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Decoupled Geometric Parameterization and its Application in Deep Homography Estimation

arXiv 2505.16599 ↗First posted 22 May 2025cs.CVcited by 0

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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.

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.

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26 of 48 references.

References · 26

  1. 2014Microsoft COCO: Common Objects in Contextcited by 17,608
  2. 2019SuperGlue: Learning Feature Matching with Graph Neural Networkscited by 1,443
  3. 2017SuperPoint: Self-Supervised Interest Point Detection and Descriptioncited by 1,320
  4. 2015FlowNet: Learning Optical Flow with Convolutional Networkscited by 1,059
  5. 2015ORB-SLAM: a Versatile and Accurate Monocular SLAM Systemcited by 988
  6. 2017PWC-Net: CNNs for Optical Flow Using Pyramid, Warping, and Cost Volumecited by 968
  7. 2017PoseCNN: A Convolutional Neural Network for 6D Object Pose Estimation in Cluttered Scenescited by 775
  8. 2019DenseFusion: 6D Object Pose Estimation by Iterative Dense Fusioncited by 355
  9. 2016LIFT: Learned Invariant Feature Transformcited by 306
  10. 2016Deep Image Homography Estimationcited by 136
  11. 2019SOSNet: Second Order Similarity Regularization for Local Descriptor Learningcited by 131
  12. 2018MAGSAC: marginalizing sample consensuscited by 123
14 more
  1. 2017Unsupervised Deep Homography: A Fast and Robust Homography Estimation Modelcited by 75
  2. 2022Category-Level 6D Object Pose and Size Estimation using Self-Supervised Deep Prior Deformation Networkscited by 74
  3. 2019Content-Aware Unsupervised Deep Homography Estimationcited by 62
  4. 2020Deep Homography Estimation for Dynamic Scenescited by 61
  5. 2022Iterative Deep Homography Estimationcited by 45
  6. 2024Instance-Adaptive and Geometric-Aware Keypoint Learning for Category-Level 6D Object Pose Estimationcited by 43
  7. 2021Deep Lucas-Kanade Homography for Multimodal Image Alignmentcited by 38
  8. 2022Affine Medical Image Registration with Coarse-to-Fine Vision Transformercited by 35
  9. 2021Motion Basis Learning for Unsupervised Deep Homography Estimation with Subspace Projectioncited by 28
  10. 2021LocalTrans: A Multiscale Local Transformer Network for Cross-Resolution Homography Estimationcited by 28
  11. 2022Unsupervised Homography Estimation with Coplanarity-Aware GANcited by 19
  12. 2018AIRNet: Self-Supervised Affine Registration for 3D Medical Images using Neural Networkscited by 12
  13. 2020Extending DeepSDF for automatic 3D shape retrieval and similarity transform estimationcited by 3
  14. 2024Fast and Interpretable 2D Homography Decomposition: Similarity-Kernel-Similarity and Affine-Core-Affine Transformationscited by 3

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