Review of Methods Inspired by Algebraic-Multigrid for Data and Image Analysis Applications. Issue 2 (28th May 2015)

• Record Type: Journal Article
• Authors: Galun, Meirav; Basri, Ronen; Yavneh, Irad
• Is Part Of: Numerical mathematics. Volume 8:Issue 2(2015)
• Page Start: 283
• Page End: 312
• Publication Date: 2015-05-28
• Subjects: Numerical analysis -- Periodicals; Numerical analysis; Periodicals; 518.05
• DOI: 10.4208/nmtma.2015.w14si
• Languages: English
• ISSNs: 1004-8979

Abstract

<abstract abstract-type="normal"> <title>Abstract</title> <p>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.</p> </abstract>