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：刚体姿态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，通过观测多个特征点实现物体姿态估计。方法：该框架利用混合模型描述物体空间中的特征点密度，并用于解释实际测量值。其优势在于无需解决单个特征的对应问题，并能在多视角应用中纳入正确的随机依赖关系。首先提出通用建模框架，其次推导出姿态估计的通用算法，最后给出两个示例模型（相机设置和距离测量设置）。结果：数值实验通过展示三种观测系统的四个仿真场景（包括对测量分辨率、物体形变和测量噪声的依赖性），验证了该建模方法及通用算法的有效性。利用混合模型的概率建模表明，在避免对应问题的同时，能够实现精准且鲁棒的姿态估计。