# Camera Calibration via Circular Patterns: A Comprehensive Framework with Detection Uncertainty and Unbiased Projection Model

arXiv: https://arxiv.org/abs/2506.16842 · HTML: https://mlsanity.com/paper/2506.16842/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 48 references that are in the map.
- First posted on arXiv 20 Jun 2025.

## Builds on (most cited first, 13 of 13)

- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [ORB-SLAM: a Versatile and Accurate Monocular SLAM System](https://mlsanity.com/paper/1502.00956/) (2015)
- [Unsupervised Monocular Depth Estimation with Left-Right Consistency](https://mlsanity.com/paper/1609.03677/) (2016)
- [VINS-Mono: A Robust and Versatile Monocular Visual-Inertial State Estimator](https://mlsanity.com/paper/1708.03852/) (2017)
- [Why Having 10,000 Parameters in Your Camera Model is Better Than Twelve](https://mlsanity.com/paper/1912.02908/) (2019)
- [Neural Visibility Field for Uncertainty-Driven Active Mapping](https://mlsanity.com/paper/2406.06948/) (2024)
- [Calibration Wizard: A Guidance System for Camera Calibration Based on Modelling Geometric and Corner Uncertainty](https://mlsanity.com/paper/1811.03264/) (2018)
- [Fusing the Old with the New: Learning Relative Camera Pose with Geometry-Guided Uncertainty](https://mlsanity.com/paper/2104.08278/) (2021)
- [Road is Enough! Extrinsic Calibration of Non-overlapping Stereo Camera and LiDAR using Road Information](https://mlsanity.com/paper/1902.10586/) (2019)
- [Ambiguity-Aware Multi-Object Pose Optimization for Visually-Assisted Robot Manipulation](https://mlsanity.com/paper/2211.00960/) (2022)
- [Inferring bias and uncertainty in camera calibration](https://mlsanity.com/paper/2107.13484/) (2021)
- [Unbiased Estimator for Distorted Conics in Camera Calibration](https://mlsanity.com/paper/2403.04583/) (2024)
- [PeLiCal: Targetless Extrinsic Calibration via Penetrating Lines for RGB-D Cameras with Limited Co-visibility](https://mlsanity.com/paper/2404.13949/) (2024)

## Built on by (most cited first, 1 of 1)

- [From Laboratory to Road: Evaluating Wearable Gaze Accuracy for Driving](https://mlsanity.com/paper/2610.07783/) (2026)

## Abstract (arXiv)

Camera calibration using planar targets has been widely favored, and two types of control points have been mainly considered as measurements: the corners of the checkerboard and the centroid of circles. Since a centroid is derived from numerous pixels, the circular pattern provides more precise measurements than the checkerboard. However, the existing projection model of circle centroids is biased under lens distortion, resulting in low performance. To surmount this limitation, we propose an unbiased projection model of the circular pattern and demonstrate its superior accuracy compared to the checkerboard. Complementing this, we introduce uncertainty into circular patterns to enhance calibration robustness and completeness. Defining centroid uncertainty improves the performance of calibration components, including pattern detection, optimization, and evaluation metrics. We also provide guidelines for performing good camera calibration based on the evaluation metric. The core concept of this approach is to model the boundary points of a two-dimensional shape as a Markov random field, considering its connectivity. The shape distribution is propagated to the centroid uncertainty through an appropriate shape representation based on the Green theorem. Consequently, the resulting framework achieves marked gains in calibration accuracy and robustness. The complete source code and demonstration video are available at https://github.com/chaehyeonsong/discocal.