Analytical Modeling and Correction of Distance Error in Homography-Based Ground-Plane Mapping

• URL: http://arxiv.org/abs/2604.10805v1
• Date: Sun, 12 Apr 2026 20:33:09 GMT
• Title: Analytical Modeling and Correction of Distance Error in Homography-Based Ground-Plane Mapping
• Abstract summary: This paper derives an explicit relationship between homography perturbations and the resulting distance error, showing that the error grows approximately quadratically with the true distance from the camera.<n>A large-scale simulation study with more than 19 million test samples demonstrates that regression achieves higher peak accuracy when the model is reliably fitted.<n>This suggests that improving geometric calibration may yield greater performance gains than increasing model complexity in many practical systems.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Accurate distance estimation from monocular cameras is essential for intelligent monitoring systems. In many deployments, image coordinates are mapped to ground positions using planar homographies initialized by manual selection of corresponding regions. Small inaccuracies in this initialization propagate into systematic distance distortions. This paper derives an explicit relationship between homography perturbations and the resulting distance error, showing that the error grows approximately quadratically with the true distance from the camera. Based on this model, two simple correction strategies are evaluated: regression-based estimation of the quadratic error function and direct optimization of the homography via coordinate-based gradient descent. A large-scale simulation study with more than 19 million test samples demonstrates that regression achieves higher peak accuracy when the model is reliably fitted, whereas gradient descent provides greater robustness against poor initial calibration. This suggests that improving geometric calibration may yield greater performance gains than increasing model complexity in many practical systems.

Related papers

• Homographic Navigation: Geometry-Driven Camera Guidance for Deterministic Planar Capture [0.9036844836403516]
  Homographic navigation is a geometry-centric framework for guiding camera acquisition toward precise capture of planar regions.<n>We generate unlimited synthetic training data via homographic augmentation and train a single-shot model for joint recognition and localization.<n> Experimental results demonstrate that accurate planar alignment can be achieved from minimal supervision.
  arXiv  Detail & Related papers  (2026-06-22T04:15:08Z)
• Research on a Camera Position Measurement Method based on a Parallel Perspective Error Transfer Model [9.335726811337617]
  Camera pose estimation from sparse correspondences is a fundamental problem in computer vision.<n>We present a geometric error propagation framework for camera pose estimation based on a parallel perspective approximation.
  arXiv  Detail & Related papers  (2026-02-08T09:40:14Z)
• Long-Range depth estimation using learning based Hybrid Distortion Model for CCTV cameras [0.0]
  This paper presents a framework for modeling a suitable distortion model that can be used for localizing the objects at longer distances.<n>It is well known that neural networks can be a better alternative to model a highly complex non-linear lens distortion function.<n>This hybrid approach has substantially improved long-range localization performance and is capable of estimating the 3D position of objects at distances up to 5 kilometres.
  arXiv  Detail & Related papers  (2025-12-19T16:54:43Z)
• Predicting ptychography probe positions using single-shot phase retrieval neural network [5.889405057118457]
  We propose a fundamentally new approach for ptychography probe position prediction for data with large position errors. A neural network is used to make single-shot phase retrieval on individual diffraction patterns, yielding the object image at each scan point. We show that our method can achieve good position prediction accuracy for data with large and accumulating errors on the order of $102$ pixels.
  arXiv  Detail & Related papers  (2024-05-31T15:21:06Z)
• SPARE: Symmetrized Point-to-Plane Distance for Robust Non-Rigid 3D Registration [77.13381026159111]
  We propose SPARE, a novel formulation that utilizes a symmetrized point-to-plane distance for robust non-rigid registration.<n>The proposed method greatly improves the accuracy of non-rigid registration problems and maintains relatively high solution efficiency.
  arXiv  Detail & Related papers  (2024-05-30T15:55:04Z)
• GDCNet: Calibrationless geometric distortion correction of echo planar imaging data using deep learning [0.1398098625978622]
  This work implements a novel approach called GDCNet, which estimates a geometric distortion map by non-linear registration to T1-weighted anatomical images. GDCNet models achieved processing speeds 14 times faster than TOPUP in the prospective dataset.
  arXiv  Detail & Related papers  (2024-02-29T00:42:33Z)
• iComMa: Inverting 3D Gaussian Splatting for Camera Pose Estimation via Comparing and Matching [14.737266480464156]
  We present a method named iComMa to address the 6D camera pose estimation problem in computer vision. We propose an efficient method for accurate camera pose estimation by inverting 3D Gaussian Splatting (3DGS)
  arXiv  Detail & Related papers  (2023-12-14T15:31:33Z)
• Model-Based Reparameterization Policy Gradient Methods: Theory and Practical Algorithms [88.74308282658133]
  Reization (RP) Policy Gradient Methods (PGMs) have been widely adopted for continuous control tasks in robotics and computer graphics. Recent studies have revealed that, when applied to long-term reinforcement learning problems, model-based RP PGMs may experience chaotic and non-smooth optimization landscapes. We propose a spectral normalization method to mitigate the exploding variance issue caused by long model unrolls.
  arXiv  Detail & Related papers  (2023-10-30T18:43:21Z)
• A Model for Multi-View Residual Covariances based on Perspective Deformation [88.21738020902411]
  We derive a model for the covariance of the visual residuals in multi-view SfM, odometry and SLAM setups. We validate our model with synthetic and real data and integrate it into photometric and feature-based Bundle Adjustment.
  arXiv  Detail & Related papers  (2022-02-01T21:21:56Z)
• Poseur: Direct Human Pose Regression with Transformers [119.79232258661995]
  We propose a direct, regression-based approach to 2D human pose estimation from single images. Our framework is end-to-end differentiable, and naturally learns to exploit the dependencies between keypoints. Ours is the first regression-based approach to perform favorably compared to the best heatmap-based pose estimation methods.
  arXiv  Detail & Related papers  (2022-01-19T04:31:57Z)
• 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)
• Attentive One-Dimensional Heatmap Regression for Facial Landmark Detection and Tracking [73.35078496883125]
  We propose a novel attentive one-dimensional heatmap regression method for facial landmark localization. First, we predict two groups of 1D heatmaps to represent the marginal distributions of the x and y coordinates. Second, a co-attention mechanism is adopted to model the inherent spatial patterns existing in x and y coordinates. Third, based on the 1D heatmap structures, we propose a facial landmark detector capturing spatial patterns for landmark detection on an image.
  arXiv  Detail & Related papers  (2020-04-05T06:51:22Z)

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.