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We introduce a method for designing and implementing quadratic correlation filters (QCFs) for shift-invariant target detection in imagery. The QCFs are a quadratic classifier that operates 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 to detect peaks in the outputs of multiple linear filters, but choosing a winner among them is an error prone task. On the other hand, all channels in a QCF work together to optimize the same performance metric and produce a combined output that leads to considerable simplification of the postprocessing scheme. In addition, QCFs also yield better performance than their linear counterparts for comparable throughput requirements. Two different methods for designing basis functions that optimize the QCF performance criterion are presented. An efficient architecture for implementing QCFs is discussed along with a case study of the proposed approach for detecting targets in LADAR imagery.