Silhouette-based 2D-3D Pose Estimation Using Algebraic Surfaces

In this contribution we present a formulation of the 2D3D pose estimation problem using implicit algebraic surfaces. To model the projective mapping, we apply novel Dixon resultant heuristics to deal with the rapidly increasing polynomial degrees of projected image outlines. The advantages as well as disadvantages of using linearised twist coordinates for pose representation are also discussed. We also show that for pose estimation purposes, using simple algebraic distance is more practical than using a first-order approximation of the exact Euclidean distance between a point and an implicitly defined entity. While not as effective as current explicit approaches, our implicit formulation offers potential improvements in silhouette-based pose estimation.