accurate camera calibration that is
robust to planar objects parallel to the image plane –
which do occur in practical set-ups.
15
Simon Donné
PhD Student
Department of telecommunication
and information processing
Image processing and interpretation
E
Simon.Donne@ugent.be
T
+32 9 264 32 70
telin.ugent.be/~sdonn
The research group delves into the robust calibration methods for linear cameras, touching upon applications in satellite and hyperspectral imaging. Existing techniques are discussed, leading to the proposal of a new approach for calibration. The complexity of the camera model and homography-like matrix calculations are explored in detail.
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Presentation Transcript
DEPARTMENT OF TELECOMMUNICATION AND INFORMATION PROCESSING RESEARCH GROUP IMAGE PROCESSING AND INTERPRETATION ROBUST PLANE-BASED CALIBRATION FOR LINEAR CAMERAS Simon Donn , ICIP 2017, 18/09/2017
PRESENTATION OVERVIEW Linear cameras and applications Existing work Proposed approach Experiments and results Conclusion 2
LINEAR CAMERAS Single sensor line Camera moving orthogonally to the sensor line (parallel to the image plane) 3
LINEAR CAMERAS Applications: satellite cameras - smaller (lighter) cameras - free linear movement 4
LINEAR CAMERAS Applications: hyperspectral cameras - 2D sensor grid: - wavelength (diffraction) - width - height through movement 5
LINEAR CAMERAS The camera model is given be ? ? 1 ? 0 0 0 ? 0 ?0 0 1 ? ?? ? ?? + ?0? ??? ? = nonlinearity ??! 6
EXISTING WORK Given the capture of a planar pattern ??,??,0? the projection from the Veronese mapping: ? ? 1 ?2 ?2 ?? ?11 ?12 ?1 0 0 0 ? ? 1 ?21?3+ ?31?2 ?31 ?22?3+ ?32?2 ?32 ?2?3 ?3 ?21?31 0 ?22?32 0 ?21?32+ ?22?31 0 ? 7
EXISTING WORK Given the capture of a planar pattern ??,??,0? yields a homography-like matrix H ? ? 1 ?2 ?2 ?? ? ? 1 ?2 ?2 ?? ? ? 1 = ? ?1 | ?2 ? 8
EXISTING WORK Multiplication with the skew matrix of each observation yields a homogeneous system in H Given the structure of H, Drareni et al. define: ? 0 ? ??0 11 12 ??,1 | ??,2 =??,3 0 0 25/ 32 32 24/ 31 31 ??????= ??,3 0 0 ?? 9
PROPOSED APPROACH However, this entails dividing by entries of the rotation matrix We propose using another alternative: ? 0 ? ??0 11 12 ??,1 | ??,2 =??,3 0 0 21 31 23 31 22 32 23 32 ??????= ??,3 0 0 ?? 10
PROPOSED APPROACH Our proposed formulation is theoretically equivalent but behaves much better near degenerate horizontal poses Using this factorization we can estimate ?,?,??,3 and ??. ? 0 ? ??0 11 12 ??,1 | ??,2 =??,3 0 0 21 31 23 31 22 32 23 32 ??????= ??,3 0 0 ?? 11
RESULTS AND EXPERIMENTS The result is not only a more robust method (applicable in our real experiments with a horizontal robot arm) But also a more accurate estimate! 12
RESULTS AND EXPERIMENTS Synthetic datasets: 13
RESULTS AND EXPERIMENTS Real experiments: those elements were always zero! Absolute error on 200 mm offsets: 1,19mm 14
CONCLUSION We formulate a more stable and robust estimation for the rotation matrix from the homography that does not entail dividing by elements of the rotation matrices. The result is a more accurate camera calibration that is robust to planar objects parallel to the image plane which do occur in practical set-ups. 15
Simon Donn PhD Student DEPARTMENT OF TELECOMMUNICATION AND INFORMATION PROCESSING IMAGE PROCESSING AND INTERPRETATION E T Simon.Donne@ugent.be +32 9 264 32 70 telin.ugent.be/~sdonn
