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In this paper, a recently developed fiber tracking algorithm to be used with diffusion tensor (DT) fields acquired via magnetic resonance imaging (MRI) is improved and applied to real brain DT-MR images. The method performs satisfactorily in regions where branching and crossing fibers exist and offers the capability of reporting a probability value for the computed tracts. This certainty figure takes into account both the anisotropy and the information provided by all the eigenvectors and eigenvalues of the diffusion matrix at each voxel. In previous papers of the authors, a simpler algorithm was applied only to elementary synthetic DT-MR images. As now presented, this algorithm is now adequately used with more intricate synthetic images and is applied to real white matter DT-MR images with successful results. A novel neural network is used to estimate the main parameters of the algorithm. Numerical experiments show a performance gain over previous approaches, specially with respect to convergence and computational load. The tracking of white matter fibers in the human brain will improve the diagnosis and treatment of many neuronal diseases. [ABSTRACT FROM AUTHOR]