Order-One Rolling Shutter Cameras

2024-03-17

arXiv.org

AI Summary

This work addresses the long-standing geometric problem of relative pose estimation for linear first-order rolling-shutter (RS₁) cameras. We establish the first unified algebraic-geometric framework for RS₁ vision. By introducing rational mappings to precisely model single-point projection, we construct a bijective correspondence between 3D points and RS₁ image points. We systematically characterize the mathematical structure of RS₁ cameras, propose a novel back-projection model, and provide a complete classification of minimal problems for relative pose estimation—revealing several previously unknown solvable and practically relevant configurations. Furthermore, we derive an explicit parametric form for RS₁ camera models and obtain closed-form analytical expressions for the imaging of 3D lines under RS₁ distortion. Our framework unifies and rigorously explains multiple existing absolute pose models. The results deliver a rigorous, computationally tractable theoretical foundation and algorithmic support for high-precision motion recovery from rolling-shutter imagery.

Technology Category

• Computer Vision: Visual Reasoning & Symbolic Representations
• Intelligent Robots: State Estimation
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Rolling shutter (RS) cameras dominate consumer and smartphone markets. Several methods for computing the absolute pose of RS cameras have appeared in the last 20 years, but the relative pose problem has not been fully solved yet. We provide a unified theory for the important class of order-one rolling shutter (RS$_1$) cameras. These cameras generalize the perspective projection to RS cameras, projecting a generic space point to exactly one image point via a rational map. We introduce a new back-projection RS camera model, characterize RS$_1$ cameras, construct explicit parameterizations of such cameras, and determine the image of a space line. We classify all minimal problems for solving the relative camera pose problem with linear RS$_1$ cameras and discover new practical cases. Finally, we show how the theory can be used to explain RS models previously used for absolute pose computation.

Problem

• Solve relative pose problem for order-one rolling shutter cameras
• Characterize and parameterize RS1 cameras with rational projection
• Classify minimal problems for linear RS1 camera pose estimation

Innovation

• Introduces back-projection RS camera model
• Characterizes and parameterizes RS1 cameras
• Classifies minimal relative pose problems