In the last lecture, we introduced the description of rigid body motion in the three-dimensional world, including the rotation matrix, rotation vector, Euler angle, quaternion, and so on. We focused on the representation of rotation, but in SLAM, we have to estimate and optimize them in addition to the representation. Because the pose is unknown in SLAM, we need to solve the problem of which camera pose best matches the current observation. A typical way is to build it into an optimization problem, solving the optimal \( \mathbf {R}, \mathbf {t}\) and minimizing the error.