Rigid Multiview Varieties

TL;DR

This paper generalizes the multiview variety in computer vision to include distance constraints among points, deriving polynomial equations and exploring applications in multiview scenarios.

Contribution

It introduces a new class of multiview varieties with distance constraints and provides their defining polynomial equations, extending prior models in computer vision.

Findings

Derived explicit polynomial equations for the new multiview variety.

Extended the multiview variety framework to include distance constraints.

Explored applications of the generalized variety in multiview scenarios.

Abstract

The multiview variety from computer vision is generalized to images by $n$ cameras of points linked by a distance constraint. The resulting five-dimensional variety lives in a product of $2n$ projective planes. We determine defining polynomial equations, and we explore generalizations of this variety to scenarios of interest in applications.