P3P

最新推荐文章于 2021-04-15 23:58:29 发布

转载最新推荐文章于 2021-04-15 23:58:29 发布 · 683 阅读

转载地址：https://en.wikipedia.org/wiki/Perspective-n-Point

PnP

Definition[edit]

Given a set of $n$ 3D points in a world reference frame and their corresponding 2D image projections as well as the calibrated intrinsic camera parameters, determine the 6 DOF pose of the camera in the form of its rotation and translation with respect to the world. This follows the perspective project model for cameras:

s\,p_{c}=K\,[\,R\,|\,T\,]\,p_{w}

where $\textstyle p_{w}={\begin{bmatrix}x&y&z&1\end{bmatrix}}^{T}$ is the homogeneous world point, $\textstyle p_{c}={\begin{bmatrix}u&v&1\end{bmatrix}}^{T}$ is the corresponding homogeneous image point, $\textstyle K$ is the matrix of intrinsic camera parameters, (where $\textstyle f_{x}$ and $f_y$ are the scaled focal lengths, $\textstyle \gamma$ is the skew(偏移)parameter which is sometimes assumed to be 0, and $\textstyle (u_{0},\,v_{0})$ is the principal point), $\textstyle s$ is a scale factor for the image point, and $\textstyle R$ and $\textstyle T$ are the desired 3D rotation and 3D translation of the camera (extrinsic parameters) that are being calculated. This leads to the following equation for the model:

s{\begin{bmatrix}u\\v\\1\end{bmatrix}}={\begin{bmatrix}f_{x}&\gamma &u_{0}\\0&f_{y}&v_{0}\\0&0&1\end{bmatrix}}{\begin{bmatrix}r_{11}&r_{12}&r_{13}&t_{1}\\r_{21}&r_{22}&r_{23}&t_{2}\\r_{31}&r_{32}&r_{33}&t_{3}\\\end{bmatrix}}{\begin{bmatrix}x\\y\\z\\1\end{bmatrix}}

Assumptions and Data Characteristics

PnP问题的对象是：相机已校正，求相机外参，即R-t；

UPnP 和 Direct Linear Transform (DLT)它们是针对projection model，即不仅估计相机外参，而且估计相机内参。

For each solution to PnP, the chosen point correspondences cannot be coplanar.（一个3D点和其对应的 2D点构成一条直线，PnP中将来会有n条直线。如果要成为PnP的解，这n条直线不能共面，这为选择3D特征点提供了依据，这句话应该是这个意思。）

In addition, PnP can have multiple solutions, and choosing a particular solution would require post-processing of the solution set. Furthermore, using more point correspondences can reduce the impact of noisy data when solving PnP. RANSAC is also commonly used with a PnP method to make the solution robust to outliers in the set of point correspondences.

一篇介绍P3P很好的博客：http://iplimage.com/blog/p3p-perspective-point-overview/

EPnP 结合 http://www.cnblogs.com/jian-li/p/5689122.html 和EPnP原始的论文 Accurate Non-Iterative O( n) Solution to the PnP Problem 理解 EPnP的基本思想，很多细节还不是清楚,自己阅读论文时，在论文上做的一些疑问