Idempotent and co-idempotent stack filters and min-max operators

Authors:
Marcel Wild
Affiliations:
Department of Mathematics, University of Stellenbosch, Private Bag X1, 7602 Stellenbosch, Matieland, South Africa
Venue:
Theoretical Computer Science
Year:
2003

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Abstract

Viewing the elements of RS as images f with pixels i ∈ S of grey-scale value f(i) motivates the study of certain nonlinear operators Φ : RS → RS. For translation invariant Φ (called stack filters in the signal processing literature) we derive the first necessary and sufficient condition for idempotency which can be tested in polynomial time. Various related properties can be tested in polynomial time as well, and many results still apply when the linear lattice (R, ≤ ) is replaced by an arbitrary distributive lattice (R, ≤), or when the condition of translation invariance is dropped. Although the main application is in nonlinear image processing several other fields will be touched upon.