Projective reconstruction in algebraic vision

TL;DR

This paper explores the algebraic geometry of rational maps in projective spaces, providing a variant of the projective reconstruction theorem relevant for algebraic vision applications.

Contribution

It introduces an algebro-geometric variant of the projective reconstruction theorem, extending prior geometric results to a broader algebraic context.

Findings

Provides a new algebraic perspective on projective reconstruction

Extends the theorem to arbitrary-dimensional projective spaces

Bridges geometric and algebraic approaches in vision

Abstract

We discuss the geometry of rational maps from a projective space of an arbitrary dimension to the product of projective spaces of lower dimensions induced by linear projections. In particular, we give an algebro-geometric variant of the projective reconstruction theorem by Hartley and Schaffalitzky [HS09].