# Decoupled Geometric Parameterization and its Application in Deep Homography Estimation

arXiv: https://arxiv.org/abs/2505.16599 · HTML: https://mlsanity.com/paper/2505.16599/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 48 references that are in the map.
- First posted on arXiv 22 May 2025.

## Builds on (most cited first, 26 of 26)

- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [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)
- [FlowNet: Learning Optical Flow with Convolutional Networks](https://mlsanity.com/paper/1504.06852/) (2015)
- [ORB-SLAM: a Versatile and Accurate Monocular SLAM System](https://mlsanity.com/paper/1502.00956/) (2015)
- [PWC-Net: CNNs for Optical Flow Using Pyramid, Warping, and Cost Volume](https://mlsanity.com/paper/1709.02371/) (2017)
- [PoseCNN: A Convolutional Neural Network for 6D Object Pose Estimation in Cluttered Scenes](https://mlsanity.com/paper/1711.00199/) (2017)
- [DenseFusion: 6D Object Pose Estimation by Iterative Dense Fusion](https://mlsanity.com/paper/1901.04780/) (2019)
- [LIFT: Learned Invariant Feature Transform](https://mlsanity.com/paper/1603.09114/) (2016)
- [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)
- [Category-Level 6D Object Pose and Size Estimation using Self-Supervised Deep Prior Deformation Networks](https://mlsanity.com/paper/2207.05444/) (2022)
- [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)
- [Iterative Deep Homography Estimation](https://mlsanity.com/paper/2203.15982/) (2022)
- [Instance-Adaptive and Geometric-Aware Keypoint Learning for Category-Level 6D Object Pose Estimation](https://mlsanity.com/paper/2403.19527/) (2024)
- [Deep Lucas-Kanade Homography for Multimodal Image Alignment](https://mlsanity.com/paper/2104.11693/) (2021)
- [Affine Medical Image Registration with Coarse-to-Fine Vision Transformer](https://mlsanity.com/paper/2203.15216/) (2022)
- [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)
- [Unsupervised Homography Estimation with Coplanarity-Aware GAN](https://mlsanity.com/paper/2205.03821/) (2022)
- [AIRNet: Self-Supervised Affine Registration for 3D Medical Images using Neural Networks](https://mlsanity.com/paper/1810.02583/) (2018)
- [Extending DeepSDF for automatic 3D shape retrieval and similarity transform estimation](https://mlsanity.com/paper/2004.09048/) (2020)
- [Fast and Interpretable 2D Homography Decomposition: Similarity-Kernel-Similarity and Affine-Core-Affine Transformations](https://mlsanity.com/paper/2402.18008/) (2024)

## Abstract (arXiv)

Planar homography, with eight degrees of freedom (DOFs), is fundamental in numerous computer vision tasks. While the positional offsets of four corners are widely adopted (especially in neural network predictions), this parameterization lacks geometric interpretability and typically requires solving a linear system to compute the homography matrix. This paper presents a novel geometric parameterization of homographies, leveraging the similarity-kernel-similarity (SKS) decomposition for projective transformations. Two independent sets of four geometric parameters are decoupled: one for a similarity transformation and the other for the kernel transformation. Additionally, the geometric interpretation linearly relating the four kernel transformation parameters to angular offsets is derived. Our proposed parameterization allows for direct homography estimation through matrix multiplication, eliminating the need for solving a linear system, and achieves performance comparable to the four-corner positional offsets in deep homography estimation.