Variation Reduction and<i>Lu Lu</i>-smoothing

Rohwer, CH

doi:10.2989/16073600209486008

Cited by 9 publications

(6 citation statements)

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“…As such, their co-idempotence follows from [39,Corollary 11]. Therefore (25) III. SHAPE PRESERVATION PROPERTIES OF AND Similar to their counterparts for sequences the operators and defined in Section II smooth the input function by removing sharp peaks (the application of ) and deep pits (the application of ).…”

Section: Hencementioning

confidence: 99%

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LULU Operators and Discrete Pulse Transform for Multidimensional Arrays

Anguelov

Fabris‐Rotelli

2010

IEEE Trans. on Image Process.

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Abstract-The LULU operators for sequences, that is L n , U n and their compositions, are extended to multidimensional arrays in a way which preserves their essential properties, e.g., consistent separation, total variation and shape preservation. The power of the operators is demonstrated by deriving the discrete pulse transform (DPT), which is a hierarchical decomposition of the input array into pulses. Similar to its 1-D counterpart this transform satisfies a basic consistency property.

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Section: Hencementioning

confidence: 99%

Section: B Total Variation and Shape Preservationmentioning

confidence: 99%

LULU Operators and Discrete Pulse Transform for Multidimensional Arrays

Anguelov

Fabris‐Rotelli

2010

IEEE Trans. on Image Process.

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“…Hence for an arbitrary sequence ξ considered as a function on Z the formulas (11) and ( 12) are reduced to (1) and (2), respectively.…”

Section: Definition 3 Let B Be An Arbitrary Non-empty Set a Family C ...mentioning

confidence: 99%

A Class of LULU Operators on Multi-Dimensional Arrays

Anguelov,

Plaskitt

2007

Preprint

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“…We intend to show that some LU LU -composition are nearly as good as the medians, but have superiority in other important aspects. An operator S satisfying property (4) is called total variation preserving, [9]. As mentioned already, the LU -operators are total variation preserving.…”

Section: Introductionmentioning

confidence: 98%

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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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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Variation Reduction andLu Lu-smoothing

Cited by 9 publications

References 0 publications

LULU Operators and Discrete Pulse Transform for Multidimensional Arrays

LULU Operators and Discrete Pulse Transform for Multidimensional Arrays

A Class of LULU Operators on Multi-Dimensional Arrays

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

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