Morphological structuring element decomposition
Computer Vision, Graphics, and Image Processing
Minimal representations for translation-invariant set mappings by mathematical morphology
SIAM Journal on Applied Mathematics
An overview of morphological filtering
Circuits, Systems, and Signal Processing - Special issue: median and morphological filters
A Combinatorial Optimization Technique for the Sequential Decomposition of Erosions and Dilations
Journal of Mathematical Imaging and Vision
Artificial Intelligence
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
Sup-Compact and Inf-Compact Representations of W-Operators
Fundamenta Informaticae
Sup-Compact and Inf-Compact Representations of W-Operators
Fundamenta Informaticae
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W-operators are discrete set operators that are both translation invariant and locally defined within a finite window W. A particularly interesting property of W-operators is that they have a sup-decomposition in terms of a family sup-generating operators, that are parameterized by the operator basis. The sup-decomposition has a parallel structure that usually is not efficient for computation in conventional sequential machines. In this paper, we formalize the problem of transforming sup-decompositions into purely sequential decompositions (when they exist). The techniques were developed for general W-operators, specialized for increasing W-operators and applied on operators built by compositions of dilations and erosions.