A novel geometric invariant of a pair of conics and its application to eyeglasses-tracking interface

This paper deals with a three-dimensional (3-D) pose estimation problem of a pair of two conics. We first introduce a novel geometric invariant derived from a pair of conics, and then propose a procedure of determining a set of three invariants when two independent conics are given. As a solution of P2C (perspective-two-conics) problem, this paper also provides a pose estimation algorithm that employs an iterative procedure, which aims to optimize the orientation parameters by involving the shape information of conics. The proposed method is verified through a series of experiments for analyzing pose estimation accuracy and precision, being compared with some general approaches. As an application example, we present an eyeglasses-tracking interface, and discuss its performance through some experiment results.