Evolutionary partial differential equations for biomedical image processing
Journal of Biomedical Informatics
Evolutionary partial differential equations for biomedical image processing
Computers and Biomedical Research
Flux-based level set method: A finite volume method for evolving interfaces
Applied Numerical Mathematics
Updating preconditioners for nonlinear deblurring and denoising image restoration
Applied Numerical Mathematics
SIAM Journal on Numerical Analysis
Segmentation of 3d tubular structures by a PDE-Based anisotropic diffusion model
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
Numerical solution of diffusion models in biomedical imaging on multicore processors
Journal of Biomedical Imaging - Special issue on Parallel Computation in Medical Imaging Applications
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We propose a finite element algorithm for computing the motion of a surface moving by mean curvature. The algorithm uses the level set formulation so that changes in topology of the surface can be accommodated. Stability is deduced by showing that the discrete solutions satisfy both $L^\infty$ and $W^{1,1}$ bounds. Existence of discrete solutions and connections with Brakke flows are established. Some numerical examples and application to related problems, such as the phase field equations, are also presented.