基于噪声点对应的闭式贝叶斯单应性估计
Closed-form Bayesian homography estimation from noisy point correspondences
- Technische Hochschule Augsburg（奥格斯堡应用技术大学）
- TTZ Landsberg am Lech（兰茨贝格技术转化中心）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
本文提出一种闭式贝叶斯单应性估计方法，融合测量不确定性与先验知识，提供后验分布，在合成和真实实验中优于DLT并输出不确定性。
中文摘要 AI 辅助
虽然单应性矩阵在许多计算机视觉任务中至关重要，但大多数传统估计技术仅提供点估计，而不直接量化由噪声观测引入的不确定性。然而，不确定性会传播到后续处理步骤，如相机标定和三维重建，并且在医疗成像、自动驾驶和国防等安全关键及社会相关领域尤为重要。我们提出了一种从点对应关系进行单应性估计的快速贝叶斯公式，该公式明确地融合了测量不确定性和先验知识，同时提供单应性参数的后验分布。在齐次坐标下推导了单应性后验均值的闭式解，并辅以迭代贝叶斯方法以处理非线性问题。合成实验证明了该方法对投影变换的适用性，并展示了在不同噪声条件下相比DLT方法更高的估计精度。图像拼接实验进一步证明了该方法对真实图像对应关系的适用性，同时额外提供了不确定性信息。
英文摘要
While homographies are fundamental to many computer vision tasks, the majority of conventional estimation techniques provide only point estimates without directly quantifying uncertainty introduced by noisy observations. Uncertainty, though, propagates to subsequent processing steps such as camera calibration and 3D reconstruction and is particularly relevant in safety-critical and socially relevant fields including medical imaging, autonomous driving, and defense. We present a fast Bayesian formulation for homography estimation from point correspondences that explicitly incorporates measurement uncertainty and prior knowledge while providing a posterior distribution over the homography parameters. A closed-form solution of the posterior mean of the homography is derived in homogeneous coordinates and supplemented by an iterative Bayesian approach to handle non-linearities. Synthetic experiments demonstrate the applicability to projective transformations and show improved estimation accuracy over DLT under varying noise conditions. Image stitching experiments further demonstrate applicability to real image correspondences while additionally providing uncertainty information.
