Fast and Interpretable 2D Homography Decomposition:
Similarity-Kernel-Similarity and Affine-Core-Affine Transformations
- URL: http://arxiv.org/abs/2402.18008v1
- Date: Wed, 28 Feb 2024 02:46:06 GMT
- Title: Fast and Interpretable 2D Homography Decomposition:
Similarity-Kernel-Similarity and Affine-Core-Affine Transformations
- Authors: Shen Cai, Zhanhao Wu, Lingxi Guo, Jiachun Wang, Siyu Zhang, Junchi
Yan, and Shuhan Shen
- Abstract summary: We present two decomposition methods for 2D homography, which are named Similarity- Kernel-Similarity (SKS) and Affine-Core-Affine (ACA) transformations respectively.
As a plug-in module, ACA facilitates the traditional feature-based Random Sample Consensus (RANSAC) pipeline.
- Score: 49.07547885674818
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: 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 ($7$th degree to $9$th 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.
Related papers
- FlatCAD: Fast Curvature Regularization of Neural SDFs for CAD Models [41.13351630648502]
We present a curvature proxy that regularizes only the mixed second-order term.<n>Because the method is drop-in and framework-agnostic, it opens a practical path toward scalable, curvature-aware SDF learning.
arXiv Detail & Related papers (2025-06-19T21:54:08Z) - Decoupled Geometric Parameterization and its Application in Deep Homography Estimation [52.96857897366727]
Planar homography, with eight degrees of freedom (DOFs), is fundamental in numerous computer vision tasks.<n>This paper presents a novel geometric parameterization of homographies, leveraging the similarity- kernel-similarity decomposition for projective transformations.<n>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.
arXiv Detail & Related papers (2025-05-22T12:33:29Z) - Variable-size Symmetry-based Graph Fourier Transforms for image compression [65.7352685872625]
We propose a new family of Symmetry-based Graph Fourier Transforms of variable sizes into a coding framework.
Our proposed algorithm generates symmetric graphs on the grid by adding specific symmetrical connections between nodes.
Experiments show that SBGFTs outperform the primary transforms integrated in the explicit Multiple Transform Selection.
arXiv Detail & Related papers (2024-11-24T13:00:44Z) - Geometry-aware Reconstruction and Fusion-refined Rendering for Generalizable Neural Radiance Fields [18.474371929572918]
Generalizable NeRF aims to synthesize novel views for unseen scenes.
We introduce an Adaptive Cost Aggregation (ACA) approach to amplify the contribution of consistent pixel pairs.
We observe the two existing decoding strategies excel in different areas, which are complementary.
arXiv Detail & Related papers (2024-04-26T16:46:28Z) - CoFiI2P: Coarse-to-Fine Correspondences for Image-to-Point Cloud Registration [9.57539651520755]
CoFiI2P is a novel I2P registration network that extracts correspondences in a coarse-to-fine manner.
In the coarse matching phase, a novel I2P transformer module is employed to capture both homogeneous and heterogeneous global information.
In the fine matching module, point/pixel pairs are established with the guidance of super-point/super-pixel correspondences.
arXiv Detail & Related papers (2023-09-26T04:32:38Z) - DPCN++: Differentiable Phase Correlation Network for Versatile Pose
Registration [18.60311260250232]
We present a differentiable phase correlation solver that is globally convergent and correspondence-free.
We evaluate DCPN++ on a wide range of registration tasks taking different input modalities, including 2D bird's-eye view images, 3D object and scene measurements, and medical images.
arXiv Detail & Related papers (2022-06-12T10:00:34Z) - Hybrid Model-based / Data-driven Graph Transform for Image Coding [54.31406300524195]
We present a hybrid model-based / data-driven approach to encode an intra-prediction residual block.
The first $K$ eigenvectors of a transform matrix are derived from a statistical model, e.g., the asymmetric discrete sine transform (ADST) for stability.
Using WebP as a baseline image, experimental results show that our hybrid graph transform achieved better energy compaction than default discrete cosine transform (DCT) and better stability than KLT.
arXiv Detail & Related papers (2022-03-02T15:36:44Z) - Copy-Move Image Forgery Detection Based on Evolving Circular Domains
Coverage [5.716030416222748]
The proposed scheme integrates both block-based and keypoint-based forgery detection methods.
The experimental results indicate that the proposed CMFD scheme can achieve better detection performance under various attacks.
arXiv Detail & Related papers (2021-09-09T16:08:03Z) - Zero-Shot Domain Adaptation in CT Segmentation by Filtered Back
Projection Augmentation [0.1197985185770095]
Domain shift is one of the most salient challenges in medical computer vision.
We address variability in computed tomography (CT) images caused by different convolution kernels used in the reconstruction process.
We propose Filtered Back-Projection Augmentation (FBPAug), a simple and surprisingly efficient approach to augment CT images in sinogram space emulating reconstruction with different kernels.
arXiv Detail & Related papers (2021-07-18T21:46:49Z) - Making Affine Correspondences Work in Camera Geometry Computation [62.7633180470428]
Local features provide region-to-region rather than point-to-point correspondences.
We propose guidelines for effective use of region-to-region matches in the course of a full model estimation pipeline.
Experiments show that affine solvers can achieve accuracy comparable to point-based solvers at faster run-times.
arXiv Detail & Related papers (2020-07-20T12:07:48Z) - RANSAC-Flow: generic two-stage image alignment [53.11926395028508]
We show that a simple unsupervised approach performs surprisingly well across a range of tasks.
Despite its simplicity, our method shows competitive results on a range of tasks and datasets.
arXiv Detail & Related papers (2020-04-03T12:37:58Z) - Region adaptive graph fourier transform for 3d point clouds [51.193111325231165]
We introduce the Region Adaptive Graph Fourier Transform (RA-GFT) for compression of 3D point cloud attributes.
The RA-GFT achieves better complexity-performance trade-offs than previous approaches.
arXiv Detail & Related papers (2020-03-04T02:47:44Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.