提出单目相机地平面映射距离误差的解析模型与校正方法
Analytical Modeling and Correction of Distance Error in Homography-Based Ground-Plane Mapping
- 建立同胚变换扰动与距离误差的显式关系，揭示误差随距离平方增长
- 回归法在模型拟合可靠时精度更高，梯度下降法对初始误差更鲁棒
- 适合需要高精度距离估计的智能监控系统，尤其关注校准质量
单目相机的精确距离估计对智能监控系统至关重要。许多部署中通过手动选取对应区域初始化平面同胚变换，将图像坐标映射到地面位置。初始化中的微小误差会引发系统性距离畸变。本文推导出同胚变换扰动与距离误差之间的显式关系，表明误差随真实距离的增加近似呈二次增长。基于该模型，评估了两种简单校正策略：基于回归的二次误差函数估计，以及基于坐标梯度下降的同胚直接优化。大规模模拟研究包含超过1900万测试样本，结果表明当模型可可靠拟合时，回归法达到更高峰值精度；而梯度下降法对初始校准不佳更具鲁棒性。这提示在多数实际系统中，提升几何校准效果可能比增加模型复杂度带来更大性能提升。
原文摘要 · Abstract (English)
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.
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