Initial Parameter Formulation

Having obtained the parameter values at the different positions, we are ready to fit functions to these values. The skew, c, is fixed to zero. For ease of use of the camera model, excluding t_z, the position and the orientation of the camera coordinate frame relative to the world coordinates are kept unchanged as the lens parameters are varied [14],[8]. Therefore, R_x, R_y, R_z, t_x and t_y are modeled with constants (zero-order terms). Constraining these parameters to be independent of optical settings makes use of the extra-degrees of freedom in the calibration (i.e., the dependency and correlation between some camera parameters for small variations [8]). The initial values for the former five terms are set to their average values throughout the whole data. Then, for each of the remaining parameters, $\alpha_u, \alpha_v, u_0, v_0,$ and t_z, a function is fitted across the optical settings using a MLFN. The topology of each (from now on, parameter) MLFN is determined experimentally independently from the others.