A study of nonlinear multiview varieties

TL;DR

This paper introduces a nonlinear extension of multiview varieties in computer vision, developing new algebraic tools to analyze their properties and compute multidegrees for various families.

Contribution

It presents the first comprehensive framework for nonlinear multiview varieties using a multigraded saturated special fiber ring.

Findings

Computed multidegrees for several nonlinear multiview varieties

Developed a multigraded algebraic framework for analysis

Extended classical multiview concepts to nonlinear settings

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.