Globally convergent iterative numerical schemes for nonlinear variational image smoothing and segmentation on a multiprocessor machine

We investigate several iterative numerical schemes for nonlinear variational image smoothing and segmentation implemented in parallel. A general iterative framework subsuming these schemes is suggested for which global convergence irrespective of the starting point can be shown. We characterize various edge-preserving regularization methods from the recent image processing literature involving auxiliary variables as special cases of this general framework. As a by-product, global convergence can be proven under conditions slightly weaker than those stated in the literature. Efficient Krylov subspace solvers for the linear parts of these schemes have been implemented on a multi-processor machine. The performance of these parallel implementations has been assessed and empirical results concerning convergence rates and speed-up factors are reported.