Direct Method (SLAM)

Optical Flow

Direct Method

p.184 of the visual SLAM book

This can also be done by solving an optimization problem, but at this time, it is not to minimize the reprojection error but to minimize the photometric error,

We have two points $p_1={\left[\begin{array}{c}u\\ v\\ 1\end{array}\right]}_1=\frac{1}{Z_1}KP$ $p_2={\left[\begin{array}{c}u\\ v\\ 1\end{array}\right]}_2=\frac{1}{Z_2}K(RP+t)$

• $R$ and $t$ are the unknowns

In the way this problem is presented, $P,Z_1,Z_2$ are knowns (because we can compute it by getting a depth image)