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Are Minimal Radial Distortion Solvers Necessary for Relative Pose Estimation?

Charalambos Tzamos, Viktor Kocur, Yaqing Ding, Torsten Sattler, Zuzana Kukelova

TL;DR

The paper investigates whether minimal radial distortion solvers are necessary for robust relative pose estimation. It introduces a simple sampling-based strategy that combines the fast 7-point pinhole solver with a small, fixed set of undistortion parameters, integrated into modern RANSAC frameworks. Through extensive experiments on Phototourism, ETH3D, and newly captured ROTUNDA/CATHEDRAL benchmarks, the authors demonstrate that this approach matches or surpasses the best minimal radial distortion solvers in accuracy while achieving substantially faster runtimes, and it outperforms faster non-minimal solvers. The work provides public benchmarks and code, and concludes that dedicated minimal radial distortion solvers are not required in practical settings, given appropriate sampling and optimization within LO.

Abstract

Estimating the relative pose between two cameras is a fundamental step in many applications such as Structure-from-Motion. The common approach to relative pose estimation is to apply a minimal solver inside a RANSAC loop. Highly efficient solvers exist for pinhole cameras. Yet, (nearly) all cameras exhibit radial distortion. Not modeling radial distortion leads to (significantly) worse results. However, minimal radial distortion solvers are significantly more complex than pinhole solvers, both in terms of run-time and implementation efforts. This paper compares radial distortion solvers with a simple-to-implement approach that combines an efficient pinhole solver with sampled radial distortion parameters. Extensive experiments on multiple datasets and RANSAC variants show that this simple approach performs similarly or better than the most accurate minimal distortion solvers at faster run-times while being significantly more accurate than faster non-minimal solvers. We clearly show that complex radial distortion solvers are not necessary in practice. Code and benchmark are available at https://github.com/kocurvik/rd.

Are Minimal Radial Distortion Solvers Necessary for Relative Pose Estimation?

TL;DR

The paper investigates whether minimal radial distortion solvers are necessary for robust relative pose estimation. It introduces a simple sampling-based strategy that combines the fast 7-point pinhole solver with a small, fixed set of undistortion parameters, integrated into modern RANSAC frameworks. Through extensive experiments on Phototourism, ETH3D, and newly captured ROTUNDA/CATHEDRAL benchmarks, the authors demonstrate that this approach matches or surpasses the best minimal radial distortion solvers in accuracy while achieving substantially faster runtimes, and it outperforms faster non-minimal solvers. The work provides public benchmarks and code, and concludes that dedicated minimal radial distortion solvers are not required in practical settings, given appropriate sampling and optimization within LO.

Abstract

Estimating the relative pose between two cameras is a fundamental step in many applications such as Structure-from-Motion. The common approach to relative pose estimation is to apply a minimal solver inside a RANSAC loop. Highly efficient solvers exist for pinhole cameras. Yet, (nearly) all cameras exhibit radial distortion. Not modeling radial distortion leads to (significantly) worse results. However, minimal radial distortion solvers are significantly more complex than pinhole solvers, both in terms of run-time and implementation efforts. This paper compares radial distortion solvers with a simple-to-implement approach that combines an efficient pinhole solver with sampled radial distortion parameters. Extensive experiments on multiple datasets and RANSAC variants show that this simple approach performs similarly or better than the most accurate minimal distortion solvers at faster run-times while being significantly more accurate than faster non-minimal solvers. We clearly show that complex radial distortion solvers are not necessary in practice. Code and benchmark are available at https://github.com/kocurvik/rd.
Paper Structure (18 sections, 18 equations, 10 figures, 10 tables)

This paper contains 18 sections, 18 equations, 10 figures, 10 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Radial Distortion Solvers
  4. Sampling Distortions
  5. Experiments
  6. Conclusion
  7. Modified Solvers for Non-minimal Fitting
  8. $\mathbf{F} \lambda$ solver for equal and unknown distortion
  9. $\mathbf{F} \lambda_1\lambda_2$ solver for different unknown distortions
  10. Inverse of the One-parameter Division Model
  11. Benchmark Details
  12. Experiments
  13. Example visualization of varying levels of distortion.
  14. Run-time measurements.
  15. Feature Matching.
  16. ...and 3 more sections

Figures (10)

  • Figure 1: Robustness to varying levels of equal distortion: (Left) The estimated undistortion parameter and (Right) the pose error. An x-axis value of $-0.3$ means that we apply a distortion that can be undistorted with the undistortion parameter $-0.3$. The cyan line indicates the ground truth $\lambda$ value on the y-axis.
  • Figure 1: Visualization of the ROTUNDA scene. We show a textured mesh of the scene to provide a clearer visualization. We also show the poses of the 157 images of the dataset.
  • Figure 2: Pose AUC@10$^\circ$ and mean absolute $\lambda$ errors plotted for different number of RANSAC iterations on the CATHEDRAL (a, b) and ROTUNDA (c,d) scenes when considering pairs of images taken by the same camera (a,c) and two different cameras (b,d).
  • Figure 2: Distribution of $\lambda$ radial undistortion parameters for the CATHEDRAL scene (a). The parameters were obtained by normalizing the ground truth parameters estimated by RealityCapture. Example images from CATHEDRAL (b, c) and ROTUNDA (d).
  • Figure 3: Example images from the ROTUNDA scene.
  • ...and 5 more figures