Fast local cross-correlations of images

Consider two multi-dimensional digital signals, each with Ns samples. For some number of lags N l Ns, the cost of computing a single cross-correlation function of these two signals is proportional to Ns × N l. By exploiting several properties of Gaussian windows, we can compute Ns local cross-correlation functions, again with computational cost proportional to Ns × N l. Here, local means the cross-correlation of signals after applying a Gaussian window centered on a single sample. Computational cost is independent of the size of the window.