# Event-based Photometric Bundle Adjustment

arXiv: https://arxiv.org/abs/2412.14111 · HTML: https://mlsanity.com/paper/2412.14111/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 75 references that are in the map.
- First posted on arXiv 18 Dec 2024.

## Builds on (most cited first, 30 of 32)

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Event-based Vision: A Survey](https://mlsanity.com/paper/1904.08405/) (2019)
- [Direct Sparse Odometry](https://mlsanity.com/paper/1607.02565/) (2016)
- [Past, Present, and Future of Simultaneous Localization And Mapping: Towards the Robust-Perception Age](https://mlsanity.com/paper/1606.05830/) (2016)
- [High Speed and High Dynamic Range Video with an Event Camera](https://mlsanity.com/paper/1906.07165/) (2019)
- [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)
- [Ultimate SLAM? Combining Events, Images, and IMU for Robust Visual SLAM in HDR and High Speed Scenarios](https://mlsanity.com/paper/1709.06310/) (2017)
- [Asynchronous, Photometric Feature Tracking using Events and Frames](https://mlsanity.com/paper/1807.09713/) (2018)
- [Event-based Stereo Visual Odometry](https://mlsanity.com/paper/2007.15548/) (2020)
- [Event-aided Direct Sparse Odometry](https://mlsanity.com/paper/2204.07640/) (2022)
- [EventNeRF: Neural Radiance Fields from a Single Colour Event Camera](https://mlsanity.com/paper/2206.11896/) (2022)
- [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)
- [E-NeRF: Neural Radiance Fields from a Moving Event Camera](https://mlsanity.com/paper/2208.11300/) (2022)
- [Taming Contrast Maximization for Learning Sequential, Low-latency, Event-based Optical Flow](https://mlsanity.com/paper/2303.05214/) (2023)
- [Globally-Optimal Contrast Maximisation for Event Cameras](https://mlsanity.com/paper/2206.05127/) (2022)
- [CMax-SLAM: Event-based Rotational-Motion Bundle Adjustment and SLAM System using Contrast Maximization](https://mlsanity.com/paper/2403.08119/) (2024)
- [Star Tracking using an Event Camera](https://mlsanity.com/paper/1812.02895/) (2018)
- [Deep Event Visual Odometry](https://mlsanity.com/paper/2312.09800/) (2023)
- [Efficient Derivative Computation for Cumulative B-Splines on Lie Groups](https://mlsanity.com/paper/1911.08860/) (2019)
- [Formulating Event-based Image Reconstruction as a Linear Inverse Problem with Deep Regularization using Optical Flow](https://mlsanity.com/paper/2112.06242/) (2021)
- [The Spatio-Temporal Poisson Point Process: A Simple Model for the Alignment of Event Camera Data](https://mlsanity.com/paper/2106.06887/) (2021)
- [Photometric Bundle Adjustment for Vision-Based SLAM](https://mlsanity.com/paper/1608.02026/) (2016)
- [Motion-prior Contrast Maximization for Dense Continuous-Time Motion Estimation](https://mlsanity.com/paper/2407.10802/) (2024)
- [Real-Time Panoramic Tracking for Event Cameras](https://mlsanity.com/paper/1703.05161/) (2017)
- [A compact formula for the derivative of a 3-D rotation in exponential coordinates](https://mlsanity.com/paper/1312.0788/) (2013)
- [Event-based Star Tracking via Multiresolution Progressive Hough Transforms](https://mlsanity.com/paper/1906.07866/) (2019)
- [Event-based Stereo Visual Odometry with Native Temporal Resolution via Continuous-time Gaussian Process Regression](https://mlsanity.com/paper/2306.01188/) (2023)

## Built on by (most cited first, 3 of 3)

- [Unsupervised Joint Learning of Optical Flow and Intensity with Event Cameras](https://mlsanity.com/paper/2503.17262/) (2025)
- [Geometric-Photometric Event-based 3D Gaussian Ray Tracing](https://mlsanity.com/paper/2512.18640/) (2025)
- [Interp3R: Continuous-time 3D Geometry Estimation with Frames and Events](https://mlsanity.com/paper/2603.14528/) (2026)

## Abstract (arXiv)

We tackle the problem of bundle adjustment (i.e., simultaneous refinement of camera poses and scene map) for a purely rotating event camera. Starting from first principles, we formulate the problem as a classical non-linear least squares optimization. The photometric error is defined using the event generation model directly in the camera rotations and the semi-dense scene brightness that triggers the events. We leverage the sparsity of event data to design a tractable Levenberg-Marquardt solver that handles the very large number of variables involved. To the best of our knowledge, our method, which we call Event-based Photometric Bundle Adjustment (EPBA), is the first event-only photometric bundle adjustment method that works on the brightness map directly and exploits the space-time characteristics of event data, without having to convert events into image-like representations. Comprehensive experiments on both synthetic and real-world datasets demonstrate EPBA's effectiveness in decreasing the photometric error (by up to 90%), yielding results of unparalleled quality. The refined maps reveal details that were hidden using prior state-of-the-art rotation-only estimation methods. The experiments on modern high-resolution event cameras show the applicability of EPBA to panoramic imaging in various scenarios (without map initialization, at multiple resolutions, and in combination with other methods, such as IMU dead reckoning or previous event-based rotation estimation methods). We make the source code publicly available. https://github.com/tub-rip/epba