Four Points in Two or Three Calibrated Views: Theory and Practice
Four Points in Two or Three Calibrated Views: Theory and Practice
复制标题
DOI：
10.1007/s11263-005-4265-x
复制
发表时间：
2006-04
影响因子：
19.5
通讯作者：
D. Nistér;F. Schaffalitzky
中科院分区：
文献类型：
--
作者：
D. Nistér;F. Schaffalitzky
假设给定四个世界点的两个透视图，并且已知其内在参数，但不知道相机姿态和世界点位置。我们证明了每个视图中的极点都被约束在一个十次曲线上。我们推导了曲线的方程，并建立了曲线的许多性质。例如，我们展示了通过每个图像点的曲线有四个分支，并且在通过四个图像点的圆锥铅笔的每个圆锥上都有四个额外的点。我们展示了如何以封闭形式计算每个二次曲线上的四个曲线点。我们证明了方向约束只允许曲线的一部分，并发现存在四个对应点对的不可能构型。给出了一种新的算法，在给定三个对应点和一个极点的情况下求解本质矩阵。然后，我们使用该理论来创建最有效的解决方案，以解决众所周知的难题，即给定四个对应点的三个视图的姿态。解是在一维参数域上的搜索，其中搜索中的每个点都可以用封闭形式求值。该解决方案的预期用途是在假设和测试架构中解决结构和运动。
Suppose two perspective views of four world points are given and that the intrinsic parameters are known but the camera poses and the world point positions are not. We prove that the epipole in each view is then constrained to lie on a curve of degree ten. We derive the equation for the curve and establish many of the curve’s properties. For example, we show that the curve has four branches through each of the image points and that it has four additional points on each conic of the pencil of conics through the four image points. We show how to compute the four curve points on each conic in closed form. We show that orientation constraints allow only parts of the curve and find that there are impossible configurations of four corresponding point pairs. We give a novel algorithm that solves for the essential matrix given three corresponding points and one of the epipoles. We then use the theory to create the most efficient solution yet to the notoriously difficult problem of solving for the pose of three views given four corresponding points. The solution is a search over a one-dimensional parameter domain, where each point in the search can be evaluated in closed form. The intended use for the solution is in a hypothesise-and-test architecture to solve for structure and motion.