Roberts, Michael ORCID: 0000-0002-3484-5031, Chen, K ORCID: 0000-0002-6093-6623 and Irion, Klaus
(2019)
Multigrid Algorithm based on Hybrid Smoothers for Variational and Selective Segmentation Models.
International Journal of Computer Mathematics, 96 (8).
pp. 1623-1647.
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Abstract
Automatic segmentation of an image to identify all meaningful parts is one of the most challenging as well as useful tasks in a number of application areas. This is widely studied. Selective segmentation, less studied, aims to use limited user specified information to extract one or more interesting objects (instead of all objects). Constructing a fast solver remains a challenge for both classes of model. However our primary concern is on selective segmentation. In this work, we develop an effective multigrid algorithm, based on a new non-standard smoother to deal with non-smooth coefficients, to solve the underlying partial differential equations (PDEs) of a class of variational segmentation models in the level set formulation. For such models, non-smoothness (or jumps) is typical as segmentation is only possible if edges (jumps) are present. In comparison with previous multigrid methods which were shown to produce an acceptable {\it mean} smoothing rate for related models, the new algorithm can ensure a small and {\it global} smoothing rate that is a sufficient condition for convergence. Our rate analysis is by Local Fourier Analysis and, with it, we design the corresponding iterative solver, improving on an ineffective line smoother. Numerical tests show that the new algorithm outperforms multigrid methods based on competing smoothers.
Item Type: | Article |
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Additional Information: | 27 pages, 7 figures, to appear in International Journal of Computer Mathematics 2018 |
Uncontrolled Keywords: | Partial differential equations, multigrid, fast solvers, local fourier analysis, image segmentation, jump coefficients |
Depositing User: | Symplectic Admin |
Date Deposited: | 03 Feb 2020 11:22 |
Last Modified: | 19 Jan 2023 01:07 |
DOI: | 10.1080/00207160.2018.1494827 |
Related URLs: | |
URI: | https://livrepository.liverpool.ac.uk/id/eprint/3031013 |
Available Versions of this Item
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Multigrid Algorithm based on Hybrid Smoothers for Variational and Selective Segmentation Models. (deposited 19 Jun 2018 06:08)
- Multigrid Algorithm based on Hybrid Smoothers for Variational and Selective Segmentation Models. (deposited 03 Feb 2020 11:22) [Currently Displayed]