Selective Image Segmentation Models and Fast Multigrid Methods

Roberts, MT
(2019) Selective Image Segmentation Models and Fast Multigrid Methods. PhD thesis, University of Liverpool.

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This thesis is concerned with developing robust and accurate variational selective image segmentation models along with fast multigrid methods to solve non-linear partial differential equations (PDEs). The first two major contributions are the development of new distance terms and new intensity fitting terms for selective image segmentation models. These give state-of-the-art segmentation results, with high robustness to the main parameters and to the user input. Therefore, these models are highly applicable to real-world applications such as segmenting single organs from medical scans. The final major contribution is to develop new novel non-standard smoothers for the non-linear full approximation scheme multigrid framework. Multigrid is an optimal O(N) iterative scheme when it converges. However, typically if we directly apply a multigrid solver to a non-linear problem, it will not converge. This is principally due to the ineffectiveness of the standard smoothing schemes such as Jacobi or Gauss-Seidel. We review the true reason that these smoothers are ineffective using local Fourier analysis and develop a smoother which is guaranteed to be effective. Experiments show that the smoother is effective and the algorithm converges as desired. These new non-standard smoothing schemes can be used to solve a whole class of non-linear PDEs quickly. This work also lays the groundwork in the development of a “black-box” non-linear multigrid solver which doesn’t require the degree of tuning that current multigrid algorithms do.

Item Type: Thesis (PhD)
Additional Information:
Divisions: Fac of Science & Engineering > School of Mathematics
Depositing User: Symplectic Admin
Date Deposited: 29 Mar 2019 10:15
Last Modified: 03 Mar 2021 17:09
DOI: 10.17638/03033217
  • Chen, Ke
  • Irion, Klaus L