Design of stack filters with specified invariant signals and associative memory behavior
Abstract
Stack filters are easily implemented nonlinear filters which include all rank-order operators and all compositions of the morphological operations known as openings and closings. All stack filters possess the threshold decomposition and stacking properties of rank-order filters but are otherwise unconstrained. The notion of the on--set of positive Boolean function is used to classify stack filters into four different types, called type-0 through type-3. The convergence behavior of stack filters are investigated. The class of type-0 stack filters is a trivial class; it contains only the identity operator and the operators which filter all binary inputs to 0 or 1. The classes of type-1 and type-2 stack filters are shown to possess the convergence property and to exhibit nontrivial behavior. The type-1 stack filter has the erosive property; it erodes any input signal to a root after a sufficient number of passes. The type-2 stack filter has the dilative property; it dilates any input signal to a root after a sufficient number of passes. Since some type-3 stack filters have the phenomenon of oscillations when they filter some input signals successively, a partial ordering is defined over the set of stack filters which allows us to determine upper bound and lower bounds for these oscillations. The associative memory of a stack filter is defined to be the set of root signals of that filter. If the root sets of two stack filters both contain a desired set of patterns, but one filter's root set is smaller than the other, then this filter is said to be better for that set of patterns. The configuration of the family of possible best filters which preserve a desired set of patterns is described by using a graphical approach. Then, a design of a near-best filter based on the existence of this configuration is proposed.
Degree
Ph.D.
Advisors
Coyle, Purdue University.
Subject Area
Electrical engineering|Artificial intelligence
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