On the application of the spectral projected gradient method in image segmentation

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.