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：刚性物体的姿态估计是光学计量学和计算机视觉中的一个实际挑战。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姿态估计。方法：该框架利用混合模型描述物体空间中的特征点密度并解释实际测量值。其优势在于避免了解决单个特征对应性问题，并能在多视角应用中纳入正确的随机依赖性。首先，介绍通用建模框架；其次，推导出姿态估计的通用算法；最后，给出两个示例模型（相机设置和测距设置）。结果：数值实验通过为三个观测系统呈现四种仿真场景（包括测量分辨率、物体形变和测量噪声的依赖性），展示了该建模方法和通用算法的有效性。利用混合模型的概率建模显示了在避免对应性问题的同时实现准确鲁棒姿态估计的潜力。