# HETA++: Global Structure-from-Motion with Hybrid Explicit Translation Averaging

arXiv: https://arxiv.org/abs/2607.15912 · HTML: https://mlsanity.com/paper/2607.15912/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 82 references that are in the map.
- First posted on arXiv 17 Jul 2026.

## Builds on (most cited first, 29 of 29)

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Mip-NeRF 360: Unbounded Anti-Aliased Neural Radiance Fields](https://mlsanity.com/paper/2111.12077/) (2021)
- [DUSt3R: Geometric 3D Vision Made Easy](https://mlsanity.com/paper/2312.14132/) (2023)
- [VGGT: Visual Geometry Grounded Transformer](https://mlsanity.com/paper/2503.11651/) (2025)
- [ORB-SLAM: a Versatile and Accurate Monocular SLAM System](https://mlsanity.com/paper/1502.00956/) (2015)
- [Grounding Image Matching in 3D with MASt3R](https://mlsanity.com/paper/2406.09756/) (2024)
- [NetVLAD: CNN architecture for weakly supervised place recognition](https://mlsanity.com/paper/1511.07247/) (2015)
- [ORB-SLAM3: An Accurate Open-Source Library for Visual, Visual-Inertial and Multi-Map SLAM](https://mlsanity.com/paper/2007.11898/) (2020)
- [Depth Anything 3: Recovering the Visual Space from Any Views](https://mlsanity.com/paper/2511.10647/) (2025)
- [π3: Permutation-Equivariant Visual Geometry Learning](https://mlsanity.com/paper/2507.13347/) (2025)
- [MapAnything: Universal Feed-Forward Metric 3D Reconstruction](https://mlsanity.com/paper/2509.13414/) (2025)
- [Global Structure-from-Motion Revisited](https://mlsanity.com/paper/2407.20219/) (2024)
- [Pixel-Perfect Structure-from-Motion with Featuremetric Refinement](https://mlsanity.com/paper/2108.08291/) (2021)
- [LaMAR: Benchmarking Localization and Mapping for Augmented Reality](https://mlsanity.com/paper/2210.10770/) (2022)
- [Rethinking Depth Estimation for Multi-View Stereo: A Unified Representation](https://mlsanity.com/paper/2201.01501/) (2022)
- [SE-Sync: A Certifiably Correct Algorithm for Synchronization over the Special Euclidean Group](https://mlsanity.com/paper/1612.07386/) (2016)
- [Detector-Free Structure from Motion](https://mlsanity.com/paper/2306.15669/) (2023)
- [Shonan Rotation Averaging: Global Optimality by Surfing SO(p)n](https://mlsanity.com/paper/2008.02737/) (2020)
- [Robust Camera Location Estimation by Convex Programming](https://mlsanity.com/paper/1412.0165/) (2014)
- [Baseline Desensitizing In Translation Averaging](https://mlsanity.com/paper/1901.00643/) (2019)
- [HARA: A Hierarchical Approach for Robust Rotation Averaging](https://mlsanity.com/paper/2111.08831/) (2021)
- [A Pose-only Solution to Visual Reconstruction and Navigation](https://mlsanity.com/paper/2103.01530/) (2021)
- [Revisiting Rotation Averaging: Uncertainties and Robust Losses](https://mlsanity.com/paper/2303.05195/) (2023)
- [ShapeFit and ShapeKick for Robust, Scalable Structure from Motion](https://mlsanity.com/paper/1608.02165/) (2016)
- [MegBA: A GPU-Based Distributed Library for Large-Scale Bundle Adjustment](https://mlsanity.com/paper/2112.01349/) (2021)
- [Reducing Drift in Structure From Motion Using Extended Features](https://mlsanity.com/paper/2008.12295/) (2020)
- [Linear Global Translation Estimation with Feature Tracks](https://mlsanity.com/paper/1503.01832/) (2015)
- [Instant Visual Odometry Initialization for Mobile AR](https://mlsanity.com/paper/2107.14659/) (2021)
- [Non-stationary Douglas-Rachford and alternating direction method of multipliers: adaptive stepsizes and convergence](https://mlsanity.com/paper/1801.03765/) (2018)

## Abstract (arXiv)

Global Structure-from-Motion (SfM) offers advantages over incremental methods in terms of efficiency and error distribution. However, the task of translation averaging remains challenging. Many existing methods rely solely on relative translations or feature tracks, which either degrade under collinear camera motion or are susceptible to outliers. In this paper, we propose a novel hybrid explicit translation averaging framework that incorporates both relative translations and feature tracks. Specifically, we first refine the relative translations using global camera rotations and remove globally inconsistent relative translations. Next, we employ convex distance-based objective functions to estimate the initial camera positions and 3D points, followed by refinement using a non-bilinear angle-based objective function. Furthermore, since camera rotations are fixed during translation averaging, inaccurate camera rotations can severely limit the accuracy of camera positions. To address this issue, we then robustly refine both camera rotations and camera positions with selected feature tracks through bounded angle-based refinement and subsequent reprojection-based bundle adjustment. In this step, feature tracks are selected to maintain a balanced spatial distribution and improve optimization efficiency. Finally, we perform a complete bundle adjustment using all reliable feature tracks to refine the camera parameters and 3D points. Extensive experiments on various sequential and unordered real-world datasets demonstrate the superior accuracy, robustness, and scalability of our approach, outperforming state-of-the-art methods in both accuracy and computational efficiency.