Computer Vision
3D Transformation
There are 3 categories of the most used methods to parameterize 3D solid body motion. i.e. matrix, quaternion and Lie group. Matrix Rotation $$ R=\begin{bmatrix} r_{11} &r_{12} &r_{13} \\ r_{21} &r_{22} &r_{23} \\ r_{31} &r_{32} &r_{33} \end{bmatrix}\in \mathbb{R^{3\times3}}, s.t. R~R^T=I, det(R)=1 $$ Transformation $$ T=\begin{bmatrix} R&t \\ 0^T&1 \end{bmatrix}\in \mathbb{R^{4\times4}} Read more…