Image Processing

By combining the last three steps, it is possible to obtain an equation that associates the computer image coordinates (M, N) with the 3-D coordinates (x, y, z) of the object points in the camera system:

$\lambda \frac{x}{z}=x^{\prime }=x^{*}+R_x=x^{*}\left(1+k{r}^2\right)=\frac{(\mathrm{M}-{\mathrm{O}}_m)S_x{L}_x}{\mu {\mathrm{M}}_x}\left(1+k{r}^2\right)\left(2.39\right)$

$\lambda \frac{y}{z}=y^{\prime }=y^{*}+R_y=y^{*}\left(1+k{r}^2\right)=\left(\mathrm{N}-{\mathrm{O}}_n\right)S_y\left(1+k{r}^2\right)\left(2.40\right)$

Taking eq. (2.28) and eq. (2.29) into the above two equations, we get

$\mathrm{M}=\lambda \frac{r_{1}X+r_{2}Y+r_{3}Z+T_x}{r_{7}X+r_{8}Y+r_{9}Z+T_z}\frac{\mu {\mathrm{M}}_x}{\left(1+k{r}^2\right)S_x{L}_x}+{\mathrm{O}}_m\left(2.41\right)$

$\mathrm{N}=\lambda \frac{r_{4}X+r_{5}Y+r_{6}Z+T_y}{r_{7}X+r_{8}Y+r_{9}Z+T_z}\frac{1}{\left(1+k{r}^2\right)}$