Global Optimization

The neurocalibration net has a central role in the global optimization step. It is trained using the Backpropagation algorithm to minimize the error in (4) over all the collected calibration data. The five zero-order terms are represented by five network weights, while the five parameter MLFNs serve to provide the central network with the rest of the weights representing the parameters that vary with the lens optical setting. Fig. 1 illustrates the central neurocalibration network and its associated MLFNs.

Fig. 1: Global optimization networks

At each lens setting, $\sigma_i$, the five parameter MLFNs provide the corresponding five model parameter values to the central network, which uses these values along with the other zero-order term parameters to project all the input vectors, to compute the calibration error at this lens setting and to update all its weights. The five updated weights are propagated to the parameter MLFNs to update their functional mapping between the parameters and the lens settings. Note that each parameter MLFN minimizes its own fitting error, which is different from the calibration error computed by the central neurocalibration network. However, the fitting error of each parameter MLFN affects the calibration error. When the errors of all six networks drop below a small value, $\epsilon$, each parameter MLFN has the final functional relationship of that particular parameter versus lens settings while the central network has the final values of the zero-order term parameters, namely R_x, R_y, R_z, t_x and t_y. Algorithm 1 shows an outline of the global optimization step.