Some Results on Minimal Euclidean Reconstruction from Four Points
Some Results on Minimal Euclidean Reconstruction from Four Points
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DOI：
10.1007/s10851-005-3632-0
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发表时间：
2006-05
影响因子：
2
通讯作者：
Long Quan;B. Triggs;B. Mourrain
中科院分区：
文献类型：
--
作者：
Long Quan;B. Triggs;B. Mourrain
用于从最小数据重建和相机估计的方法通常用于引导鲁棒（RANSAC和LMS）和最优（束调整）结构和运动估计。最小方法是已知的投影重建从两个或两个以上的未校准的图像，并为“5点”的相对取向和欧几里德重建从两个校准的参数，但我们知道没有有效的最小方法为三个或三个以上的校准相机除了由霍尔特和Netravali的唯一性证明。我们重新制定的欧氏重建问题的最小数据的四个点在三个或更多的校准图像，并开发了一个随机合理的模拟方法，显示一些新的结果在这个问题上。除了在一般情况下的解决方案的唯一性的另一种证明，我们进一步表明，未知的共面配置不是奇异的，但真正的解决方案是一个双重根。来自已知共面配置的解通常也是唯一的。一些特别对称的点相机配置导致多个解决方案，但只有点或相机的对称性才能给出唯一的解决方案。
Methods for reconstruction and camera estimation from miminal data are often used to boot-strap robust (RANSAC and LMS) and optimal (bundle adjustment) structure and motion estimates. Minimal methods are known for projective reconstruction from two or more uncalibrated images, and for “5 point” relative orientation and Euclidean reconstruction from two calibrated parameters, but we know of no efficient minimal method for three or more calibrated cameras except the uniqueness proof by Holt and Netravali. We reformulate the problem of Euclidean reconstruction from minimal data of four points in three or more calibrated images, and develop a random rational simulation method to show some new results on this problem. In addition to an alternative proof of the uniqueness of the solutions in general cases, we further show that unknown coplanar configurations are not singular, but the true solution is a double root. The solution from a known coplanar configuration is also generally unique. Some especially symmetric point-camera configurations lead to multiple solutions, but only symmetry of points or the cameras gives a unique solution.