On Two Multigrid Algorithms for Modeling Variational Multiphase Image Segmentation

In this paper, we present two related multigrid algorithms for multiphase image segmentation. Algorithm I solves the model by Vese-Chan. We first generalize our recently developed multigrid method to this multiphase segmentation model (MG1); we also give a local Fourier analysis for the local smooth...

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Veröffentlicht in:IEEE transactions on image processing Jg. 18; H. 5; S. 1097 - 1106
Hauptverfasser: Badshah, N., Ke Chen
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York, NY IEEE 01.05.2009
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Active contours
Additive operator splitting (AOS)
Algorithms
Applied sciences
Computer vision
Exact sciences and technology
Fourier analysis
Histograms
Image analysis
Image processing
Image segmentation
Information, signal and communications theory
Level set
level set formulation
local Fourier analysis
Mathematical models
Multigrid methods
multigrids
Multiphase
Object detection
Robustness
Segmentation
Signal processing
Splitting
Telecommunications and information theory
Image segmentation
Image processing
Multigrid
level set formulation
Additive operator splitting (AOS)
Fourier analysis
Hierarchical system
Algorithm
Modeling
local Fourier analysis
multigrids
ISSN:1057-7149, 1941-0042
Online-Zugang:Volltext
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Beschreibung
Zusammenfassung:In this paper, we present two related multigrid algorithms for multiphase image segmentation. Algorithm I solves the model by Vese-Chan. We first generalize our recently developed multigrid method to this multiphase segmentation model (MG1); we also give a local Fourier analysis for the local smoother which leads to a new and more effective smoother. Although MG1 is found many magnitudes faster than the fast method of additive operator splitting (AOS), both algorithms are not robust with regard to the initial guess. To overcome this dependence on the initial guess, we consider a hierarchical segmentation model which achieves multiphase segmentation by repeated use of the Chan-Vese two-phase model; our algorithm II solves this model by a multigrid algorithm (MG2). Numerical experiments show that both algorithms are efficient and in particular MG2 is more robust than MG1 with respect to initial guesses. AMS subject classifications : 68U10, 65F10, 65K10.
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ISSN:1057-7149
1941-0042
DOI:10.1109/TIP.2009.2014260