Accurate estimation of camera matrices is an important step in structure from motion algorithms. In this paper we introduce a novel rank constraint on collections of fundamental matrices in multi-view settings. We show that in general, with the selection of proper scale factors, a matrix formed by stacking fundamental matrices between pairs of images has rank 6. Moreover, this matrix forms the symmetric part of a rank 3 matrix whose factors relate directly to the corresponding camera matrices. We use this new characterization to produce better estimations of fundamental matrices by optimizing an L1-cost function using Iterative Re-weighted Least Squares and Alternate Direction Method of Multiplier. We further show that this procedure can improve the recovery of camera locations, particularly in multi-view settings in which fewer images are available.

本文利用基础矩阵的秩等性构造了一个对称的秩3矩阵，矩阵内的元素与对应的相机矩阵相关。通过优化L1-Cost函数使用迭代加权最小二乘法和交替方向乘数法可以更好地估计基础矩阵，特别是在图片数量不够多的多视图设置下可以提高相机位置的恢复精度。

多视图基础矩阵的新排名约束及其在相机位置恢复中的应用