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Variation of Camera Parameters due to Common Physical Changes in Focal Length and Camera Pose

Hsin-Yi Chen, Chuan-Kai Fu, Jen-Hui Chuang

TL;DR

This paper tackles the problem of calibrating camera intrinsic parameters when focal length and camera pose vary, a scenario common in zoom-lens systems and real-world deployments. It advocates a geometry-based calibration method (Chuang's) and designs dedicated experiments to separately characterize major focal-length–driven PP shifts and minor gravity-driven PP shifts, comparing against Zhang's traditional algebraic method. The results reveal monotonic, direction-specific PP shifts with focal length changes that differ by camera type, and gravity-aligned minor shifts that are more consistent across cameras when using the geometry-based approach. Cross-validation of reprojection errors confirms the practical significance of correctly accounting for these variations, suggesting that re-calibration may be needed for each focal length or pose in many settings, while the geometry-based method often yields more reliable estimates than algebraic counterparts.

Abstract

Accurate calibration of camera intrinsic parameters is crucial to various computer vision-based applications in the fields of intelligent systems, autonomous vehicles, etc. However, existing calibration schemes are incompetent for finding general trend of the variation of camera parameters due to common physical changes. In this paper, it is demonstrated that major and minor variations due to changes in focal length and camera pose, respectively, can be identified with a recently proposed calibration method. It is readily observable from the experimental results that the former variations have different trends (directions) of principal point deviation for different types of camera, possibly due to different internal lens configurations, while the latter have very similar trends in the deviation which is most likely due to direction of gravity. Finally, to confirm the validity of such unprecedented findings, 3D to 2D reprojection errors are compared for different methods of camera calibration.

Variation of Camera Parameters due to Common Physical Changes in Focal Length and Camera Pose

TL;DR

This paper tackles the problem of calibrating camera intrinsic parameters when focal length and camera pose vary, a scenario common in zoom-lens systems and real-world deployments. It advocates a geometry-based calibration method (Chuang's) and designs dedicated experiments to separately characterize major focal-length–driven PP shifts and minor gravity-driven PP shifts, comparing against Zhang's traditional algebraic method. The results reveal monotonic, direction-specific PP shifts with focal length changes that differ by camera type, and gravity-aligned minor shifts that are more consistent across cameras when using the geometry-based approach. Cross-validation of reprojection errors confirms the practical significance of correctly accounting for these variations, suggesting that re-calibration may be needed for each focal length or pose in many settings, while the geometry-based method often yields more reliable estimates than algebraic counterparts.

Abstract

Accurate calibration of camera intrinsic parameters is crucial to various computer vision-based applications in the fields of intelligent systems, autonomous vehicles, etc. However, existing calibration schemes are incompetent for finding general trend of the variation of camera parameters due to common physical changes. In this paper, it is demonstrated that major and minor variations due to changes in focal length and camera pose, respectively, can be identified with a recently proposed calibration method. It is readily observable from the experimental results that the former variations have different trends (directions) of principal point deviation for different types of camera, possibly due to different internal lens configurations, while the latter have very similar trends in the deviation which is most likely due to direction of gravity. Finally, to confirm the validity of such unprecedented findings, 3D to 2D reprojection errors are compared for different methods of camera calibration.
Paper Structure (15 sections, 15 figures, 1 table)

This paper contains 15 sections, 15 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Work
  3. Camera Calibration Schemes
  4. Camera Calibration for Zoom-lens Cameras
  5. Change of PP After Camera Rotation
  6. Design of Experimental Procedure
  7. Maintaining Best Camera PT Angles
  8. Identifying and Improving CB Images of Poor Quality
  9. Fixing Camera Pose for Calibrating Zoom-lens Cameras
  10. Devising Camera Pose for Investigating the Effect of Gravity
  11. Experiments
  12. Experimental Settings
  13. PP Distribution due to Focal Length Change
  14. PP Distribution due to Camera Pose Change
  15. Conclusion

Figures (15)

  • Figure 1: (a) Eight PLs (one of them, the yellow one, obtained with extremely nonuniform illumination). (b) The problem in (a) resolved.
  • Figure 2: (a) A downward camera setting. (b) Auxiliary lines displayed on a viewing screen for image-CB alignment.
  • Figure 3: PP shifts due to focal length changes, estimated with Chuang's method (left) and Zhang's method (right).
  • Figure 4: Side view of a camera with downward pose (left). A PP shift opposite to the direction of the gravity component in the image plane (green arrow) may occur in ICS when camera is rotated northward (right).
  • Figure 5: PP shifts due to (N, W, and E) camera pose changes, with PP shifts due to changes in camera focal length also displayed (in gray).
  • ...and 10 more figures