A study of nonlinear multiview varieties

2021/12/12 by Yairon Cid‐Ruiz, Cid-Ruiz, Yairon, Oliver Clarke +3
Computer Science · #13D02 #13D45 #13P99 #14E05 #Advanced Image Processing Techniques #Advanced Vision and Imaging #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #Image and Video Stabilization

paper · pdf · doi:10.48550/arxiv.2112.06216

openalex publication_date 2021/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We study the nonlinear generalization of the classical multiview variety, which is a fundamental concept in computer vision. In this paper, we take the first comprehensive step to develop the nonlinear analogue of multiview varieties. To this end, we introduce a multigraded version of the saturated special fiber ring. By applying this tool, we are able to compute the multidegrees of several families of nonlinear multiview varieties.

Related

• Ideals of the Multiview Variety
• Two Hilbert schemes in computer vision
• Problems and related results in Algebraic Vision and Multiview Geometry
• Projections of Higher Dimensional Subspaces and Generalized Multiview Varieties
• One-parameter families of multiview varieties via quotient lattices