An automatic Optimum Trade-Off Maximum Average Correlation Height (OT-MACH) filter generator for use in a gray-scale optical correlator (GOC) has been developed for improved target detection. While the OT-MACH filter has been shown to be an optimal filter for target detection, actually solving for the optimum is too computationally intensive for multiple targets. Instead, an adaptive step gradient descent method was tested to iteratively optimize the three OT-MACH parameters a, b, and g. The feedback for the gradient descent method was a composite of the performance measures, correlation peak height, and peak to side-lobe ratio.
The automated method generated and tested multiple filters in order to approach the optimal filter quicker and more reliably than the current manual method. Initial usage and testing has shown preliminary success at finding an approximation of the optimal filter in terms of α, β, and g values. This corresponds to a substantial improvement in detection performance where the true positive rate increased for the same average false positives per image.
The approach taken to automate the filter generation process was to select the training images and properly size them to perform correlation with a test image. From these training images, half are used to generate the filter using initial seed values for α, β, and γ. An incremental constant is added to these values to measure the effect on the performance metrics in order to use the adaptive step gradient descent algorithm. The derivative is assumed to be linear because the change in α, β, and γ is small.
The performance measures are calculated by testing the newly generated filters on the other half of the trained images; the ones not used to build the filter. The filter is correlated with the test images, and the performance score is counted from the known target position from the test images. In order to reduce the performance score to a single metric, the correlation peak and PSR measures are combined in an equation favoring optimization of the peak value. The adaptive gradient descent algorithm maintains a user input minimum PSR threshold while the peak score is optimized. The increased peak score benefits the true positive rate at the cost of an increase in false positives. A higher PSR score makes the filter better able to discern between true positives and false positives. In some alternate cases, the filter can be optimized via PSR values, while retaining a minimum peak value.