Abstract
A new technique is proposed for designing the two-dimensional digital filters which will be applied to play a central role in image processing. Basic ideas of this technique are the separable sum of one-dimensional recursive filters and the zero phase sum. So, in this technique, the difficulty of stability problem of two-dimensional recursive filters does not arise and the implementation of the filters becomes simple. And because of the structure of the zero phase sum, the filtered images by this filter are not degraded by a phase error.
Filters having an arbitrarily prescribed frequency response are designed to minimize the error criterion function by using the non-linear optimization algorithm.
The frequency responses of resulting filters and the results of the application of these filters to some images are illustrated. Experimental results show that the filters designed by this technique give good responses approximating the desired non-separable frequency responses and are sufficiently practical to be applied in image processing.
