Minimal Solvers for Full-DoF Motion Estimation from Asynchronous Differential SfM
Authors: Shuo Pan, Banglei Guan, Bin Li, Zhenbao Yu, Zibin Liu, Zi Wang, Yang Shang, Qifeng Yu
Abstract
As a bio-inspired intelligent sensor, event cameras have introduced a new paradigm in the intelligent perception of spatiotemporal information and visual motion estimation, characterized by their high temporal resolution, low latency, and minimal power consumption. However, their asynchronous data streams present significant challenges to traditional synchronous, frame-based algorithms. To address these challenges, this paper presents a novel framework for full degree of freedom (DoF) egomotion estimation directly from asynchronous optical flow, specifically targeting the joint recovery of angular and linear velocities. We decouple the differential epipolar constraint into distinct angular and linear velocity components, and derive its formulation for asynchronous data. Based on this formulation, an optimization algorithm is developed that enables full-DoF egomotion estimation leveraging at least five points. Furthermore, by applying a first-order approximation to rotational dynamics, we transform the constraint equations into a polynomial form, resulting in the first algebraic minimal 5-point solver for this formulation. To ensure real-time performance in high-speed scenarios, we additionally propose an accelerated solver achieved by truncating high-order angular velocity terms. Extensive evaluations on both synthetic and real-world datasets demonstrate that the asynchronous approach outperforms traditional synchronous methods, particularly in its accuracy and robustness to spatiotemporal noise. We believe that this work establishes a critical foundation for efficient and accurate continuous-time motion estimation in high-speed robotics applications.
Traditional Visual Odometry (VO) and Visual Inertial Odometry (VIO) methods rely on a 'pose-centric' paradigm, which computes absolute camera poses from the local map thus requires large-scale landmark maintenance and continuous map optimization. This approach is computationally expensive, limiting their real-time performance on resource-constrained devices. To overcome these limitations, we introduce Sparse Motion Field Visual Odometry (SMF-VO), a lightweight, 'motion-centric' framework. Our approach directly estimates instantaneous linear and angular velocity from sparse optical flow, bypassing the need for explicit pose estimation or expensive landmark tracking. We also employed a generalized 3D ray-based motion field formulation that works accurately with various camera models, including wide-field-of-view lenses. SMF-VO demonstrates superior efficiency and competitive accuracy on benchmark datasets, achieving over 100 FPS on a Raspberry Pi 5 using only a CPU. Our work establishes a scalable and efficient alternative to conventional methods, making it highly suitable for mobile robotics and wearable devices.
Event-based vision sensors offer asynchronous, high-temporal-resolution measurements that are attractive for low-latency robotic perception, but many event-based motion estimation methods are computationally intensive and difficult to map to FPGA hardware. We present a streaming velocity estimator that discretizes asynchronous events into fixed-duration time bins, constructs a 1-bit spatial occupancy grid, and evaluates multiple velocity hypotheses in parallel using only fixed-width integer logic - shift registers, counters, comparators, and small LUT-mapped multiplies - with no dividers and no DSP blocks. It requires no frame reconstruction, no floating-point arithmetic, and no iterative optimization. The method deliberately trades dense sub-pixel optical flow for a sparse, quantized velocity estimate at each active pixel, suited to low-latency tasks such as reactive obstacle avoidance on size-, weight-, and power-constrained platforms. On noisy synthetic data with known ground-truth velocities, the method recovers both magnitude and direction, with magnitude estimates being most challenged when objects of different velocities intersect. On a real event-camera sequence, directional accuracy reaches 99.5% across all four evaluated motion segments, with performance remaining robust across occupancy densities in the 10-40% range. We characterize the algorithm's density-dependent behavior, present a parameter sensitivity analysis, show that the proposed datapath requires less than 2 kB of storage, and implement a single-axis prototype on a low-cost Xilinx Artix-7.
Arianna Alonso Bizzi, Fernando Cladera, C. J. Taylor
Estimating continuous optical flow is a fundamental yet challenging problem in dynamic visual perception. Event-based cameras, with microsecond latency and high dynamic range, capture brightness changes asynchronously, offering a unique opportunity to model motion with fine temporal precision. However, the scarcity of temporally dense ground-truth annotations limits the effectiveness of supervised learning, while contrast maximization (CM) frameworks, focused on sharpening the Image of Warped Events (IWE), often neglect temporal continuity and structural coherence, leading to distorted trajectories under complex motion. To overcome these challenges, we propose a hybrid-supervised framework for continuous-time optical flow estimation, grounded in the principle of Spatio-temporal Structural Consistency (STSC). This paradigm jointly enforces local structural stability and trajectory continuity, ensuring physically coherent motion across time. To further enhance representation and robustness, we design a bidirectionally complementary multi-scale architecture and employ a curriculum-guided hybrid training strategy, enabling a smooth transition from supervised point constraints to self-supervised manifold regularization. Comprehensive experiments across multiple benchmarks show that our method achieves state-of-the-art performance in both continuous-time and standard optical flow estimation, demonstrating the effectiveness of the proposed learning paradigm.