Fast, Hierarchical Correlations with Gaussian-Like Kernels

摘要

This paper describes a new method for computing correlations which is particularly well suited for image processing. The method, called hierarchical discrete correlation, or HDC, is computationally efficient, typically requiring two or three orders of magnitude fewer computational steps than direct correlation or correlation computed in the spatial frequency domain using the Fast Fourier transform. In addition the method simultaneously generates correlations for kernels (operators) of many sizes. These kernels closely approximate the Gaussian probability distribution, so that the correlation is equivalent to low pass filtering. The operators commonly used in image processing can be readily obtained from sums and differences of Gaussian-like correlations at nearby image points.