RiemanLine: Riemannian Manifold Representation of 3D Lines for Factor Graph Optimization
This addresses the challenge of efficiently encoding structural regularities like parallel lines in man-made environments for camera localization and mapping, offering a domain-specific improvement.
The paper tackled the problem of representing 3D lines in robotics and computer vision by introducing RiemanLine, a minimal Riemannian manifold representation that handles both individual lines and parallel-line groups, reducing parameter space from 4n to 2n+2 for n parallel lines and achieving significantly more accurate pose estimation and line reconstruction in experiments.
Minimal parametrization of 3D lines plays a critical role in camera localization and structural mapping. Existing representations in robotics and computer vision predominantly handle independent lines, overlooking structural regularities such as sets of parallel lines that are pervasive in man-made environments. This paper introduces \textbf{RiemanLine}, a unified minimal representation for 3D lines formulated on Riemannian manifolds that jointly accommodates both individual lines and parallel-line groups. Our key idea is to decouple each line landmark into global and local components: a shared vanishing direction optimized on the unit sphere $\mathcal{S}^2$, and scaled normal vectors constrained on orthogonal subspaces, enabling compact encoding of structural regularities. For $n$ parallel lines, the proposed representation reduces the parameter space from $4n$ (orthonormal form) to $2n+2$, naturally embedding parallelism without explicit constraints. We further integrate this parameterization into a factor graph framework, allowing global direction alignment and local reprojection optimization within a unified manifold-based bundle adjustment. Extensive experiments on ICL-NUIM, TartanAir, and synthetic benchmarks demonstrate that our method achieves significantly more accurate pose estimation and line reconstruction, while reducing parameter dimensionality and improving convergence stability.