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We have developed an algorithm for neural fiber tracts visualization by means of anisotropic diffusion, employing the Allen-Cahn equation to carry out the diffusion process of the initial condition in the form of a noisy 3D image. This paper focuses on the mathematical details of the numerical solution of the given problem. Several finite volume schemes with different orders of accuracy are introduced and their properties are investigated with respect to the occurrence of numerical dissipation, which becomes inconvenient as the diffusion anisotropy strength grows. Furthermore, some results of the experimental convergence analysis are presented, as well as some remarks on the parallel algorithm used to implement the finite volume solver. |
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