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, Martìnez and Raydan (SIAM J. Optim., 10(4), 2000). We provide a convergence analysis and perform numerical experiments on several images, showing the effectiveness of this procedure.
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