GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Algorithms for Computing Motion by Mean Curvature
SIAM Journal on Numerical Analysis
Level set methods for curvature flow, image enhancement, and shape recovery in medical images
Visualization and mathematics
SIAM Review
Relations Between Regularization and Diffusion Filtering
Journal of Mathematical Imaging and Vision
Scale-Space Theory in Computer Vision
Scale-Space Theory in Computer Vision
Inverse Problems in Medical Imaging and Nondestructive Testing
Inverse Problems in Medical Imaging and Nondestructive Testing
BoomerAMG: a parallel algebraic multigrid solver and preconditioner
Applied Numerical Mathematics - Developments and trends in iterative methods for large systems of equations—in memoriam Rüdiger Weiss
Comparing Images Using the Hausdorff Distance
IEEE Transactions on Pattern Analysis and Machine Intelligence
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Jacobian-free Newton-Krylov methods: a survey of approaches and applications
Journal of Computational Physics
Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences)
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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 asmeasure of efficiency we consider convergence history, execution time, speedup, and parallel efficiency. This analysis is carried out in a multicore-based parallel computing environment.