Euclidean distance degree of the multiview variety

2018/12/13 by Laurenţiu Maxim, Maxim, Laurentiu G., Jose Israel Rodriguez +3 · 4 citations
Computer Science · Engineering · #13P25 #57R20 #90C26 #Advanced Numerical Analysis Techniques #Advanced Vision and Imaging #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1812.05648

openalex publication_date 2018/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Euclidean distance degree of an algebraic variety is a well-studied topic in applied algebra and geometry. It has direct applications in geometric modeling, computer vision, and statistics. We use non-proper Morse theory to give a topological interpretation of the Euclidean distance degree of an affine variety in terms of Euler characteristics. As a concrete application, we solve the open problem in computer vision of determining the Euclidean distance degree of the affine multiview variety.

Citations

• Stratifications de Whitney et théorème de Bertini-Sard

Cited by

• The Euclidean distance degree of curves: from rational to line multiview varieties
• Triangulation of Points Constrained to a Plane
• A Morse complex for the homology of vanishing cycles
• Infinite Euclidean Distance Discriminants

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