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3D localization (3D $\rightarrow$ 2D)

\[\left[ x_i, y_i \right]^T = \left[ \frac{fX_i}{Z_i}, \frac{fY_i}{Z_i} \right]^T\] \[\begin{pmatrix} \tilde p_i\\ 1 \end{pmatrix} = \begin{pmatrix} \tilde x_i\\ \tilde y_i\\\ 1 \end{pmatrix} = K^{-1} \begin{pmatrix} \bar x_i\\ \bar y_i\\\ 1 \end{pmatrix}\] \[x_i = \frac{^CX_i}{^CZ_i} = \frac{r_{11}X_i+r_{11}X_i+r_{11}X_i+t_x}{1}\]