  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.
