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$$ \begin{array}{c} x_{distorted} = x + [ 2p_1xy + p_2(r^2+2x^2)] \\ y_{distorted} = y + [ p_1(r^2+ 2y^2)+ 2p_2xy] \end{array} $$
$$ \begin{aligned} x_{\text {distorted }} & =x\left(1+k_{1} r^{2}+k_{2} r^{4}+k_{3} r^{6}\right)+2 p_{1} x y+p_{2}\left(r^{2}+2 x^{2}\right) \\ y_{\text {distorted }} & =y\left(1+k_{1} r^{2}+k_{2} r^{4}+k_{3} r^{6}\right)+p_{1}\left(r^{2}+2 y^{2}\right)+2 p_{2} x y\end{aligned} $$
$$
Distortion ; coefficients=(k_1 \hspace{10pt} k_2 \hspace{10pt} p_1 \hspace{10pt} p_2 \hspace{10pt} k_3)
$$
$$ camera \; matrix = \left [ \begin{matrix} f_x & 0 & c_x \\ 0 & f_y & c_y \\ 0 & 0 & 1 \end{matrix} \right ] $$
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