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

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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.

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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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Authors and Affiliations

  1. Institute for High-Performance Computing and Networking (ICAR), CNR, via P. Castellino 111, 80131, Naples, Italy

    Laura Antonelli

  2. Department of Mathematics and Physics, Second University of Naples, viale A. Lincoln 5, 81100, Caserta, Italy

    Valentina De Simone & Daniela di Serafino

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  1. Laura Antonelli
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  2. Valentina De Simone
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  3. Daniela di Serafino
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Correspondence to Daniela di Serafino.

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Antonelli, L., De Simone, V. & di Serafino, D. On the Application of the Spectral Projected Gradient Method in Image Segmentation. J Math Imaging Vis 54, 106–116 (2016). https://doi.org/10.1007/s10851-015-0591-y

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