# Beyond Reprojection Error: Camera Calibration with 3D Targets

arXiv: https://arxiv.org/abs/2608.05066 · HTML: https://mlsanity.com/paper/2608.05066/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 58 references that are in the map.
- First posted on arXiv 5 Aug 2026.

## Builds on (most cited first, 11 of 11)

- [Why Having 10,000 Parameters in Your Camera Model is Better Than Twelve](https://mlsanity.com/paper/1912.02908/) (2019)
- [Wide-angle Image Rectification: A Survey](https://mlsanity.com/paper/2011.12108/) (2020)
- [LiFCal: Online Light Field Camera Calibration via Bundle Adjustment](https://mlsanity.com/paper/2408.11682/) (2024)
- [A Comprehensive Overview of Fish-Eye Camera Distortion Correction Methods](https://mlsanity.com/paper/2401.00442/) (2023)
- [Unconstrained Two-parallel-plane Model for Focused Plenoptic Cameras Calibration](https://mlsanity.com/paper/1608.04509/) (2016)
- [Geometric Wide-Angle Camera Calibration: A Review and Comparative Study](https://mlsanity.com/paper/2306.09014/) (2023)
- [How to turn your camera into a perfect pinhole model](https://mlsanity.com/paper/2309.11326/) (2023)
- [Stable radial distortion calibration by polynomial matrix inequalities programming](https://mlsanity.com/paper/1409.5753/) (2014)
- [Calibration of fisheye camera using entrance pupil](https://mlsanity.com/paper/1907.01759/) (2019)
- [Single-image camera calibration with model-free distortion correction](https://mlsanity.com/paper/2403.01263/) (2024)
- [Rotating-star Pattern for Camera Calibration](https://mlsanity.com/paper/2410.13371/) (2024)

## Abstract (arXiv)

In 3D reconstruction, camera calibration is an essential element for achieving high fidelity and accuracy of the reconstructed geometry. While existing approaches rely upon 2D planar calibration, this work proposes a framework tailored for 3D reconstruction that is based on predicting scene rays, which adds flexibility to the reconstruction pipeline and enables the use of recent advances in camera models. Novel metrics, reconstruction and intersection error, derived from predicted scene rays are employed in combination with a bootstrapping procedure that statistically evaluates different calibration objects and calibration pipelines for both intrinsic and extrinsic camera parameters. The results show that the generalized distortion model more faithfully captures physical camera effects and yields an improvement in calibration accuracy. Reprojection error is shown to be a potentially misleading indicator of 3D accuracy, and the proposed ray-based metrics provide a more holistic assessment. An icosahedron calibration target is designed to enrich calibration information for 3D reconstruction together with a ring-feature-based detector. The icosahedral target yields approximately 40% lower mean intersection and more stable calibration across bootstrap trials on synthetic data, while real-data performance demands very tight fabrication tolerances.