A method for designing and implementing quadratic correlation filters (QCFs) for shift-invariant target detection in imagery is presented. The QCFs are quadratic classifiers that operate directly on the image data without feature extraction or segmentation. In this sense the QCFs retain the main advantages of conventional linear correlation filters while offering significant improvements in other respects. Not only is more processing required for detection of peaks in the outputs of multiple linear filters but choosing the most suitable among them is an error-prone task. All channels in a QCF work together to optimize the same performance metric and to produce a combined output that leads to considerable simplification of the postprocessing scheme. The QCFs that are developed involve hard constraints on the output of the filter. Inasmuch as this design methodology is indicative of the synthetic discriminant function (SDF) approach for linear filters, the filters that we develop here are referred to as quadratic SDFs (QSDFs). Two methods for designing QSDFs are presented, an efficient architecture for achieving them is discussed, and results from the Moving and Stationary Target Acquisition and Recognition synthetic aperture radar data set are presented.
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