<title>Quadratic Gabor correlation filters for object detection</title>

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We present a new class of quadratic filters that are capable of creating spherical, elliptical, hyperbolic and linear decision surfaces which result in better detection and classification capabilities than the linear decision surfaces obtained from correlation filters. Each filter comprises of a number of separately designed linear basis filters. These filters are linearly combined into several macro filters; the output from these macro filters are passed through a magnitude square operation and are then linearly combined using real weights to achieve the quadratic decision surface. This nonlinear fusion algorithm is called the extended piecewise quadratic neural network (E-PQNN). For detection, the creation of macro filters allows for a substantial computational saving by reducing the number of correlation operations required. In this work, we consider the use of Gabor basis filters; the Gabor filter parameters are separately optimized; the fusion parameters to combine the Gabor filter outputs are optimized using the conjugate gradient method; they and the nonlinear combination of filter outputs are included in our E-PQNN algorithm. We demonstrate methods for selecting the number of macro Gabor filters, the filter parameters and the linear and nonlinear combination coefficients. We prove that our simple E-PQNN architecture is able to generate arbitrary piecewise quadratic decision surfaces. We present preliminary results obtained for an IR vehicle detection problem.