A Nonlinear Method for Estimating the Projective Geometry of Three Views

Given three partially overlapping views of a scene from which a set of point correspondences have been extracted, recover the three trifocal tensors between the three views. We give a new way of deriving the trifocal tensor based on Grassmann-Cayley algebra that sheds some new light on its structure. We show that our derivation leads to a complete characterization of its geometric and algebraic properties which is fairly intuitive, i.e. geometric. We give a set of algebraic constraints which are satisfied by the 27 coefficients of the trifocal tensor and 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. Our experimental results show that this method is superior to the linear methods which had been previously published. Key-words: Multiple-view geometry, Trifocal tensor, Fundamental matrix, GrassmannCayley algebra, Calibration