The Euclidean distance degree of one-parameter anchored multiview varieties

TL;DR

This paper derives a formula for the Euclidean distance degree of certain multiview varieties, aiding in understanding the algebraic complexity of 3D reconstruction from images, and resolves existing conjectures in computer vision.

Contribution

It provides a new formula for the ED degree of rationally parameterized curves and applies it to confirm conjectures in line multiview varieties.

Findings

Derived a formula for ED degree of rational curves

Resolved conjectures on line multiview varieties

Enhanced understanding of algebraic complexity in 3D reconstruction

Abstract

Multiview varieties are mathematical models for the set of image feature correspondences that can be produced by a given camera arrangement. They possess an invariant known as their Euclidean distance (ED) degree, which measures the algebraic complexity of determining the 3D features that minimize the reprojection error when computing the scene structure by triangulation. In this article, we prove a formula for the ED degree of curves parameterized by rational functions with mild genericity assumptions. We apply our results to resolve conjectures on one-dimensional line multiview varieties from computer vision proposed by Duff and Rydell.