Computation of correlation sequences in two-dimensional digital filters

Two approaches to the computation of correlations or variances in 2-D digital filters are presented. The first one establishes the correlation equations and shows that the equations are consistent for the special cases of one-dimensional (1-D) filters and 2-D symmetric filters. The second one is a direct application of the theory of 2-D complex integrals, whereby the first of the two integrations becomes a Euclid problem and the second becomes a 1-D complex integration problem. This second method is applicable to general 2-D digital filters.