Sensor Models

Camera

OpenCv 5-parameter Brown-Conrady model

Let the pinhole parameters be $f_x, f_y, s, c_x, c_y$, and the distortion parameters be $k_1, k_2, k_3, k_4$.

$$\mathbf{t}^s_{sx_i} = \left[\begin{array}{c}t_x\\t_y\\t_z)\end{array}\right]$$ $$\mathbf{P}\left(\mathbf{t}^s_{sx_i}\right) = \left[\begin{matrix}f_x & s \\ 0 & f_y \end{matrix}\right]\mathbf{p}_d + \left[\begin{array}{c}c_x\\c_y\end{array}\right]$$ $$\mathbf{p}_d = s\mathbf{p}_m + \left(2\mathbf{p}_m\mathbf{p}_m^T + r^2\mathbf{I}\right)\left[\begin{array}{c}p_2\\p_1\end{array}\right]$$ $$s = 1 + k_1r^2 + k_2r^4 + k_3r^6$$ $$r^2 = \mathbf{p}_m^T\mathbf{p}_m$$ $$\mathbf{p}_m = \left[\begin{array}{c}t_x / t_z\\ t_y / t_z\end{array}\right]$$