Calculating the output distribution of stack filters that are erosion-dilation cascades, in particular Lulu-filters
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Date
Authors
Anguelov, Roumen
Butler, P.W.
Rohwer, Carl (Carl H.)
Wild, M.
Journal Title
Journal ISSN
Volume Title
Publisher
Routledge
Abstract
Two procedures to compute the output distribution ϕS of certain stack
lters S (so called erosion-dilation cascades) are given. One rests on the disjunctive
normal form of S and also yields the rank selection probabilities. The other is based
on inclusion-exclusion and e.g. yields ϕS for some important LULU-operators S.
Properties of ϕS can be used to characterize smoothing properties of S. Also, in
the same way as our polynomials ϕS are computed one could compute the reliability
polynomial of a connected graph, or more generally the reliability polynomial w.r.t.
any positive Boolean function.
Description
Keywords
Stack lter, Output distribution, LULU filter, Reliability polynomial, Inclusion-exclusion
Sustainable Development Goals
Citation
R. Anguelov, P.W. Butler, C.H. Rohwer & M. Wild (2015) Calculating the output distribution of stack filters that are erosion-dilation cascades, in particular LU LU -filters, Quaestiones Mathematicae, 38:4, 463-482, DOI: 10.2989/16073606.2014.981684.