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Stack filters are nonlinear digital filters that are based on
positive Boolean functions as the window operators and contain
some roots (fixed points) which are invariant under filtering
operations. For some applications, it is useful to understand
the root structure of a stack filter (e.g. median filter).
Provably, the problem determining whether a specific signal is
a fixed point of some stack filter can be regarded as a pattern
recognizing problem by a deterministic finite automaton which
corresponds to the specified stack filter and generates the
regular language. We will introduce a concise and direct
algorithm to obtain a simplified deterministic finite automaton
that describes the root set of a specified stack filter. From
the automaton, we can easily determine root properties of a
stack filter. We will also introduce a new class of stack
filters called K-monotone stack filters that are
generalizations of median filters and apply our algorithm to
analyze root properties of K-monotone stack filters (K
.ltorsim. 2N+1). An open problem concerning the root structures
of median filters under circular appending strategy is analyzed
by the approach of state description.
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