# Fast and Interpretable 2D Homography Decomposition: Similarity-Kernel-Similarity and Affine-Core-Affine Transformations

arXiv: https://arxiv.org/abs/2402.18008 · HTML: https://mlsanity.com/paper/2402.18008/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 93 references that are in the map.
- First posted on arXiv 28 Feb 2024.

## Builds on (most cited first, 22 of 22)

- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [SuperPoint: Self-Supervised Interest Point Detection and Description](https://mlsanity.com/paper/1712.07629/) (2017)
- [ORB-SLAM3: An Accurate Open-Source Library for Visual, Visual-Inertial and Multi-Map SLAM](https://mlsanity.com/paper/2007.11898/) (2020)
- [LIFT: Learned Invariant Feature Transform](https://mlsanity.com/paper/1603.09114/) (2016)
- [DSAC - Differentiable RANSAC for Camera Localization](https://mlsanity.com/paper/1611.05705/) (2016)
- [Image Matching across Wide Baselines: From Paper to Practice](https://mlsanity.com/paper/2003.01587/) (2020)
- [MAGSAC++, a fast, reliable and accurate robust estimator](https://mlsanity.com/paper/1912.05909/) (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)
- [Deep Homography Estimation for Dynamic Scenes](https://mlsanity.com/paper/2004.02132/) (2020)
- [Unsupervised Deep Image Stitching: Reconstructing Stitched Features to Images](https://mlsanity.com/paper/2106.12859/) (2021)
- [SOLD2: Self-supervised Occlusion-aware Line Description and Detection](https://mlsanity.com/paper/2104.03362/) (2021)
- [Iterative Deep Homography Estimation](https://mlsanity.com/paper/2203.15982/) (2022)
- [Deep Hough-Transform Line Priors](https://mlsanity.com/paper/2007.09493/) (2020)
- [Deep Lucas-Kanade Homography for Multimodal Image Alignment](https://mlsanity.com/paper/2104.11693/) (2021)
- [Motion Basis Learning for Unsupervised Deep Homography Estimation with Subspace Projection](https://mlsanity.com/paper/2103.15346/) (2021)
- [LocalTrans: A Multiscale Local Transformer Network for Cross-Resolution Homography Estimation](https://mlsanity.com/paper/2106.04067/) (2021)
- [Depth-Aware Multi-Grid Deep Homography Estimation with Contextual Correlation](https://mlsanity.com/paper/2107.02524/) (2021)
- [Unsupervised Homography Estimation with Coplanarity-Aware GAN](https://mlsanity.com/paper/2205.03821/) (2022)

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

- [RePoseD: Efficient Relative Pose Estimation With Known Depth Information](https://mlsanity.com/paper/2501.07742/) (2025)
- [Robust Image Stitching with Optimal Plane](https://mlsanity.com/paper/2508.05903/) (2025)
- [Decoupled Geometric Parameterization and its Application in Deep Homography Estimation](https://mlsanity.com/paper/2505.16599/) (2025)

## Abstract (arXiv)

In this paper, we present two fast and interpretable decomposition methods for 2D homography, which are named Similarity-Kernel-Similarity (SKS) and Affine-Core-Affine (ACA) transformations respectively. Under the minimal 4-point configuration, the first and the last similarity transformations in SKS are computed by two anchor points on target and source planes, respectively. Then, the other two point correspondences can be exploited to compute the middle kernel transformation with only four parameters. Furthermore, ACA uses three anchor points to compute the first and the last affine transformations, followed by computation of the middle core transformation utilizing the other one point correspondence. ACA can compute a homography up to a scale with only 85 floating-point operations (FLOPs), without even any division operations. Therefore, as a plug-in module, ACA facilitates the traditional feature-based Random Sample Consensus (RANSAC) pipeline, as well as deep homography pipelines estimating 4-point offsets. In addition to the advantages of geometric parameterization and computational efficiency, SKS and ACA can express each element of homography by a polynomial of input coordinates (7th degree to 9th degree), extend the existing essential Similarity-Affine-Projective (SAP) decomposition and calculate 2D affine transformations in a unified way. Source codes are released in https://github.com/cscvlab/SKS-Homography.