On the stability of two-dimensional continuous filters

The Hermite stability criterion for one-dimensional filters is applied to prove the stability theorems for two-dimensional continuous filters. It is shown that the problem in the stability theorems for the two-dimensional continuous filters when the leading coefficient becomes zero is inherent in the Hermite stability criterion for the one-dimensional filters. It is in sharp contrast to the Schur-Cohn criterion which does not have such a problem.