系统分类了投影SfM中的点线最小问题，发现291个可解问题。
PLMP -- Point-Line Minimal Problems for Projective SfM
- 基于多视角未标定相机，构建点线构型的最小问题分类框架。
- 73个问题有唯一解，可线性求解；多数问题最多9个相机、7个点、12条线。
- 通过几何对称性分析，实现问题分解与非最小性的严格证明。
我们完全分类了在多个未标定针孔相机下，点与线构型完全观测时的结构从运动（SfM）最小问题。共发现291个最小问题，其中73个具有唯一解，因此可线性求解。两个线性问题允许任意数量视图，其余最小问题最多包含9台相机。所有最小问题最多含7个点和12条线。我们计算了每个最小问题的解的数量，以衡量其内在难度，发现该数值相对较低（与标定相机的最小问题相比）。最后，通过研究子构型的稳定子群，我们提出一种几何且系统化的方法：1）将最小问题分解为更小的问题；2）在欠约束问题中识别最小问题；3）正式证明非最小性。
原文摘要 · Abstract (English)
We completely classify all minimal problems for Structure-from-Motion (SfM) where arrangements of points and lines are fully observed by multiple uncalibrated pinhole cameras. We find 291 minimal problems, 73 of which have unique solutions and can thus be solved linearly. Two of the linear problems allow an arbitrary number of views, while all other minimal problems have at most 9 cameras. All minimal problems have at most 7 points and at most 12 lines. We compute the number of solutions of each minimal problem, as this gives a measurement of the problem's intrinsic difficulty, and find that these number are relatively low (e.g., when comparing with minimal problems for calibrated cameras). Finally, by exploring stabilizer subgroups of subarrangements, we develop a geometric and systematic way to 1) factorize minimal problems into smaller problems, 2) identify minimal problems in underconstrained problems, and 3) formally prove non-minimality.
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