Non-Rigid Alignment and Real-Time Tracking Using the Geometric Algebra Framework

Abstract

This paper presents two applications of geometric algebras: the main is a variant of the thin-plate - robust point matching algorithm, named by us "robust sphere matching", to register 3D objects modeled as sets of spheres using the representation of such spheres in the conformal geometric algebra. By this way, we take advantage and combine the geometric interpretation of entities of such algebra with the statistical methods used in the algorithm. In the experimental part, examples using synthetic and real data are presented to show how the algorithm works reliably, aligning volumetric models based on spheres. The second application is the real time tracking of devices