On rank selection probabilities

Synthesis of stack filters by rank selection probabilities

“…The positive Boolean function S(•) of a stack filter can be written as S1() = i + 2 + + m (8) where irk, 1 < p m is a product of the variables x1 ,x2, . , XN, given by p = xj(p,l)xj(p,2) .…”

“…It has been shown that Mi's have a very simple connection with RSPs [8]. Based on the connection, an algorithm was proposed to compute RSPs of a stack filter which reduces the complexity from previous O(N!)…”

“…Recently, Rank Selection Probabilities (RSPs) was introduced to analyze stack filters and a number of algorithms were developed to compute the RSPs of stack filters [6,7,8]. From another point of view, a set of parameters, called Mi's, was proposed to describe weighted median filters, an important subclass of stack filters.…”

Computing the Output Distribution and Selection Probabilities of a Stack Filter from the DNF of Its Positive Boolean Function

“…Section 3 is dedicated to its theoretic assessment. Section 4 touches upon five related matters, among which a numeric evaluation, and extensions of the stack filter n-algorithm that deliver the telling selection probabilities of [8], respectively handle the balanced stack filters of [12]. 2 The stack filter n-algorithm i.e.…”

<title>Spectral approach to selection probabilities of stack filters</title>

“…The ouipni Y(n) ofa continuous siackfihier (CSF) specified by ihe posilive continuous logic function F(X) with the input signal X(n) is simply given by Y(n) = SF(X(n)) = F(X(n)). (4) The continuous stack filter also defined in the following way10 if one wants to have a continuous analogy of threshold decomposition. Y(n) = Sp(X(n)) = max{t f(o(X(n),t)) = 1), which we assume to be i.i.d.…”