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Order-One Rolling Shutter Cameras
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Develops an algebraic-geometry theory of order-one rolling shutter (RS1) cameras, characterizing, parameterizing and classifying them and enumerating 31 minimal relative-pose problems for linear RS1 cameras.
Problem
Relative pose of rolling shutter cameras has not been fully solved; a general RS camera can see a space point multiple times, so standard multi-view perspective geometry does not apply.
Approach
Defines order-one RS cameras as those projecting a generic space point to exactly one image point via a rational map; shows their rolling planes intersect in a line and gives explicit parameterizations, a back-projection RS model, and classification of minimal relative pose problems for linear RS1 cameras.
Key results
- Classifies exactly 31 minimal problems for 2, 3, 4, and 5 cameras for linear RS1 cameras, all new.
- Identifies practical two-camera problems with degrees 28, 48, 60 (small) and 140, 364 (moderate), e.g., a 9-point problem.
- Shows the picture-taking map of a general RS1 camera has degree 2d+δ+1 or similar per parameter space; image of a line is a rational curve of that degree with a singularity at (0:1:0).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Classify minimal point-line reconstruction problems for linear RS1 cameras | Linear RS1 cameras · Point-line SfM with 2, 3, 4, and 5 cameras | number of minimal problems: exactly 31 | Helped |
| Use the first two parameter cases satisfying the rolling-plane intersection constraints | Straight-Cayley RS cameras · Straight-Cayley RS camera model | camera order: order one | Helped |
| Use the third parameter case satisfying the rolling-plane intersection constraints | Straight-Cayley RS cameras · Straight-Cayley RS camera model | camera order: order three; order one if and only if the parameters also satisfy the conditions in either 1. or 2. | Mixed |
| Use either order-one Straight-Cayley parameter case | Straight-Cayley RS cameras · Generic lines in space | image-curve degree: degree four | Helped |
Surprising findings
- No minimal problems exist for a single camera or for more than 5 cameras.
- General linear RS cameras have order two; they have order one only when the motion line is parallel to the projection plane.
Limitations
- Solvers for the identified minimal problems are not implemented or tested for practicality yet.
- Higher-degree minimal problems (more than three cameras) are impractical unless decomposed.
- Theory restricted to order-one cameras and linear (constant rotation, constant-speed translation) RS1 models for minimal problems.
Experimental setup
Metrics: degree of minimal problem (number of solutions)
Baselines: Dai et al. linear RS relative pose formulation Straight-Cayley absolute pose solver
Builds on: Straight-Cayley RS model linear RS camera model (Dai et al. uniform RS) line congruences / photographic camera maps (Yang et al.)
Closest papers by meaning
- Rolling Shutter Camera Relative Pose: Generalized Epipolar Geometry (CVPR 2016 · similarity 0.91)
- Rolling Shutter Absolute Pose Problem With Known Vertical Direction (CVPR 2016 · similarity 0.91)
- Scanline Homographies for Rolling-Shutter Plane Absolute Pose (CVPR 2022 · similarity 0.90)
- From Two Rolling Shutters to One Global Shutter (CVPR 2020 · similarity 0.88)
- Single Image Rolling Shutter Removal with Diffusion Models (AAAI 2025 · similarity 0.84)
- USB-NeRF: Unrolling Shutter Bundle Adjusted Neural Radiance Fields (ICLR 2024 · similarity 0.83)
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