Optimal window functions for image correlation in the presence of geometric distortion

The detection performance of the two-dimensional cross correlation algorithm applied to two images with relative geometric distortion is presented. The performance measure used is the peak-to-sidelobe ratio. The geometric distortion is modeled by an affine transformation of image coordinates. A spatial window function applied to one of the images before cross correlation is optimized for a given distortion. The expression for peak-to-sidelobe ratio is shown to be maximized by the window functionh₀(x) = Rₚ[(I - A)x]wherexis the two-dimensional variable in the image plane,Rₚ(x)is the autocorrelation function of the image random pattern, and the 2 × 2 matrixArepresents the geometric distortion coordinate transformation. The maximum achievable peak-to-sidelobe ratio is shown to be1/| (I - A)|1/2. The performance sensitivity to changes in distortion and window function parameters is demonstrated for the special case of Gaussian shaped image autocorrelation and window functions.