The Euclidean distance degree of one-parameter anchored multiview varieties
Algebraic Geometry
2026-03-10 v2
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.
Keywords
Cite
@article{arxiv.2512.18521,
title = {The Euclidean distance degree of one-parameter anchored multiview varieties},
author = {Bella Finkel and Jose Israel Rodriguez},
journal= {arXiv preprint arXiv:2512.18521},
year = {2026}
}