Implementation of two-dimensional semicausal recursive digital filters

The use of semicausal or half-plane filters in image processing generally requires a large amount of extra grid points to produce the output image compared with the case employing causal or quarter-plane filters. This is due to the inherent nature of semicausal filters. In this paper, a practical aspect of implementing 2D semicausal filters for image processing is investigated in terms of state-space realization, and a method to reduce the total number of spatial grid points necessary to evaluate the output image, termed simplified implementation, is presented.