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

A New Rank Constraint on Multi-view Fundamental Matrices, and its  Application to Camera Location Recovery

Many objects, especially these made by humans, are symmetric, e.g. cars and
aeroplanes. This paper addresses the estimation of 3D structures of symmetric
objects from multiple images of the same object category, e.g. different cars,
seen from various viewpoints. We assume that the deformation between different
instances from the same object category is non-rigid and symmetric. In this
paper, we extend two leading non-rigid structure from motion (SfM) algorithms
to exploit symmetry constraints. We model the both methods as energy
minimization, in which we also recover the missing observations caused by
occlusions. In particularly, we show that by rotating the coordinate system,
the energy can be decoupled into two independent terms, which still exploit
symmetry, to apply matrix factorization separately on each of them for
initialization. The results on the Pascal3D+ dataset show that our methods
significantly improve performance over baseline methods.

本文针对多个视角下同一对象类别的多张图像中的对称性进行了研究，提出了两种利用对称性约束的非刚性运动结构算法，并在 Pascal3D+ 数据集上验证了其性能。