On Degeneracy of Linear Reconstruction from Three Views: Linear Line Complex and Applications

This paper investigates the linear degeneracies of projective structure estimation from point and line features across three views. We show that the rank of the linear system of equations for recovering the trilinear tensor of three views reduces to 23 (instead of 26) in the case when the scene is a Linear Line Complex (set of lines in space intersecting at a common line) and is 21 when the scene is planar. The LLC situation is only linearly degenerate, and we show that one can obtain a unique solution when the admissibility constraints of the tensor are accounted for. The line configuration described by an LLC, rather than being some obscure case, is in fact quite typical. It includes, as a particular example, the case of a camera moving down a hallway in an office environment or down an urban street. Furthermore, an LLC situation may occur as an artifact such as in direct estimation from spatio-temporal derivatives of image brightness. Therefore, an investigation into degeneracies and their remedy is important also in practice

A nonlinear method for estimating the projective geometry of three views

Theme 3 - Interaction homme-machine, images, donnees, connaissances - Projet RobotVisSIGLEAvailable from INIST (FR), Document Supply Service, under shelf-number : 14802 E, issue : a.1997 n.3221 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

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