The Euclidean distance degree of curves: from rational to line multiview varieties

Abstract: The Euclidean distance (ED) degree is an invariant that measures the algebraic complexity of optimizing the distance function of a point to a model. It has been studied in algebraic statistics, machine learning, and computer vision. 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.