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Journal of Mathematical Imaging and Vision

, Volume 54, Issue 1, pp 106–116 | Cite as

On the Application of the Spectral Projected Gradient Method in Image Segmentation

  • Laura Antonelli
  • Valentina De Simone
  • Daniela di Serafino
Article

Abstract

We investigate the application of the nonmonotone spectral projected gradient (SPG) method to a region-based variational model for image segmentation. We consider a “discretize-then-optimize” approach and solve the resulting nonlinear optimization problem by an alternating minimization procedure that exploits the SPG2 algorithm by Birgin et al. (SIAM J Optim 10(4):1196–1211, 2000). We provide a convergence analysis and perform numerical experiments on several images, showing the effectiveness of this procedure.

Keywords

Image segmentation Region-based variational model  Spectral projected gradient 

Mathematics Subject Classification

68U10 65K05 90C30 

Notes

Acknowledgments

We wish to thank Giovanni Pisante for useful discussions concerning variational models for image segmentation. We are also grateful to the anonymous referees for their useful comments, which helped us to improve the quality of this work. This work was partially supported by INdAM-GNCS (2014 Project First-order optimization methods for image restoration and analysis; 2015 Project Numerical Methods for Non-convex/Nonsmooth Optimization and Applications) and by MIUR (FIRB 2010 Project No. RBFR106S1Z002).

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Laura Antonelli
    • 1
  • Valentina De Simone
    • 2
  • Daniela di Serafino
    • 2
  1. 1.Institute for High-Performance Computing and Networking (ICAR), CNRNaplesItaly
  2. 2.Department of Mathematics and PhysicsSecond University of NaplesCasertaItaly

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