Algebraic Relations and Triangulation of Unlabeled Image Points

TL;DR

This paper introduces a novel algebraic approach to multiview geometry problems involving unlabeled image points, modeling them as points on Chow varieties and providing algorithms for triangulation without known correspondences.

Contribution

It presents a new algebraic framework for unlabeled point configurations and develops an algorithm for triangulation with unknown correspondences in multiview geometry.

Findings

Algorithm successfully triangulates two unlabeled points.

Models unlabeled points as elements of Chow varieties.

Analyzes the structure of the unlabeled multiview variety.

Abstract

In multiview geometry when correspondences among multiple views are unknown the image points can be understood as being unlabeled. This is a common problem in computer vision. We give a novel approach to handle such a situation by regarding unlabeled point configurations as points on the Chow variety $\text{Sym}_m(\mathbb{P}^2)$. For two unlabeled points we design an algorithm that solves the triangulation problem with unknown correspondences. Further the unlabeled multiview variety $\text{Sym}_m(V_A)$ is studied.