Calculating Pose with Vanishing Points of Visual-Sphere Perspective Model

Abstract: The goal of the proposed method is to directly obtain a pose matrix of a known rectangular target, without estimation, using geometric techniques. This method is specifically tailored for real-time, extreme imaging setups exceeding 180{\deg} field of view, such as a fish-eye camera view. The introduced algorithm employs geometric algebra to determine the pose for a pair of coplanar parallel lines (ideally a tangent pair as in a rectangle). This is achieved by computing vanishing points on a visual unit sphere, which correspond to pose matrix vectors. The algorithm can determine pose for an extremely distorted view source without prior rectification, owing to a visual-sphere perspective model mapping of view coordinates. Mapping can be performed using either a perspective map lookup or a parametric universal perspective distortion model, which is also presented in this paper. The outcome is a robust pose matrix computation that can be executed on an embedded system using a microcontroller, offering high accuracy and low latency. This method can be further extended to a cubic target setup for comprehensive camera calibration. It may also prove valuable in other applications requiring low latency and extreme viewing angles.