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Review of Methods Inspired by Algebraic-Multigrid for Data and Image Analysis Applications

Published online by Cambridge University Press:  28 May 2015

Meirav Galun ,
Ronen Basri  and
Irad Yavneh
Meirav Galun*
Affiliation:
Weizmann Institute of Science, Rehovot, Israel
Ronen Basri
Affiliation:
Weizmann Institute of Science, Rehovot, Israel
Irad Yavneh
Affiliation:
Technion, Israel Institute of Technology, Haifa, Israel
*
*Email addresses: meirav.galun@weizmann.ac.il (Meirav Galun), ronen.basri@weizmann.ac.il (Ronen Basri), irad@cs.technion.ac.il (Irad Yavneh)
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Abstract

Algebraic Multigrid (AMG) methods were developed originally for numerically solving Partial Differential Equations (PDE), not necessarily on structured grids. In the last two decades solvers inspired by the AMG approach, were developed for non PDE problems, including data and image analysis problems, such as clustering, segmentation, quantization and others. These solvers share a common principle in that there is a crosstalk between fine and coarse representations of the problems, with flow of information in both directions, fine-to-coarse and coarse-to-fine. This paper surveys some of these problems and the AMG-inspired algorithms for their solution.

Keywords

65F1065F5065H1068U10Algebraic MultigridImage AnalysisData AnalysisMultiscale AlgorithmsMultilevel Optimization

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Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 8 , Issue 2 , May 2015 , pp. 283 - 312
Copyright
Copyright © Global-Science Press 2015 

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