Fully Trend Preserving Operators

Abstract. Two procedures to compute the output distribution ϕS of certain stack filters 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 LU LU -operators S. Properties of ϕS can be used to characterize smoothing properties of S. Also, in the same way as our polynomials phiS 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.Mathematics Subject Classification (2010): 94A12, 05A15, 68M15.

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“…The robustness of the median filter M n can be obtained from (7). Obviously p = 0 is a root of order n + 1.…”

Section: Definition 1 An Operatormentioning

confidence: 99%

Calculating the output distribution of stack filters that are erosion-dilation cascades, in particularLU LU-filters

Anguelov

Butler

Rohwer

et al. 2015

Quaestiones Mathematicae

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“…Moreover, the supports of all pulses φ ns , s = 1, ..., γ(n), n = 1, ..., N are either disjoint or nested, that is, (9)- (10). Then it follows from Theorem 1 that (id−P n )( Q n−1 (f ) is a sum of pulses of size n. For n = 1 the function f is trivially 1-monotone and hence (id − P 1 )(f ) is a sum of pulses of size 1.…”

Section: Sum Of Pulses Of the Formmentioning

confidence: 99%

Discrete Pulse Transform of Images

Anguelov

Fabris‐Rotelli

2008

Lecture Notes in Computer Science

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Abstract. The Discrete Pulse Transform (DPT) of images is defined by using a new class of LULU operators on multidimensional arrays. This transform generalizes the DPT of sequences and replicates its essential properties, e.g. total variation preservation. Furthermore, the discrete pulses in the transform capture the contrast in the original image on the boundary of their supports. Since images are perceived via the contrast between neighbour pixels, the DPT may be a convenient new tool for image analysis.

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“…Remark 15 Definition 13 and Definition 14 generalize the concepts of neighbor trend preserving and fully trend preserving for operators on sequences. In the context of sequences the property (18) is called difference reducing, [3,4,5].…”

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confidence: 99%