While homographies are fundamental to many computer vision tasks, the majority of conventional estimation techniques provide only point estimates without directly quantifying uncertainty introduced by noisy observations. Uncertainty, though, propagates to subsequent processing steps such as camera calibration and 3D reconstruction and is particularly relevant in safety-critical and socially relevant fields including medical imaging, autonomous driving, and defense. We present a fast Bayesian formulation for homography estimation from point correspondences that explicitly incorporates measurement uncertainty and prior knowledge while providing a posterior distribution over the homography parameters. A closed-form solution of the posterior mean of the homography is derived in homogeneous coordinates and supplemented by an iterative Bayesian approach to handle non-linearities. Synthetic experiments demonstrate the applicability to projective transformations and show improved estimation accuracy over DLT under varying noise conditions. Image stitching experiments further demonstrate applicability to real image correspondences while additionally providing uncertainty information.
Robust geometric model estimation is a fundamental problem in computer vision. RANSAC and its variants remain widely used for this task; however, they rely on stochastic minimal sampling. In this article, we propose Density Search Sample Consensus (DS-SAC), a deterministic robust estimation framework, that avoids repeated random sampling by searching dense regions. Starting from an initial model estimated from the available points, the method performs local exploration via forward and backward search. To facilitate global exploration, DS-SAC recursively partitions the point set using signed residuals and searches each valid partition for high-consensus models. We show that DS-SAC has polynomial complexity with respect to the number of points, making it an efficient alternative to stochastic consensus-based methods. Experiments on large-scale real-world datasets for homography, fundamental matrix, and essential matrix estimation show that DS-SAC achieves higher AUC scores, competitive or lower median pose errors, and faster runtime compared with widely used robust estimators, including RANSAC, MAGSAC, LO-RANSAC, and GC-RANSAC.
The adoption of vision neural networks in regulated industries requires formal robustness guarantees, especially in safety-critical domains such as healthcare, autonomous vehicles, and aerospace. However, current approaches are confined to incomplete statistical verification or robustness to ℓp-norm and affine transforms, which cover only a narrow subset of perturbations to the image formation process. In particular, robustness to camera motion remains an open problem despite being key to deploy many vision applications. We present a formal verification approach that targets robustness against 3D motion perturbations of the capturing camera. We first establish a closed-form mapping from camera pose to pixel values. By analyzing the continuity properties of the resulting homographies, we show that recent work on Lipschitz optimization and piecewise continuity can be extended to derive tight linear bounds on perturbed pixel values. Our approach applies to scenes with predominantly planar structure, such as ground planes in augmented reality, road markings and traffic signs in autonomous driving, or planar workspaces in robotic manipulation. This enables the first formal verification of projective geometry transforms, without complex simulation, surrogate networks, or explicit image-formation models. We validate our implementation and show up to 89% speedup and 7% tighter bounds over prior work. We then evaluate our method on the VNN-COMP benchmark and reveal systematic weaknesses to projective perturbations. Finally, we demonstrate a real-world case study on a safety-critical runway classifier, highlighting practical vulnerabilities to camera motion, and addressing a key challenge in the certification of learned models. Data and code are publicly available at https://github.com/jeangud/homography-verification .
Jean-Guillaume Durand, Panagiotis Kouvaros, Maxime Gariel +1
Homography estimation, as one of the fundamental problems in computer vision, remains challenged by scale variation scenarios where image pairs potentially exhibit significant scale discrepancies. Existing deep learning frameworks frequently suffer from a significant performance degradation in such cases, as they rely on limited displacement assumptions and local feature consistency that might not hold under large scale gaps. In this paper, we propose SA-Homo, a novel scale-adaptive homography estimation framework designed to achieve robust alignment across a wide range of scale discrepancy ratios. We adopt a hierarchical scale alignment strategy that transitions from the global perspective with a heavy module to a local perspective with a light module. Specifically, we introduce the Scale-aware Discrepancy Bridging Module (SDBM) for initial alignment, which utilizes a Multi-scale Linear Attention Cascade (MLAC) to capture long-range dependencies and mitigate feature inconsistencies, along with a global Cross-scale Similarity Matrix Block (CSMB) for scale robust correlation representation. Once the initial scale gap is bridged, a lightweight Iterative Homography Estimation Refinement Module (IHERM) progressively polishes the result using local correlations. To facilitate this research, we contribute the HMSA dataset, a high-resolution, multi-modal satellite benchmark specifically tailored for scale-variant challenges. Extensive experiments demonstrate that SA-Homo maintains high precision even under 8× scale discrepancies, outperforming state-of-the-art methods in both conventional scale-similar scenarios and challenging scale variation scenarios. Code and collected datasets are available at https://github.com/shangxuanx330/SA_Homo