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Single-View Rolling-Shutter SfM

Sofía Errázuriz Muñoz, Kim Kiehn, Petr Hruby, Kathlén Kohn

Abstract

Rolling-shutter (RS) cameras are ubiquitous, but RS SfM (structure-from-motion) has not been fully solved yet. This work suggests an approach to remedy this: We characterize RS single-view geometry of observed world points or lines. Exploiting this geometry, we describe which motion and scene parameters can be recovered from a single RS image and systematically derive minimal reconstruction problems. We evaluate several representative cases with proof-of-concept solvers, highlighting both feasibility and practical limitations.

Single-View Rolling-Shutter SfM

Abstract

Rolling-shutter (RS) cameras are ubiquitous, but RS SfM (structure-from-motion) has not been fully solved yet. This work suggests an approach to remedy this: We characterize RS single-view geometry of observed world points or lines. Exploiting this geometry, we describe which motion and scene parameters can be recovered from a single RS image and systematically derive minimal reconstruction problems. We evaluate several representative cases with proof-of-concept solvers, highlighting both feasibility and practical limitations.
Paper Structure (18 sections, 19 theorems, 77 equations, 4 figures, 1 table)

This paper contains 18 sections, 19 theorems, 77 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Camera Model
  3. RS images
  4. Line SfM
  5. Pure rotation
  6. Pure center motion
  7. Center motion and rotation
  8. Point SfM
  9. Experiments
  10. Conclusion
  11. Algebraic Geometry Prerequisites
  12. Minimal Problems
  13. Proofs
  14. Image Curve Constraint for $d=0,\delta=1$
  15. Details on Experiments
  16. ...and 3 more sections

Key Result

theorem 1

The order of almost all RS cameras in $\mathcal{P}_{d,\delta}$ is $1 + d + 2 \delta$.

Figures (4)

  • Figure 1: Examples of RS images: left: iPhone 3GS sequence from DBLP:conf/cvpr/ForssenR10, middle: sequence 06 from DBLP:conf/cvpr/HedborgFFR12, right: synthetic image generated by DBLP:conf/eccv/SeiskariYKRTKRS24.
  • Figure 2: Noiseless stability. Histogram of the velocity and line direction errors (for $\delta=0$) and the axis and norm errors (for $d=0$), calculated from $10^5$ noiseless samples.
  • Figure 3: Noise test. Recall curve of the velocity and line direction errors (for $\delta=0$) and the axis and norm errors (for $d=0$), calculated from $10^5$ samples with noise $\sigma=1px$, $||V||=0.2$ for $\delta=0$, $||A||=0.2$ for $d=0$.
  • Figure 4: Real-world experiments. Recall curves of the velocity and line direction errors of the proposed solvers with $\delta=0$ on the dataset DBLP:conf/cvpr/HedborgFFR12 (left), and of the axis and norm errors of the proposed solvers with $d=0$ on the dataset DBLP:conf/cvpr/ForssenR10.

Theorems & Definitions (37)

  • theorem 1
  • proof
  • theorem 2
  • proof
  • proposition 1
  • proof
  • proposition 2
  • proposition 3
  • proof
  • proposition 4
  • ...and 27 more