Mathematical morphology for structure without translation symmetry
TLDR
In this paper, the theory can be generalized to arbitrary complete atomic Boolean lattices with a commutative group structure on the set of atoms, and give some simple examples of such lattices.About:
This article is published in Signal Processing.The article was published on 1988-10-01 and is currently open access. It has received 32 citations till now. The article focuses on the topics: Euclidean group & Complete Boolean algebra.read more
Citations
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Journal ArticleDOI
Morphological systems for multidimensional signal processing
Petros Maragos,R. Schafer +1 more
TL;DR: The basic theory and applications of a set-theoretic approach to image analysis called mathematical morphology are reviewed in this article, where the concepts of mathematical morphology geometrical structure in signals are used to illuminate the ways that morphological systems can enrich the theory and application of multidimensional signal processing.
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Why mathematical morphology needs complete lattices
TL;DR: It is shown that it is also necessary for a mathematically coherent application of morphological operators to grey-level images, and dilations and erosions can be defined directly with lattice-theoretic methods, without recourse to umbras.
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Theoretical Foundations of Spatially-Variant Mathematical Morphology Part I: Binary Images
TL;DR: The ubiquity of SV morphological operators is demonstrated by providing an SV kernel representation of increasing operators by a generalization of Matheron's representation theorem of increasing and translation-invariant operators.
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Locally adaptable mathematical morphology using distance transformations
TL;DR: It is shown that when the structuring elements are balls of a metric, locally adaptable erosion and dilation can be efficiently implemented as a variant of distance transformation algorithms.
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Anisotropic Morphological Filters With Spatially-Variant Structuring Elements Based on Image-Dependent Gradient Fields
TL;DR: Results of spatially-variant erosions/dilations and openings/closings-based filters prove the validity of this theoretical sound and novel approach to spatially variant dilation/erosion and opening/closing for binary and gray-level images using exclusively the structuring function, without resorting to complement.
References
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Book
Image Analysis and Mathematical Morphology
TL;DR: This invaluable reference helps readers assess and simplify problems and their essential requirements and complexities, giving them all the necessary data and methodology to master current theoretical developments and applications, as well as create new ones.