A nonlinear method for estimating the projective geometry of 3 views

Abstract

This article deals with the problem of recovering the three trifocal tensors between three views from a set of point correspondences. We give a new way of deriving the trifocal tensor based on Grassmann-Cayley algebra that sheds some new light on its structure and leads to a complete characterization of its geometric and algebraic properties which is fairly institute, i.e. geometric. We give a set of algebraic constraints satisfied by the 27 coefficients of the trifocal tensor which allow to parameterize it minimally with 18 coefficients. We then describe a robust method for estimating the trifocal tensor from point and line correspondences that uses this minimal parameterization. Experimental results show that this method as superior to the linear methods which had been previously published.