On the Structure and Properties of the Quadrifocal Tensor

The quadrifocal tensor which connects image measurements along 4 views is not yet well understood as its counterparts the fundamental matrix and the trifocal tensor. This paper establishes the structure of the tensor as an epipolehomography" pairing Qijkl = v0jHikl ,v00kHijl + v000lHijk where v0;v00;v000 are the epipoles in views 2,3,4, H is the homography tensor" the 3-view analogue of the homography matrix, and the indices i;j;k;l are attached to views 1,2,3,4 respectively | i.e., Hikl is the homography tensor of views 1,3,4. In the course of deriving the structure Qijkl we show that Linear Line Complex LLC mappings are the basic building block in the process. We also introduce a complete break-down of the tensor slices: 3 3 3 slices are homography tensors, and 3 3 slices are LLC mappings. Furthermore, we present a closed-form formula of the quadrifocal tensor described by the trifocal tensor and fundamental matrix, and also show how to recover projection matrices from ...

• Type: Conference
• Year: 2000
• Where: ECCV
• Authors: Amnon Shashua, Lior Wolf
• Keywords: Complex LLC Mappings, Computer Vision, ECCV 2000, Homography Tensor, Quadrifocal Tensor, Tensor Slices, Trifocal Tensor