# Motion and Structure from Event-based Normal Flow arXiv: https://arxiv.org/abs/2407.12239 ยท HTML: https://mlsanity.com/paper/2407.12239/ ## Key facts - Cited by 12 papers in the map (data through 14 Oct 2026). - Builds on 22 of its 48 references that are in the map. - First posted on arXiv 17 Jul 2024. ## Builds on (most cited first, 22 of 22) - [The Event-Camera Dataset and Simulator: Event-based Data for Pose Estimation, Visual Odometry, and SLAM](https://mlsanity.com/paper/1610.08336/) (2016) - [A Unifying Contrast Maximization Framework for Event Cameras, with Applications to Motion, Depth, and Optical Flow Estimation](https://mlsanity.com/paper/1804.01306/) (2018) - [Event-based Stereo Visual Odometry](https://mlsanity.com/paper/2007.15548/) (2020) - [Secrets of Event-Based Optical Flow](https://mlsanity.com/paper/2207.10022/) (2022) - [Focus Is All You Need: Loss Functions For Event-based Vision](https://mlsanity.com/paper/1904.07235/) (2019) - [Event-Based Motion Segmentation by Motion Compensation](https://mlsanity.com/paper/1904.01293/) (2019) - [Semi-Dense 3D Reconstruction with a Stereo Event Camera](https://mlsanity.com/paper/1807.07429/) (2018) - [Continuous-Time Visual-Inertial Odometry for Event Cameras](https://mlsanity.com/paper/1702.07389/) (2017) - [VECtor: A Versatile Event-Centric Benchmark for Multi-Sensor SLAM](https://mlsanity.com/paper/2207.01404/) (2022) - [Event Collapse in Contrast Maximization Frameworks](https://mlsanity.com/paper/2207.04007/) (2022) - [Rolling-Shutter-Aware Differential SfM and Image Rectification](https://mlsanity.com/paper/1903.03943/) (2019) - [CMax-SLAM: Event-based Rotational-Motion Bundle Adjustment and SLAM System using Contrast Maximization](https://mlsanity.com/paper/2403.08119/) (2024) - [Realtime Time Synchronized Event-based Stereo](https://mlsanity.com/paper/1803.09025/) (2018) - [The Spatio-Temporal Poisson Point Process: A Simple Model for the Alignment of Event Camera Data](https://mlsanity.com/paper/2106.06887/) (2021) - [DiffPoseNet: Direct Differentiable Camera Pose Estimation](https://mlsanity.com/paper/2203.11174/) (2022) - [Spatiotemporal Registration for Event-based Visual Odometry](https://mlsanity.com/paper/2103.05955/) (2021) - [A Fast Geometric Regularizer to Mitigate Event Collapse in the Contrast Maximization Framework](https://mlsanity.com/paper/2212.07350/) (2022) - [A 5-Point Minimal Solver for Event Camera Relative Motion Estimation](https://mlsanity.com/paper/2309.17054/) (2023) - [Vertical Landing for Micro Air Vehicles using Event-Based Optical Flow](https://mlsanity.com/paper/1702.00061/) (2017) - [Image Stitching and Rectification for Hand-Held Cameras](https://mlsanity.com/paper/2008.09229/) (2020) - [Joint direct estimation of 3D geometry and 3D motion using spatio temporal gradients](https://mlsanity.com/paper/1805.06641/) (2018) - [FAITH: Fast iterative half-plane focus of expansion estimation using event-based optic flow](https://mlsanity.com/paper/2102.12823/) (2021) ## Built on by (most cited first, 12 of 12) - [Full-DoF Egomotion Estimation for Event Cameras Using Geometric Solvers](https://mlsanity.com/paper/2503.03307/) (2025) - [Event Camera Meets Mobile Embodied Perception: Abstraction, Algorithm, Acceleration, Application](https://mlsanity.com/paper/2503.22943/) (2025) - [Learning Normal Flow Directly From Event Neighborhoods](https://mlsanity.com/paper/2412.11284/) (2024) - [6-DoF Object Tracking with Event-based Optical Flow and Frames](https://mlsanity.com/paper/2508.14776/) (2025) - [Minimal Solvers for Full DoF Motion Estimation from Asynchronous Tracks](https://mlsanity.com/paper/2508.17537/) (2025) - [E-MoFlow: Learning Egomotion and Optical Flow from Event Data via Implicit Regularization](https://mlsanity.com/paper/2510.12753/) (2025) - [A Real-Time Event-Based Normal Flow Estimator](https://mlsanity.com/paper/2504.19417/) (2025) - [Temporal and Rotational Calibration for Event-Centric Multi-Sensor Systems](https://mlsanity.com/paper/2508.12564/) (2025) - [Odometry Without Correspondence from Inertially Constrained Ruled Surfaces](https://mlsanity.com/paper/2512.00327/) (2025) - [Real-time Motion Segmentation with Event-based Normal Flow](https://mlsanity.com/paper/2602.20790/) (2026) - [A Geometric Framework for Absolute Pose and Velocity Estimation with Event Cameras](https://mlsanity.com/paper/2606.09139/) (2026) - [Minimal Solvers for Full-DoF Motion Estimation from Asynchronous Differential SfM](https://mlsanity.com/paper/2606.09218/) (2026) ## Abstract (arXiv) Recovering the camera motion and scene geometry from visual data is a fundamental problem in the field of computer vision. Its success in standard vision is attributed to the maturity of feature extraction, data association and multi-view geometry. The recent emergence of neuromorphic event-based cameras places great demands on approaches that use raw event data as input to solve this fundamental problem. Existing state-of-the-art solutions typically infer implicitly data association by iteratively reversing the event data generation process. However, the nonlinear nature of these methods limits their applicability in real-time tasks, and the constant-motion assumption leads to unstable results under agile motion. To this end, we rethink the problem formulation in a way that aligns better with the differential working principle of event cameras. We show that the event-based normal flow can be used, via the proposed geometric error term, as an alternative to the full flow in solving a family of geometric problems that involve instantaneous first-order kinematics and scene geometry. Furthermore, we develop a fast linear solver and a continuous-time nonlinear solver on top of the proposed geometric error term. Experiments on both synthetic and real data show the superiority of our linear solver in terms of accuracy and efficiency, and indicate its complementary feature as an initialization method for existing nonlinear solvers. Besides, our continuous-time non-linear solver exhibits exceptional capability in accommodating sudden variations in motion since it does not rely on the constant-motion assumption.