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

2025-06-20

AI Summary

Systematic bias in the projected centers of circular calibration targets under lens distortion limits camera calibration accuracy. Method: We propose the first unbiased circular projection model and an end-to-end uncertainty-aware framework: (1) an analytical, distortion-compensated circle-center projection model eliminating geometric bias; (2) modeling circle boundary points as a Markov random field and deriving closed-form uncertainty propagation for the centroid using Green’s theorem; (3) uncertainty-weighted nonlinear optimization coupled with distortion-adaptive circle-center estimation. Results: Our method significantly outperforms conventional chessboard- and state-of-the-art circular-based calibration approaches, achieving superior accuracy, robustness, and repeatability. All code, datasets, and demonstration videos are publicly released, accompanied by a comprehensive reproduction guide.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Computer Vision: Bias, Fairness & Privacy
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• Responsible Web: Measurement, analysis, and circumvention of Web censorship

Abstract

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.

Problem

• Unbiased projection model for circular patterns under lens distortion
• Introducing uncertainty into circular patterns to enhance calibration robustness
• Modeling boundary points as Markov random field for accurate centroid uncertainty

Innovation

• Unbiased projection model for circular patterns
• Uncertainty integration in circular pattern calibration
• Markov random field for boundary point modeling