仿射相机模型下视图图的可解性
Solvability of the Viewing Graph Under the Affine Camera Model
为 SfM 提供一种在仿射相机模型下判定视图图是否可解（相机是否被唯一确定）的线性系统方法，可用于在增量式/全局式 SfM 中预先筛除不可解或退化配置，并指导视图图构建与边选择。
原文依据 this work represents the first study under the affine camera model
摘要译文
由模型翻译 · 术语统一 · 请对照原文核对关键结论本文关注视图图，在运动恢复结构（Structure from Motion）的语境中，视图图用节点表示相机、用边表示相机之间的成对关系。通过分析该图，可以判定现有的成对关系（例如未标定情形下的基础矩阵）在理论上是否足以唯一确定各相机；若足以确定，则称该图是“可解的”。已有结果分别考虑了标定与未标定两种设定，而其他相机模型在视图图可解性方面尚未被探索：本工作是在仿射相机模型下的首次研究。我们以线性系统的形式给出该问题的刻画，并由此导出一个检验仿射可解性的实用方法。作为补充，我们还给出若干理论结果，提供仿射可解性的充分条件与必要条件，以进一步加深对该问题的理解。借助实验，我们分析了合成图以及来自运动恢复结构数据集的真实图，重点在于理解不同相机模型（标定、未标定与仿射）在可解性方面的差异。在此背景下，我们还提出了一个开放的研究问题，并猜想了一个可能的答案，该猜想得到了经验证据的支持。
英文原文摘要 1353 字符
In this paper we focus on the viewing graph, which is used to represent cameras (as nodes) and their pairwise relationships (as edges) in the context of Structure from Motion. By analyzing this graph, it is possible to establish if the available pairwise relationships (e.g., fundamental matrices in the uncalibrated case) are theoretically enough to uniquely determine the cameras, in which case the graph is termed "solvable". Previous results considered calibrated and uncalibrated settings, whereas other camera models have not been explored in the context of viewing graph solvability: this work represents the first study under the affine camera model. We provide a characterization of the problem in terms of a linear system, from which we derive a practical method to check affine solvability. We complement this by some theoretical results providing sufficient/necessary conditions for affine solvability, in order to give further insights on the problem. Thanks to our experiments, we analyze synthetic graphs and real graphs coming from structure-from-motion datasets, where we focus on understanding the differences among different camera models (calibrated, uncalibrated and affine) in terms of solvability. In this context, we also raise an open research question and conjecture a possible answer, which is supported by empirical evidence.