Grassmann Tensors and their applications in geometry

TL;DR

This paper introduces Grassmann tensors, explores their properties, and demonstrates their application in multiview geometry and polytope representation in Euclidean space.

Contribution

It defines Grassmann tensors via tensor products, investigates their properties, and applies tensor language to geometry and polytope representation.

Findings

Grassmann tensors can be used to express relations in multiview geometry

Properties of Grassmann tensors are systematically analyzed

Polytopes in Euclidean space can be represented as Grassmann tensors

Abstract

In this paper, we introduce the Grassmann tensor by tensor product of vectors and some basic terminology in tensor theory. Some basic properties of the Grassmann tensors are investigated and the tensor language is used to rewrite some relations and correspondences in the mutliview geometry. Finally we show that a polytope in the Euclidean space $\R^{n}$ can also be concisely expressed as the Grassmann tensor generated by its vertices.