Robust Fundamental Matrix Estimation from Single Image Motion Blur

Accurate six-degree-of-freedom (6-DOF) motion estimation is essential for robotic manipulation, autonomous systems, and structural displacement monitoring. Conventional 3D-2D methods estimate absolute camera poses independently at each time and recover platform motion through camera-to-platform extrinsics, making them sensitive to extrinsic calibration errors, especially for micromotion. We present a differential pose estimation method that directly recovers platform motion from inter-frame image displacements and known 3D control points. By differencing perspective projection equations, using a depth-invariance approximation, and modeling motion on SE(3), the method avoids independent absolute-pose estimation and supports both monocular and multi-camera systems. We prove that translational extrinsic errors cancel exactly, while rotational errors induce a bounded perturbation determined by calibration error, motion magnitude, and observation geometry. We also derive generic observability conditions, a Cramer-Rao lower bound, and a bias-eliminated consistent estimator, and characterize the validity limits of the approximations. Extensive synthetic and real-world experiments establish a new state of the art for 6-DOF platform micromotion estimation, outperforming representative PnP and generalized-PnP methods in accuracy, calibration robustness, and computational efficiency. With five control points and 0.5-pixel image noise, the monocular solver obtains a combined pitch-yaw rotation RMSE of 10.09 arcsec, a translation RMSE of 3.70 mm, and a runtime of 0.34 ms. The binocular solver achieves a rotation RMSE of 10.58 arcsec, a translation RMSE of 3.91 mm, and a runtime of 0.27 ms. Code will be released upon publication at https://github.com/zyoungszu/pami2026.

We address the inverse problem of blind 3D scene reconstruction from extremely motion-blurred images, a scenario where traditional Structure-from-Motion (SfM) pipelines fail. Existing approaches typically circumvent this bottleneck by relying on impractical sharp-image supervision. In this work, we introduce PRISM3D, a unified framework enabling robust reconstruction directly from severely degraded inputs. To overcome the lack of a reliable starting point, we propose a Robust Initialization strategy utilizing deep dense tracking method (VGGSfM) to recover global topology where feature matching fails. To the best of our knowledge, we are the first to effectively leverage this paradigm to bootstrap 3D Gaussian Splatting from extreme motion blur. However, while robust, this initialization yields sparse and noisy geometry that causes deterministic optimization to diverge. To resolve this, we propose a coupled solution driven by probability and physics: we adopt a probabilistic formulation for geometric densification via Markov Chain Monte Carlo (MCMC) to robustly populate the sparse priors, while simultaneously modeling physical image formation via continuous Bezier Trajectories. Furthermore, while PRISM3D establishes a highly robust standalone pipeline, the availability of complementary event streams offers an opportunity to push the reconstruction fidelity further. To exploit this, we introduce PRISM3D-E, a multi-modal (RGB + Events) extension that seamlessly integrates high-temporal-resolution events as structural priors to maximize geometric recovery. Because existing datasets lack paired event streams under such severe degradation, we concurrently contribute the PRISM3D-E Benchmark to facilitate rigorous evaluation. Extensive experiments demonstrate that both our standalone RGB framework and its multi-modal extension establish new state-of-the-art performance.

Estimating 2D camera motion is fundamental to computer vision and computational photography. Existing homography-based methods work well for planar scenes or pure rotation, but struggle with camera translation, depth variation, and local parallax; local homography and mesh-based models improve flexibility but still rely on piecewise planar assumptions. We introduce CamFlow+, a hybrid-basis framework that represents 2D camera motion directly in dense-flow space. CamFlow+ combines homography-derived physical bases, stochastic bases sampled from homography flows, and depth-translational bases derived from depth and camera intrinsics, relaxing the single-plane constraint while preserving camera-motion regularity. A depth-aware smoothness term further regularizes translation-induced parallax in continuous-depth regions while preserving motion changes near depth boundaries. We evaluate CamFlow+ on GHOF-Cam, a camera-motion benchmark that masks out dynamic objects and ill-posed occlusion regions in an optical-flow benchmark to isolate camera-induced motion. Experiments show that CamFlow+ improves sparse and dense camera-motion estimation. In digital video stabilization, CamFlow+ also improves global and local stability, achieving the best top-1 preference rate in a blind user study. Code and datasets will be available on the project page: https://lhaippp.github.io/CamFlow+.