  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.
