E-WAVE: Event-based Continuous Optical Flow via Warping-Aligned Visual Encoding

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.

Event cameras capture brightness changes asynchronously with microsecond resolution, yet existing optical flow methods fail to fully exploit this temporal continuity. Frame-based approaches impose artificial accumulation latency and suffer from domain overfitting, while model-based local methods operate statelessly, discarding temporal history between predictions and yielding inaccurate flows. We propose \textbf{LC-Flow}, the first temporally continuous, learning-based optical flow estimator that operates purely from local events. At its core, a Continuous Local Recurrent Network maintains persistent hidden states per spatial grid, incrementally accumulating temporal context as events arrive. Unlike frame-based methods constrained to fixed accumulation windows, and unlike stateless model-based methods that recompute motion from scratch at each step, LC-Flow produces sparse local flow estimates at arbitrary timestamps with full motion history. To address the inherent ambiguity of local observations, we jointly learn a confidence score that quantifies the reliability of each prediction, explicitly handling event sparsity and the aperture problem. This confidence serves a dual role: filtering unreliable estimates for downstream tasks such as visual odometry, and providing principled weights for a multi-scale confidence-guided aggregation that reconstructs globally consistent flow from the sparse local outputs. LC-Flow achieves state-of-the-art performance among local methods on both MVSEC and DSEC, while the confidence-guided aggregation establishes a new overall state-of-the-art on the MVSEC benchmark, surpassing heavy frame-based networks that rely on global spatial priors.

Event cameras capture intensity changes asynchronously with high temporal resolution, requiring novel preprocessing methods for downstream tasks. Unlike static intensity snapshots, event data inherently encode information about scene dynamics and object motion, meaning that features derived from events can exhibit behaviors with no direct analogue in frame-based vision. In this paper, we analyze two features used in event-based corner detection---the eigenvalues of the structure tensor and the spatiotemporal density values---and show that they are \emph{motion cues}. We hypothesize that these features, combined with local geometric information, can enhance motion estimation tasks. To validate this, we first theoretically analyze how the eigenvalues of the structure tensor at moving corner points relate to the direction of motion. We then design controlled experiments on a synthetic dataset, confirming that extending local geometric features with eigenvalues and density values provides complementary motion information and is robust to texture and shot noise. Finally, we integrate the proposed features into a state-of-the-art event-based optical flow network and evaluate on the real-world DSEC benchmark, where the added features consistently improve accuracy, with the largest gains in data-scarce scenarios and for lower-capacity models. The code for this paper can be found at: \href{https://github.com/hesamaraghi/static-in-frames-dynamic-in-events}{https://github.com/hesamaraghi/static-in-frames-dynamic-in-events}.