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 function
h_{0}(x) = R_{p}[(I - A)x]
where
x
is the two-dimensional variable in the image plane,
R_{p}(x)
is the autocorrelation function of the image random pattern, and the 2 × 2 matrix
A
represents the geometric distortion coordinate transformation. The maximum achievable peak-to-sidelobe ratio is shown to be
1/|\det (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.