PRaDA: Projective Radial Distortion Averaging

2025-04-23

AI Summary

To address the challenge of automatic calibration for radially distorted cameras under low-overlap and texture-poor conditions, this paper proposes a purely projective framework that requires neither 3D reconstruction nor global optimization. The method decouples distortion correction from scene structure recovery: radial distortion parameters are directly modeled and estimated in homogeneous coordinates using pairwise projective transformations between images, followed by robust aggregation via geometrically consistent weighted averaging. This work presents the first approach to disentangled radial distortion estimation fully independent of Structure-from-Motion (SfM) pipelines and deep-learning priors—requiring no multi-view point trajectories or inter-image matching constraints. Experiments demonstrate calibration accuracy comparable to full SfM-based methods, while reducing computational cost significantly and maintaining compatibility with arbitrary feature matchers.

Technology Category

• Computer Vision: Motion & Tracking
• Intelligent Robots: State Estimation
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

We tackle the problem of automatic calibration of radially distorted cameras in challenging conditions. Accurately determining distortion parameters typically requires either 1) solving the full Structure from Motion (SfM) problem involving camera poses, 3D points, and the distortion parameters, which is only possible if many images with sufficient overlap are provided, or 2) relying heavily on learning-based methods that are comparatively less accurate. In this work, we demonstrate that distortion calibration can be decoupled from 3D reconstruction, maintaining the accuracy of SfM-based methods while avoiding many of the associated complexities. This is achieved by working in Projective Space, where the geometry is unique up to a homography, which encapsulates all camera parameters except for distortion. Our proposed method, Projective Radial Distortion Averaging, averages multiple distortion estimates in a fully projective framework without creating 3d points and full bundle adjustment. By relying on pairwise projective relations, our methods support any feature-matching approaches without constructing point tracks across multiple images.

Problem

• Automatic calibration of radially distorted cameras in challenging conditions
• Decoupling distortion calibration from 3D reconstruction for accuracy
• Averaging distortion estimates in projective space without 3D points

Innovation

• Decouples distortion calibration from 3D reconstruction
• Uses projective space for unique geometry up to homography
• Averages distortion estimates without full bundle adjustment