Line Multiview Varieties

IF 1.6 2区 数学 Q2 MATHEMATICS, APPLIED
Paul Breiding, Felix Rydell, Elima Shehu, Ang'elica Torres
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引用次数: 10

Abstract

We present an algebraic study of line correspondences for pinhole cameras, in contrast to the thoroughly studied point correspondences. We define the line multiview variety as the Zariski closure of the image of the map projecting lines in 3-space to tuples of image lines in 2-space. We prove that in the case of generic camera matrices the line multiview variety is a determinantal variety and we provide a complete set-theoretic description for any camera arrangement. We investigate basic properties of this variety such as dimension, smoothness, and multidegree. Finally, we give experimental results for the Euclidean distance degree and robustness under noise for the triangulation of lines.
多视图品种
我们提出了针孔相机的直线对应的代数研究,与彻底研究的点对应形成对比。我们将线多视图变化定义为地图图像的扎里斯基闭包,该图像将3空间中的线投射到2空间中的图像线元组。我们证明了在一般相机矩阵的情况下,线多视图变化是一个行列式变化,并对任何相机排列提供了完整的集合论描述。我们研究了这种变化的基本性质,如维度,平滑度和多度。最后,给出了直线三角剖分的欧氏距离度和噪声下的鲁棒性实验结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
2.20
自引率
0.00%
发文量
19
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