Homography tensors: On algebraic entities that represent three views of static or moving planar points

Abstract

We introduce a 3 × 3 × 3 tensor Hijk and its dual Hijk which represent the 2D projective mapping of points across three projections (views). The tensor Hijk is a generalization of the well known 2D collineation matrix (homography matrix) and it concatenates two homography matrices to represent the joint mapping across three views. The dual tensor Hijk concatenates two dual homography matrices (mappings of line space) and is responsible for representing the mapping associated with moving points along straight-line paths, i.e., Hijk can be recovered from line-of-sight measurements only.