Multiscale Edge Detection using a Finite Element Framework for Hexagonal Pixel-based Images

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13 Citations (Scopus)

Abstract

In recent years the processing of hexagonal pixel-based images has been investigated, and as a result, a number of edge detection algorithms for direct application to such image structures have been developed. We build on this research by presenting a novel and efficient approach to the design of hexagonal image processing operators using linear basis and test functions within the finite element framework. Development of these scalable first order and Laplacian operators using this approach presents a framework both for obtaining large-scale neighbourhood operators in an efficient manner and for obtaining edge maps at different scales by efficient reuse of the 7-point Linear operator. We evaluate the accuracy of these proposed operators and compare the algorithmic performance using the efficient linear approach with conventional operator convolution for generating edge maps at different scale levels.
LanguageEnglish
Pages1849-1861
JournalIEEE Transactions on Image Processing
Volume25
Issue number4
Early online date12 Feb 2016
DOIs
Publication statusPublished - Apr 2016

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Edge detection
Mathematical operators
Pixels
Convolution
Image processing
Processing

Keywords

  • Hexagonal image processing
  • edge map scaling
  • scalable operator
  • finite element.

Cite this

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title = "Multiscale Edge Detection using a Finite Element Framework for Hexagonal Pixel-based Images",
abstract = "In recent years the processing of hexagonal pixel-based images has been investigated, and as a result, a number of edge detection algorithms for direct application to such image structures have been developed. We build on this research by presenting a novel and efficient approach to the design of hexagonal image processing operators using linear basis and test functions within the finite element framework. Development of these scalable first order and Laplacian operators using this approach presents a framework both for obtaining large-scale neighbourhood operators in an efficient manner and for obtaining edge maps at different scales by efficient reuse of the 7-point Linear operator. We evaluate the accuracy of these proposed operators and compare the algorithmic performance using the efficient linear approach with conventional operator convolution for generating edge maps at different scale levels.",
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AB - In recent years the processing of hexagonal pixel-based images has been investigated, and as a result, a number of edge detection algorithms for direct application to such image structures have been developed. We build on this research by presenting a novel and efficient approach to the design of hexagonal image processing operators using linear basis and test functions within the finite element framework. Development of these scalable first order and Laplacian operators using this approach presents a framework both for obtaining large-scale neighbourhood operators in an efficient manner and for obtaining edge maps at different scales by efficient reuse of the 7-point Linear operator. We evaluate the accuracy of these proposed operators and compare the algorithmic performance using the efficient linear approach with conventional operator convolution for generating edge maps at different scale levels.

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