# E-MoFlow: Learning Egomotion and Optical Flow from Event Data via Implicit Regularization

arXiv: https://arxiv.org/abs/2510.12753 · HTML: https://mlsanity.com/paper/2510.12753/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 47 of its 73 references that are in the map.
- First posted on arXiv 14 Oct 2025.

## Builds on (most cited first, 30 of 47)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Event-based Vision: A Survey](https://mlsanity.com/paper/1904.08405/) (2019)
- [ORB-SLAM3: An Accurate Open-Source Library for Visual, Visual-Inertial and Multi-Map SLAM](https://mlsanity.com/paper/2007.11898/) (2020)
- [Direct Sparse Odometry](https://mlsanity.com/paper/1607.02565/) (2016)
- [Lipschitz regularity of deep neural networks: analysis and efficient estimation](https://mlsanity.com/paper/1805.10965/) (2018)
- [Unsupervised Event-based Learning of Optical Flow, Depth, and Egomotion](https://mlsanity.com/paper/1812.08156/) (2018)
- [DSEC: A Stereo Event Camera Dataset for Driving Scenarios](https://mlsanity.com/paper/2103.06011/) (2021)
- [The Multi Vehicle Stereo Event Camera Dataset: An Event Camera Dataset for 3D Perception](https://mlsanity.com/paper/1801.10202/) (2018)
- [EV-FlowNet: Self-Supervised Optical Flow Estimation for Event-based Cameras](https://mlsanity.com/paper/1802.06898/) (2018)
- [Global Structure-from-Motion Revisited](https://mlsanity.com/paper/2407.20219/) (2024)
- [End-to-End Learning of Representations for Asynchronous Event-Based Data](https://mlsanity.com/paper/1904.08245/) (2019)
- [A Unifying Contrast Maximization Framework for Event Cameras, with Applications to Motion, Depth, and Optical Flow Estimation](https://mlsanity.com/paper/1804.01306/) (2018)
- [Multiple Object Tracking: A Literature Review](https://mlsanity.com/paper/1409.7618/) (2014)
- [E-RAFT: Dense Optical Flow from Event Cameras](https://mlsanity.com/paper/2108.10552/) (2021)
- [Back to Event Basics: Self-Supervised Learning of Image Reconstruction for Event Cameras via Photometric Constancy](https://mlsanity.com/paper/2009.08283/) (2020)
- [Event-based Stereo Visual Odometry](https://mlsanity.com/paper/2007.15548/) (2020)
- [Exactly Computing the Local Lipschitz Constant of ReLU Networks](https://mlsanity.com/paper/2003.01219/) (2020)
- [Self-Supervised Learning of Event-Based Optical Flow with Spiking Neural Networks](https://mlsanity.com/paper/2106.01862/) (2021)
- [Spike-FlowNet: Event-based Optical Flow Estimation with Energy-Efficient Hybrid Neural Networks](https://mlsanity.com/paper/2003.06696/) (2020)
- [Secrets of Event-Based Optical Flow](https://mlsanity.com/paper/2207.10022/) (2022)
- [Neural Scene Flow Prior](https://mlsanity.com/paper/2111.01253/) (2021)
- [Focus Is All You Need: Loss Functions For Event-based Vision](https://mlsanity.com/paper/1904.07235/) (2019)
- [Learning Dense and Continuous Optical Flow from an Event Camera](https://mlsanity.com/paper/2211.09078/) (2022)
- [Spatio-Temporal Recurrent Networks for Event-Based Optical Flow Estimation](https://mlsanity.com/paper/2109.04871/) (2021)
- [Dense Continuous-Time Optical Flow from Events and Frames](https://mlsanity.com/paper/2203.13674/) (2022)
- [Taming Contrast Maximization for Learning Sequential, Low-latency, Event-based Optical Flow](https://mlsanity.com/paper/2303.05214/) (2023)

## Built on by (most cited first, 2 of 2)

- [Minimal Solvers for Full-DoF Motion Estimation from Asynchronous Differential SfM](https://mlsanity.com/paper/2606.09218/) (2026)
- [GoStop: Reinforcement Learning for Adaptive Temporal Aggregation in Event-Based Feature Tracking](https://mlsanity.com/paper/2607.15699/) (2026)

## Abstract (arXiv)

The estimation of optical flow and 6-DoF ego-motion, two fundamental tasks in 3D vision, has typically been addressed independently. For neuromorphic vision (e.g., event cameras), however, the lack of robust data association makes solving the two problems separately an ill-posed challenge, especially in the absence of supervision via ground truth. Existing works mitigate this ill-posedness by either enforcing the smoothness of the flow field via an explicit variational regularizer or leveraging explicit structure-and-motion priors in the parametrization to improve event alignment. The former notably introduces bias in results and computational overhead, while the latter, which parametrizes the optical flow in terms of the scene depth and the camera motion, often converges to suboptimal local minima. To address these issues, we propose an unsupervised framework that jointly optimizes egomotion and optical flow via implicit spatial-temporal and geometric regularization. First, by modeling camera's egomotion as a continuous spline and optical flow as an implicit neural representation, our method inherently embeds spatial-temporal coherence through inductive biases. Second, we incorporate structure-and-motion priors through differential geometric constraints, bypassing explicit depth estimation while maintaining rigorous geometric consistency. As a result, our framework (called E-MoFlow) unifies egomotion and optical flow estimation via implicit regularization under a fully unsupervised paradigm. Experiments demonstrate its versatility to general 6-DoF motion scenarios, achieving state-of-the-art performance among unsupervised methods and competitive even with supervised approaches.