# Unbiased Estimator for Distorted Conics in Camera Calibration

arXiv: https://arxiv.org/abs/2403.04583 · HTML: https://mlsanity.com/paper/2403.04583/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 29 references that are in the map.
- First posted on arXiv 7 Mar 2024.

## Builds on (most cited first, 7 of 7)

- [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)
- [Sparse Depth Enhanced Direct Thermal-infrared SLAM Beyond the Visible Spectrum](https://mlsanity.com/paper/1902.10892/) (2019)
- [Ambiguity-Aware Multi-Object Pose Optimization for Visually-Assisted Robot Manipulation](https://mlsanity.com/paper/2211.00960/) (2022)

## Built on by (most cited first, 5 of 5)

- [Rotating-star Pattern for Camera Calibration](https://mlsanity.com/paper/2410.13371/) (2024)
- [Camera Calibration via Circular Patterns: A Comprehensive Framework with Detection Uncertainty and Unbiased Projection Model](https://mlsanity.com/paper/2506.16842/) (2025)
- [Generic Camera Calibration using Blurry Images](https://mlsanity.com/paper/2603.05159/) (2026)
- [TIDY: Thermal Infrared Image Denoising via Wavelet Domain Entropy and Directional Stripe Index](https://mlsanity.com/paper/2606.19813/) (2026)
- [Calousel: Extrinsic Calibration of Non-overlapping Multi-camera Systems from Pure Rotation](https://mlsanity.com/paper/2606.25646/) (2026)

## Abstract (arXiv)

In the literature, points and conics have been major features for camera geometric calibration. Although conics are more informative features than points, the loss of the conic property under distortion has critically limited the utility of conic features in camera calibration. Many existing approaches addressed conic-based calibration by ignoring distortion or introducing 3D spherical targets to circumvent this limitation. In this paper, we present a novel formulation for conic-based calibration using moments. Our derivation is based on the mathematical finding that the first moment can be estimated without bias even under distortion. This allows us to track moment changes during projection and distortion, ensuring the preservation of the first moment of the distorted conic. With an unbiased estimator, the circular patterns can be accurately detected at the sub-pixel level and can now be fully exploited for an entire calibration pipeline, resulting in significantly improved calibration. The entire code is readily available from https://github.com/ChaehyeonSong/discocal.