Background: Pose estimation of rigid objects is a practical challenge in optical metrology and computer vision. This paper presents a novel stochastic-geometrical modeling framework for object pose estimation based on observing multiple feature points. Methods: This framework utilizes mixture models for feature point densities in object space and for interpreting real measurements. Advantages are the avoidance to resolve individual feature correspondences and to incorporate correct stochastic dependencies in multi-view applications. First, the general modeling framework is presented, second, a general algorithm for pose estimation is derived, and third, two example models (camera and lateration setup) are presented. Results: Numerical experiments show the effectiveness of this modeling and general algorithm by presenting four simulation scenarios for three observation systems, including the dependence on measurement resolution, object deformations and measurement noise. Probabilistic modeling utilizing mixture models shows the potential for accurate and robust pose estimations while avoiding the correspondence problem.

翻译：背景：刚性物体的位姿估计是光学计量和计算机视觉中的实际挑战。本文提出了一种新颖的随机几何建模框架，用于基于观测多个特征点的物体位姿估计。方法：该框架利用混合模型描述物体空间中的特征点密度以及解释实际测量数据。其优势在于避免了解决单个特征对应问题的需求，并在多视角应用中纳入了正确的随机依赖关系。首先，介绍了通用建模框架；其次，推导了位姿估计的通用算法；最后，给出了两个示例模型（相机设置和测距设置）。结果：数值实验通过四个模拟场景展示了该建模方法和通用算法的有效性，涉及三种观测系统，包括对测量分辨率、物体形变和测量噪声的依赖性分析。利用混合模型的概率建模展示了在避免对应问题的同时实现精确且鲁棒位姿估计的潜力。