Perspective-n-Point Algorithm (PnP)

PnP estimates the pose of a calibrated camera given 3D points in the world and their corresponding 2D projections on the camera’s image plane.

PnP (Perspective-n-Point) is a method to solve 3D to 2D motion estimation.

Several ways to solve this:

• DLT
• P3P

The SLAM textbook introduces an approach that is basically bundle adjustment, where we try to minimize the reprojection error.

We know that to relate from 3D to 2D, we have the equation $s_i\left[\begin{array}{c}{u}_i\\ v_i\\ 1\end{array}\right]=KT\left[\begin{array}{c}{X}_i\\ Y_i\\ Z_i\\ 1\end{array}\right]$ To solve for $T$, we can simply construct the least squares problem and minimize $T$

$T={\text{argmin}}_T\frac{1}{2}\Vert u_i-\frac{1}{s_i}KT{P}_i{\Vert }_2^2$

$e(x+\Delta x)\approx e(x)+J^T\Delta x$

• This is essentially linearization

Related

• 8 Point Algorithm