Dynamical behavior of two-dimensional symmetric weighted threshold filter for bounded sequences

The two-dimensional symmetric weighted threshold filter is a generalization of the two-dimensional symmetric weighted median filter. The dynamical behavior of the two-dimensional symmetric weighted median filter has been studied. In this paper we will discuss the dynamical behavior of the two-dimensional symmetric threshold filter, i.e., what property does the two-dimensional symmetric weighted threshold filter has if we apply iteratively two-dimensional symmetric weighted threshold filter to a fixed sequence. For bounded sequences, we prove that iterated sequences with even index as well as iterated sequences with odd index both converge.