CvxPnPL: A Unified Convex Solution to the Absolute Pose Estimation Problem from Point and Line Correspondences
文章提出了一個2D-3D點或線集對應求解相機的旋轉和平移矩陣，文章主要是通過求解QCQP 優化問題，並把優化放鬆爲SDP問題。
The absolute pose problem is challenging because under certain geometric configurations of 2D-3D points and/or lines, there can exist more than a unique valid 3D pose
以前的PnP問題通常存在不止一個解的情況
Our method is designed for a central camera and non-minimal combinations of points and lines, despite being able to handle the minimal or planar points-only cases
1.投影模型
此處的ui指的是圖像二維點反向投影到相機座標系的點，二維點乘與K^-1
lnj爲法線，可通過直線的投影點反向投影叉乘，uj1,uj2的叉乘
2.優化目標
where Z = ˜r˜r> is a 10×10 matrix with rank 1 by construction. The rank constraint is not convex and therefore it is dropped, relaxing the original problem. As it turns out, without this relaxation it is unlikely that we would be able to retrieve meaningful solutions in situations where there are more than one, as discussed in Section 5.
由於Z的秩爲一，這個約束並不是凸的，此處先去掉這個約束（矩陣的解與秩的關係）
Q矩陣的求解
矩陣知識
RR^t=I,得到6個約束方程
R^tR=I同理
通過以上方程求解Z
3.R求解
根據z的秩不同，分爲三種情況
K爲Z非零特徵值個數，v爲相應特徵向量
代碼：cvxpnpl