Grassman–Cayley algebra for modelling systems of cameras and the algebraic equations of the manifold of trifocal tensors

Abstract

We show how to use the Grassmann–Cayley algebra to model systems of one, two and three cameras. We start with a brief introduction of the Grassmann–Cayley or double algebra and proceed to demonstrate its use for modelling systems of cameras. In the case of three cameras, we give a new interpretation of the trifocal tensors and study in detail some of the constraints that they satisfy. In particular we prove that simple subsets of those constraints characterize the trifocal tensors, in other words, we give the algebraic equations of the manifold of trifocal tensors.