Efficient Perspective-n-Point (PnP)

Overview

The perspective-n-point algorithm, or PnP for short (also known as the projective-n-point algorithm), is used frequently in computer vision to efficiently and accurately estimate the pose of a camera in 3D space. It accomplishes this by solving a system of equations, which involve the camera’s intrinsic parametersThe internal properties of the camera, such as focal length, the image center, and skew., a collection of $n$ points in 3D space, and $n$ corresponding points in the 2D space of the camera.

The perspective-n-point algorithm

The purpose of the PnP algorithm is to estimate all six degrees of freedom of a calibrated camera. That is, it estimates the rotation $R$ and translation $T$ of the camera. It requires a set of $n$ points with 3D world coordinates and corresponding 2D camera space coordinates. The PnP algorithm finds the $3 \times 3$ rotation matrix $R$ and $1 \times 3$ translation matrix $T$ that minimize the reprojection error between a collection of world points $p_w^i$ and camera points $p_c^i$ where $0 \le i \lt n$.