Geometric Computation Theory for Morphological Filtering on Freeform Surfaces

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8 Citations (Scopus)

Abstract

Surfaces govern functional behaviours of geometrical products, especially high-precision and high-addedvalue products. Compared with the mean line-based filters, morphological filters, evolved from the traditional E-system, are relevant to functional performance of surfaces. The conventional implementation of morphological filters based on image-processing does not work for state-of-the-art surfaces, for example, freeform surfaces. A set of novel geometric computation theory is developed by applying the alpha shape to the computation. Divide and conquer optimization is employed to speed up the computational performance of the alpha-shape method and reduce memory usage. To release the dependence of the alpha-shape method on the Delaunay triangulation, a set of definitions and propositions for the search of contact points is presented and mathematically proved based on alpha shape theory, which are applicable to both circular and horizontal flat structuring elements. The developed methods are verified through experimentation.

Original languageEnglish
Article number20130150
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume469
Issue number2159
DOIs
Publication statusPublished - 8 Nov 2013

Fingerprint

Computation theory
Free-form Surface
Filtering
Morphological Filter
filters
Delaunay triangulation
Divide and conquer
triangulation
Point contacts
experimentation
Triangulation
products
Proposition
Experimentation
image processing
Image Processing
Image processing
Speedup
Horizontal
Contact

Cite this

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title = "Geometric Computation Theory for Morphological Filtering on Freeform Surfaces",
abstract = "Surfaces govern functional behaviours of geometrical products, especially high-precision and high-addedvalue products. Compared with the mean line-based filters, morphological filters, evolved from the traditional E-system, are relevant to functional performance of surfaces. The conventional implementation of morphological filters based on image-processing does not work for state-of-the-art surfaces, for example, freeform surfaces. A set of novel geometric computation theory is developed by applying the alpha shape to the computation. Divide and conquer optimization is employed to speed up the computational performance of the alpha-shape method and reduce memory usage. To release the dependence of the alpha-shape method on the Delaunay triangulation, a set of definitions and propositions for the search of contact points is presented and mathematically proved based on alpha shape theory, which are applicable to both circular and horizontal flat structuring elements. The developed methods are verified through experimentation.",
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AB - Surfaces govern functional behaviours of geometrical products, especially high-precision and high-addedvalue products. Compared with the mean line-based filters, morphological filters, evolved from the traditional E-system, are relevant to functional performance of surfaces. The conventional implementation of morphological filters based on image-processing does not work for state-of-the-art surfaces, for example, freeform surfaces. A set of novel geometric computation theory is developed by applying the alpha shape to the computation. Divide and conquer optimization is employed to speed up the computational performance of the alpha-shape method and reduce memory usage. To release the dependence of the alpha-shape method on the Delaunay triangulation, a set of definitions and propositions for the search of contact points is presented and mathematically proved based on alpha shape theory, which are applicable to both circular and horizontal flat structuring elements. The developed methods are verified through experimentation.

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