Critical Curves and Surfaces for Euclidean Reconstruction
Critical Curves and Surfaces for Euclidean Reconstruction
复制标题
欧几里德重构的关键曲线和曲面
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
R. Hartley
中科院分区：
文献类型：
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作者：
Fredrik Kahl;R. Hartley
从图像中恢复场景结构和相机运动的问题具有许多固有的模糊性。本文分析了点和摄像机的配置，其中单独的图像点不足以唯一地恢复场景几何。这样的配置被认为是关键的。对于两个视图，众所周知，只有当两个相机中心和所有点位于直纹二次曲面上时，配置才是关键的。然而，这只是一个必要条件。我们给出了一个完整的表征两个校准相机和任何数量的点的临界表面。给出了这类曲面的代数和几何刻画。最近文献中报道了n-视图投影重建的临界集的存在性。我们表明，有临界集的n-视图欧几里德重建。例如，它示出，对于任何位置的三个校准的摄像机，总是存在一个关键的一组组成的任何数量的点上的四度曲线。
The problem of recovering scene structure and camera motion from images has a number of inherent ambiguities. In this paper, configurations of points and cameras are analyzed for which the image points alone are insufficient to recover the scene geometry uniquely. Such configurations are said to be critical. For two views, it is well-known that a configuration is critical only if the two camera centres and all points lie on a ruled quadric. However, this is only a necessary condition. We give a complete characterization of the critical surfaces for two calibrated cameras and any number of points. Both algebraic and geometric characterizations of such surfaces are given. The existence of critical sets for n-view projective reconstruction has recently been reported in the literature. We show that there are critical sets for n-view Euclidean reconstruction as well. For example, it is shown that for any placement of three calibrated cameras, there always exists a critical set consisting of any number of points on a fourth-degree curve.