In this paper, we consider nonlinear partial differential equations (PDEs) of diffusion/advection type underlying most problems in image analysis. As case study, we address the segmentation of medical structures. We perform a comparative study of numerical algorithms arising from using the semi-implicit and the fully implicit discretization schemes. Comparison criteria take into account both the accuracy and the efficiency of the algorithms. As measure of accuracy, we consider the Hausdorff distance and the residuals of numerical solvers, while as measure of efficiency we consider convergence history, execution time, speedup, and parallel efficiency. This analysis is carried out in a multicore-based parallel computing environment.
We describe a fast, reliable and automatic algorithm for image sequence inpainting that combines spatiotemporal interpolation with fine texture preservation inside missing areas. The algorithm provides an estimate of the inpainting error by using an automatic geometric recognition of missing regions. Computational kernels are sparse linear systems solved using Generalized Minimum RESidual iterative method equipped with AMG multigrid preconditioner. Experiments on synthetic and real data are discussed.
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