Structural Foundations of Nonlinear Systems with Unknown Inputs: The UID-Induced Normal Form and Minimal-Sensing Structure-from-Motion

Accurately recovering the camera's calibration and metric poses for any unconstrained video would unlock large-scale training data for navigation and scene understanding. The dominant approaches to this problem are severely limited: Simultaneous Localization and Mapping (SLAM) is sensitive to initialization and transient failures due to its causal, incremental nature; it is often over-optimized for real-time operation and generally requires known camera calibration; while Structure-from-Motion (SfM) typically forgoes any image ordering, enabling optimal initialization and global optimization, but lacks robustness to visual symmetries and extreme motions. To bridge this gap, we introduce a system that combines the strong sequential constraints of SLAM with the flexibility and global optimization of offline SfM, enabling the metric reconstruction of arbitrary, long, uncalibrated videos. This system leverages recent advances in wide-baseline dense image matching, treats temporal ordering as a first-class citizen for reliable loop closure, and augments global optimization with metric monocular depth priors. As a result, thorough evaluations on diverse, challenging datasets that exhibit extreme motion and visual symmetries reveal that our approach is significantly more robust and accurate than both state-of-the-art SLAM and SfM, classical or learned, with given or unknown camera calibration. The code is publicly available at https://github.com/cvg/vidmap.

Visual navigation in unknown environments remains a core challenge in mobile robotics, especially for resource-constrained platforms. Most existing approaches rely on loosely coupled modular pipelines and strong assumptions on perception quality or environmental structure, often resorting to multi-modal sensor suites that increase system complexity and deployment cost. Vision-only navigation offers a lightweight alternative, but its performance degrades severely under motion blur, low texture, and illumination changes, largely because they neglect the tight coupling between commanded motion and perception. While perception-aware methods partially address this issue, they typically optimize individual modules and fail to propagate uncertainty consistently across the navigation stack. In this paper, we present UNSEEN, a unified uncertainty- and perception-aware navigation framework that explicitly couples localization, mapping, and planning using only a front-mounted camera. UNSEEN estimates sparse maps and robot poses with associated uncertainties at 6Hz, and leverages them to plan trajectories that jointly optimize task progress and estimation accuracy in receding-horizon. Simulations and extensive real-world experiments in unknown environments demonstrate the robustness of the proposed approach, with UNSEEN-SLAM reducing absolute translational error by 9.8% and UNSEEN-Plan improving estimation accuracy by up to 45% compared to state-of-the-art methods, while achieving a 100% task success rate.

Solving non-linear least-squares problem for pose estimation (rotation and translation) is often a time consuming yet fundamental problem in several real-time computer vision applications. With an adequate rotation parametrization, the optimization problem can be reduced to the solution of a~system of polynomial equations and solved in closed form. Recent advances in efficient closed form solvers utilizing resultant matrices have shown a promising research direction to decrease the computation time while preserving the estimation accuracy. In this paper, we propose a new class of resultant-based solvers that exploit Sylvester forms to further reduce the complexity of the resolution. We demonstrate that our proposed methods are numerically as accurate as the state-of-the-art solvers, and outperform them in terms of computational time. We show that this approach can be applied for pose estimation in two different types of problems: estimating a pose from 3D to 3D correspondences, and estimating a pose from 3D points to 2D points correspondences.