论文标题
线多视图品种
Line Multiview Varieties
论文作者
论文摘要
与彻底研究的点对应关系相反，我们提出了针孔摄像机的线路对应关系的代数研究。我们将线多视图变体定义为Zariski在3个空间中以2空间的图像线的图像的Zariski闭合。我们证明，在通用相机矩阵的情况下，线多视图品种是确定性品种，我们为任何摄像机布置提供了完整的设定理论描述。我们研究了这种品种的基本特性，例如维度，平滑度和多维。最后，我们为噪声下的欧几里得距离度和鲁棒性提供了实验结果，以实现线条的三角剖分。
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.
