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Calibration Curves: Linear Least Squares

A calibration curve is a plot of the instrument's response against a series of known concentrations of a substance. This curve is used to set the instrument response levels, using the substance and its concentrations as standards. Alternatively, or additionally, an equation is fitted to the calibration curve plot and subsequently used to calculate the unknown concentrations of other samples reliably.
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3D LIDAR-camera extrinsic calibration using an arbitrary trihedron.

Xiaojin Gong1, Ying Lin, Jilin Liu

  • 1Department of Information Science and Electronic Engineering, Zhejiang University, Hangzhou 310027, Zhejiang, China. gongxj@zju.edu.cn

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This study introduces a new method for 3D LIDAR-camera extrinsic calibration using a trihedral object and nonlinear least squares. Precise initial estimates improve iterative refinement for accurate sensor alignment.

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Area of Science:

  • Robotics
  • Computer Vision
  • Sensor Fusion

Background:

  • Extrinsic calibration is crucial for integrating 3D LIDAR and camera data.
  • Existing methods may lack robustness or require specific calibration targets.
  • Accurate sensor alignment is essential for 3D reconstruction and scene understanding.

Purpose of the Study:

  • To develop a novel and convenient extrinsic calibration method for 3D LIDAR-camera systems.
  • To improve the accuracy and robustness of sensor calibration using geometric constraints.
  • To enable efficient calibration in structured environments using readily available trihedral objects.

Main Methods:

  • Formulating the extrinsic calibration as a nonlinear least squares (NLS) problem based on trihedral object geometry.
  • Decomposing the NLS problem into two sub-problems for precise initial estimation.
  • Iteratively refining calibration parameters using the obtained initializations.
  • Validating the algorithm with simulated and real-world datasets.

Main Results:

  • Demonstrated accurate extrinsic calibration of 3D LIDAR and camera systems.
  • Achieved precise relative transformation estimation between sensors.
  • Successfully applied the calibration method in a 3D reconstruction task.
  • Showcased the convenience and effectiveness of using trihedral targets in structured environments.

Conclusions:

  • The proposed NLS-based method offers a robust and accurate solution for 3D LIDAR-camera extrinsic calibration.
  • The technique leverages geometric constraints of trihedral objects for efficient and convenient calibration.
  • The validated results confirm the method's applicability in real-world scenarios and 3D reconstruction.