Background
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We propose an extrinsic calibration algorithm for multiple cameras, even if there is no overlapping field of view among them.
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We propose an extrinsic calibration algorithm between a camera and a 2D laser scanner using AprilTag array calibration target, and it is integrated with the multi-camera extrinsic calibration into a multi-sensor joint extrinsic calibration with a final global optimization.
Related work
Calibration pattern
AprilTag-based pose estimation
Design of calibration target
Extrinsic calibration of multi-sensor system
Multiple-camera extrinsic calibration
Dual-camera extrinsic calibration
Single-camera localization optimization
Camera and laser extrinsic calibration
Global optimization
Algorithm: Multi-sensor system extrinsic calibration |
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Inputs: |
1. Simultaneous images and laser scan points’ coordinates. |
2. Intrinsic parameters of each camera. |
3. The transformations between two arbitrary tags in the calibration target. |
Procedure: |
1. Dual-camera extrinsic calibration |
(a) Single-camera extrinsic calibration using AprilTag. |
(b) Optimization of single-camera extrinsic parameters by a nonlinear minimization process. |
(c) Computing the extrinsic parameters (R
D
F
, t
D
F
) by the matrix transformations. |
2. Camera and laser extrinsic calibration |
(a) Using plane-line correspondence for the geometry constraints. |
(b) Solving these equations for the linear solution. |
(c) Optimizing the linear solution to refine the camera and laser extrinsic parameters. |
3. Global optimization to refine the multi-sensor system extrinsic parameters. |
(a) Computing the extrinsic parameters between other cameras and the laser. |
(b) Global optimization of all the sensors extrinsic parameters. |
Output: Extrinsic parameters of multi-sensor system |
Experiments
Single-camera pose estimation
Index | Axes | Multiple tags (RMSE) | Optimization results |
---|---|---|---|
1 |
X (m) | 0.034 | 0.020 |
Y (m) | 0.020 | 0.003 | |
Z (m) | 0.025 | 0.021 | |
2 |
X (m) | 0.020 | 0.013 |
Y (m) | 0.018 | 0.001 | |
Z (m) | 0.009 | 0.008 | |
3 |
X (m) | 0.069 | 0.069 |
Y (m) | 0.008 | 0.008 | |
Z (m) | 0.017 | 0.010 | |
4 |
X (m) | 0.018 | 0.011 |
Y (m) | 0.019 | 0.002 | |
Z (m) | 0.012 | 0.009 |
Index | Axes | Multiple tags (RMSE) | Optimization results |
---|---|---|---|
1 | Yaw (°) | 2.8339 | 1.9307 |
Pitch (°) | 0.4180 | 0.4491 | |
Roll (°) | 0.9443 | 0.7802 | |
2 | Yaw (°) | 2.7023 | 1.8842 |
Pitch (°) | 0.3993 | 0.5832 | |
Roll (°) | 0.4032 | 0.3400 |