## RPnP Ciation

Shiqi Li, Chi Xu*, Ming Xie, "A Robust O(n) Solution to the Perspective-n-Point Problem," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 34, no. 7, pp. 1444-1450, July 2012, doi:10.1109/TPAMI.2012.41

title={A Robust O (n) Solution to the Perspective-n-Point Problem},

author={Li, S. and Xu, C. and Xie, M.},

journal={Pattern Analysis and Machine Intelligence, IEEE Transactions on},

volume={34},

number={7},

pages={1444--1450},

year={2012}

}

**Bibtex**

@article{li2012robust,title={A Robust O (n) Solution to the Perspective-n-Point Problem},

author={Li, S. and Xu, C. and Xie, M.},

journal={Pattern Analysis and Machine Intelligence, IEEE Transactions on},

volume={34},

number={7},

pages={1444--1450},

year={2012}

}

## The MATLAB code of RPnP

rpnp1.0.zip | |

File Size: | 74 kb |

File Type: | zip |

**How To Use RPnP Algorithm**

The RPnP algorithm is implemented in "RPnP.m" file, its full path is "code3/func/RPnP.m"

*% function [R t]= RPnP(XX,xx)*

% XX is the 3D coordinate of the point set.

% xx is the

% R is the estimated rotation matrix.

% t is the estimated translation vector.

% XX is the 3D coordinate of the point set.

% xx is the

*****normalized*****2D coordinate of the projected point set.% R is the estimated rotation matrix.

% t is the estimated translation vector.

For more details about the code, please refer to "readme.txt".

**Converting from image coordinate to normalized coordinate**

The algorithm uses the normalized coordinate as input, because

__the normalized coordinate is independent from the camera model used__. The conversion from the image coordinate to the normalized coordinate is described as follows:

(1) For a

*considering only focal length and center point*

**simple camera model**As can be seen in the figure below, OXYZ is a camera coordinate frame, and its Z-axis is defined along the camera optical axis. UV is the image plane, and xnyn is the normalized image plane parallel to UV. The distance form O to the center of the image plane equals the focal length, and the distance form O to the center of the

**normalized image plane**equals

**1**, that's why the plane is called "

**normalized**".

Let the image coordinate be (u,v), the image center be (cu,cv), and the focal length = f, the normalized coordinates (xn,yn) are calculated as follow:

xn = (u - cu)/f

yn = (v - cv)/f

Usually, cu = w/2 and cv = h/2, in which w and h are the width and height of the image respectively.

(2) For more

*considering distortion and so on, please refer to:*

**complex camera model**J Heikkila, O Silven. A four-step camera calibration procedure with implicit image correction, Computer Vision and Pattern Recognition. 1997

## Related Papers

[1] Shiqi Li, Chi Xu*. A Stable Direct Solution of Perspective-Three-Point Problem [J]. International Journal of Pattern Recognition and Artificial Intelligence, 2011, 25(5): 643-673

[2] Shiqi Li, Chi Xu*. Efficient Lookup Table Based Camera Pose Estimation for Augmented Reality [J]. Computer Animation and Virtual Worlds, 2011, 22(1): 47-58