4,723 research outputs found
Computing the output distribution and selection probabilities of a stack filter from the DNF of its positive Boolean function
Many nonlinear filters used in practise are stack filters. An algorithm is
presented which calculates the output distribution of an arbitrary stack filter
S from the disjunctive normal form (DNF) of its underlying positive Boolean
function. The so called selection probabilities can be computed along the way.Comment: This is the version published in Journal of Mathematical Imaging and
Vision, online first, 1 august 201
Conditional Transition Systems with Upgrades
We introduce a variant of transition systems, where activation of transitions
depends on conditions of the environment and upgrades during runtime
potentially create additional transitions. Using a cornerstone result in
lattice theory, we show that such transition systems can be modelled in two
ways: as conditional transition systems (CTS) with a partial order on
conditions, or as lattice transition systems (LaTS), where transitions are
labelled with the elements from a distributive lattice. We define equivalent
notions of bisimilarity for both variants and characterise them via a
bisimulation game.
We explain how conditional transition systems are related to featured
transition systems for the modelling of software product lines. Furthermore, we
show how to compute bisimilarity symbolically via BDDs by defining an operation
on BDDs that approximates an element of a Boolean algebra into a lattice. We
have implemented our procedure and provide runtime results
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