Viewing Graph Solvability via Cycle Consistency
Viewing Graph Solvability via Cycle Consistency
复制标题
通过循环一致性查看图的可解性
DOI：
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
T. Pajdla
中科院分区：
文献类型：
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作者：
F. Arrigoni;Andrea Fusiello;Elisa Ricci;T. Pajdla
在从运动恢复结构中，观察图是顶点对应于相机并且边缘表示基本矩阵的图。我们提供了一个新的配方和算法，用于建立是否观看图是可解的，即它唯一地确定一组投影相机。已知的理论条件要么不完全表征所有视图的可解性，要么非常难以计算，因为它们涉及求解具有大量未知数的多项式方程组。本文的主要结果是一种方法，减少未知数的数量，利用循环的一致性。我们推进的可解性的理解（一）完成所有以前未决定的最小图的分类到9个节点，（二）扩展到最小的图与最多90个节点的实际可解性测试，和（三）明确回答一个开放的研究问题，表明有限的可解性是不等价的可解性。最后，我们提出了一个实验上的真实的数据显示，不可解的图形出现在实际情况中。
In structure-from-motion the viewing graph is a graph where vertices correspond to cameras and edges represent fundamental matrices. We provide a new formulation and an algorithm for establishing whether a viewing graph is solvable, i.e. it uniquely determines a set of projective cameras. Known theoretical conditions either do not fully characterize the solvability of all viewing graphs, or are exceedingly hard to compute for they involve solving a system of polynomial equations with a large number of unknowns. The main result of this paper is a method for reducing the number of unknowns by exploiting the cycle consistency. We advance the understanding of the solvability by (i) finishing the classification of all previously undecided minimal graphs up to 9 nodes, (ii) extending the practical solvability testing up to minimal graphs with up to 90 nodes, and (iii) definitely answering an open research question by showing that the finite solvability is not equivalent to the solvability. Finally, we present an experiment on real data showing that unsolvable graphs are appearing in practical situations.
影响因子：
2.5
作者：
Singer, A.
通讯作者：
Singer, A.