# Motion Basis Learning for Unsupervised Deep Homography Estimation with Subspace Projection

arXiv: https://arxiv.org/abs/2103.15346 · HTML: https://mlsanity.com/paper/2103.15346/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 33 references that are in the map.
- First posted on arXiv 29 Mar 2021.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [SuperGlue: Learning Feature Matching with Graph Neural Networks](https://mlsanity.com/paper/1911.11763/) (2019)
- [Spatial Transformer Networks](https://mlsanity.com/paper/1506.02025/) (2015)
- [SuperPoint: Self-Supervised Interest Point Detection and Description](https://mlsanity.com/paper/1712.07629/) (2017)
- [LIFT: Learned Invariant Feature Transform](https://mlsanity.com/paper/1603.09114/) (2016)
- [Learning Two-View Correspondences and Geometry Using Order-Aware Network](https://mlsanity.com/paper/1908.04964/) (2019)
- [Deep Image Homography Estimation](https://mlsanity.com/paper/1606.03798/) (2016)
- [SOSNet: Second Order Similarity Regularization for Local Descriptor Learning](https://mlsanity.com/paper/1904.05019/) (2019)
- [MAGSAC: marginalizing sample consensus](https://mlsanity.com/paper/1803.07469/) (2018)
- [Unsupervised Deep Homography: A Fast and Robust Homography Estimation Model](https://mlsanity.com/paper/1709.03966/) (2017)
- [Content-Aware Unsupervised Deep Homography Estimation](https://mlsanity.com/paper/1909.05983/) (2019)
- [Deep Homography Estimation for Dynamic Scenes](https://mlsanity.com/paper/2004.02132/) (2020)
- [LSM: Learning Subspace Minimization for Low-level Vision](https://mlsanity.com/paper/2004.09197/) (2020)

## Built on by (most cited first, 28 of 28)

- [Multiway Non-rigid Point Cloud Registration via Learned Functional Map Synchronization](https://mlsanity.com/paper/2111.12878/) (2021)
- [Deep Learning for Camera Calibration and Beyond: A Survey](https://mlsanity.com/paper/2303.10559/) (2023)
- [Unsupervised Homography Estimation with Coplanarity-Aware GAN](https://mlsanity.com/paper/2205.03821/) (2022)
- [Multi-Object Discovery by Low-Dimensional Object Motion](https://mlsanity.com/paper/2307.08027/) (2023)
- [Towards Real-World HDR Video Reconstruction: A Large-Scale Benchmark Dataset and A Two-Stage Alignment Network](https://mlsanity.com/paper/2405.00244/) (2024)
- [Minimum Latency Deep Online Video Stabilization](https://mlsanity.com/paper/2212.02073/) (2022)
- [Semi-supervised Deep Large-baseline Homography Estimation with Progressive Equivalence Constraint](https://mlsanity.com/paper/2212.02763/) (2022)
- [GyroFlow+: Gyroscope-Guided Unsupervised Deep Homography and Optical Flow Learning](https://mlsanity.com/paper/2301.10018/) (2023)
- [FlowSeek: Optical Flow Made Easier with Depth Foundation Models and Motion Bases](https://mlsanity.com/paper/2509.05297/) (2025)
- [MASIV: Toward Material-Agnostic System Identification from Videos](https://mlsanity.com/paper/2508.01112/) (2025)
- [AbHE: All Attention-based Homography Estimation](https://mlsanity.com/paper/2212.03029/) (2022)
- [SCPNet: Unsupervised Cross-modal Homography Estimation via Intra-modal Self-supervised Learning](https://mlsanity.com/paper/2407.08148/) (2024)
- [Supervised Homography Learning with Realistic Dataset Generation](https://mlsanity.com/paper/2307.15353/) (2023)
- [Decoupling Degradations with Recurrent Network for Video Restoration in Under-Display Camera](https://mlsanity.com/paper/2403.05660/) (2024)
- [SSHNet: Unsupervised Cross-modal Homography Estimation via Problem Reformulation and Split Optimization](https://mlsanity.com/paper/2409.17993/) (2024)
- [Fast and Interpretable 2D Homography Decomposition: Similarity-Kernel-Similarity and Affine-Core-Affine Transformations](https://mlsanity.com/paper/2402.18008/) (2024)
- [CodingHomo: Bootstrapping Deep Homography With Video Coding](https://mlsanity.com/paper/2504.12165/) (2025)
- [Leveraging Synthetic Data to Learn Video Stabilization Under Adverse Conditions](https://mlsanity.com/paper/2208.12763/) (2022)
- [SSORN: Self-Supervised Outlier Removal Network for Robust Homography Estimation](https://mlsanity.com/paper/2208.14093/) (2022)
- [Parallax-Tolerant Image Stitching with Epipolar Displacement Field](https://mlsanity.com/paper/2311.16637/) (2023)
- [SeFENet: Robust Deep Homography Estimation via Semantic-Driven Feature Enhancement](https://mlsanity.com/paper/2412.06352/) (2024)
- [UDC-VIT: A Real-World Video Dataset for Under-Display Cameras](https://mlsanity.com/paper/2501.18545/) (2025)
- [Towards Generalized Multimodal Homography Estimation](https://mlsanity.com/paper/2603.03956/) (2026)
- [Multi-task Learning for Camera Calibration](https://mlsanity.com/paper/2211.12432/) (2022)
- [Dynamic in Static: Hybrid Visual Correspondence for Self-Supervised Video Object Segmentation](https://mlsanity.com/paper/2404.13505/) (2024)
- [Decoupled Geometric Parameterization and its Application in Deep Homography Estimation](https://mlsanity.com/paper/2505.16599/) (2025)
- [Estimating 2D Camera Motion with Hybrid Motion Basis](https://mlsanity.com/paper/2507.22480/) (2025)
- [CamFlow+: Hybrid Motion Bases for 2D Camera Motion Estimation with Stabilization Applications](https://mlsanity.com/paper/2606.05915/) (2026)

## Abstract (arXiv)

In this paper, we introduce a new framework for unsupervised deep homography estimation. Our contributions are 3 folds. First, unlike previous methods that regress 4 offsets for a homography, we propose a homography flow representation, which can be estimated by a weighted sum of 8 pre-defined homography flow bases. Second, considering a homography contains 8 Degree-of-Freedoms (DOFs) that is much less than the rank of the network features, we propose a Low Rank Representation (LRR) block that reduces the feature rank, so that features corresponding to the dominant motions are retained while others are rejected. Last, we propose a Feature Identity Loss (FIL) to enforce the learned image feature warp-equivariant, meaning that the result should be identical if the order of warp operation and feature extraction is swapped. With this constraint, the unsupervised optimization is achieved more effectively and more stable features are learned. Extensive experiments are conducted to demonstrate the effectiveness of all the newly proposed components, and results show that our approach outperforms the state-of-the-art on the homography benchmark datasets both qualitatively and quantitatively. Code is available at https://github.com/megvii-research/BasesHomo.