# GeoMoE: Divide-and-Conquer Motion Field Modeling with Mixture-of-Experts for Two-View Geometry

arXiv: https://arxiv.org/abs/2508.00592 · HTML: https://mlsanity.com/paper/2508.00592/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Vision mixture-of-experts, one of 12 directions in Mixture-of-experts.
- Builds on 19 of its 41 references that are in the map.
- First posted on arXiv 1 Aug 2025.

## Placed in

- Mixture-of-experts / [Vision mixture-of-experts](https://mlsanity.com/moe/vision-mixture-of-experts/)

## Builds on (most cited first, 19 of 19)

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- [GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding](https://mlsanity.com/paper/2006.16668/) (2020)
- [SuperGlue: Learning Feature Matching with Graph Neural Networks](https://mlsanity.com/paper/1911.11763/) (2019)
- [SuperPoint: Self-Supervised Interest Point Detection and Description](https://mlsanity.com/paper/1712.07629/) (2017)
- [ORB-SLAM: a Versatile and Accurate Monocular SLAM System](https://mlsanity.com/paper/1502.00956/) (2015)
- [3DMatch: Learning Local Geometric Descriptors from RGB-D Reconstructions](https://mlsanity.com/paper/1603.08182/) (2016)
- [LIFT: Learned Invariant Feature Transform](https://mlsanity.com/paper/1603.09114/) (2016)
- [HPatches: A benchmark and evaluation of handcrafted and learned local descriptors](https://mlsanity.com/paper/1704.05939/) (2017)
- [Learning to Find Good Correspondences](https://mlsanity.com/paper/1711.05971/) (2017)
- [MAGSAC++, a fast, reliable and accurate robust estimator](https://mlsanity.com/paper/1912.05909/) (2019)
- [Learning Two-View Correspondences and Geometry Using Order-Aware Network](https://mlsanity.com/paper/1908.04964/) (2019)
- [PointDSC: Robust Point Cloud Registration using Deep Spatial Consistency](https://mlsanity.com/paper/2103.05465/) (2021)
- [Neural-Guided RANSAC: Learning Where to Sample Model Hypotheses](https://mlsanity.com/paper/1905.04132/) (2019)
- [Progressive Correspondence Pruning by Consensus Learning](https://mlsanity.com/paper/2101.00591/) (2021)
- [Learnable Motion Coherence for Correspondence Pruning](https://mlsanity.com/paper/2011.14563/) (2020)
- [BCLNet: Bilateral Consensus Learning for Two-View Correspondence Pruning](https://mlsanity.com/paper/2401.03459/) (2024)
- [VSFormer: Visual-Spatial Fusion Transformer for Correspondence Pruning](https://mlsanity.com/paper/2312.08774/) (2023)
- [CorrMoE: Mixture of Experts with De-stylization Learning for Cross-Scene and Cross-Domain Correspondence Pruning](https://mlsanity.com/paper/2507.11834/) (2025)

## Abstract (arXiv)

Recent progress in two-view geometry increasingly emphasizes enforcing smoothness and global consistency priors when estimating motion fields between pairs of images. However, in complex real-world scenes, characterized by extreme viewpoint and scale changes as well as pronounced depth discontinuities, the motion field often exhibits diverse and heterogeneous motion patterns. Most existing methods lack targeted modeling strategies and fail to explicitly account for this variability, resulting in estimated motion fields that diverge from their true underlying structure and distribution. We observe that Mixture-of-Experts (MoE) can assign dedicated experts to motion sub-fields, enabling a divide-and-conquer strategy for heterogeneous motion patterns. Building on this insight, we re-architect motion field modeling in two-view geometry with GeoMoE, a streamlined framework. Specifically, we first devise a Probabilistic Prior-Guided Decomposition strategy that exploits inlier probability signals to perform a structure-aware decomposition of the motion field into heterogeneous sub-fields, sharply curbing outlier-induced bias. Next, we introduce an MoE-Enhanced Bi-Path Rectifier that enhances each sub-field along spatial-context and channel-semantic paths and routes it to a customized expert for targeted modeling, thereby decoupling heterogeneous motion regimes, suppressing cross-sub-field interference and representational entanglement, and yielding fine-grained motion-field rectification. With this minimalist design, GeoMoE outperforms prior state-of-the-art methods in relative pose and homography estimation and shows strong generalization. The source code and pre-trained models are available at https://github.com/JiajunLe/GeoMoE.