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The primary goal of brain image segmentation is to partition a given brain image into different regions representing anatomical structures. Magnetic resonance image (MRI) segmentation is especially interesting, since accurate segmentation in white matter, grey matter and cerebrospinal fluid provides a way to identify many brain disorders such as dementia, schizophrenia or Alzheimer's disease (AD). Then, image segmentation results in a very interesting tool for neuroanatomical analyses. In this paper we show three alternatives to MR brain image segmentation algorithms, with the Self-Organizing Map (SOM) as the core of the algorithms. The procedures devised do not use any a priori knowledge about voxel class assignment, and results in fully-unsupervised methods for MRI segmentation, making it possible to automatically discover different tissue classes. Our algorithm has been tested using the images from the Internet Brain Image Repository (IBSR) outperforming existing methods, providing values for the average overlap metric of 0.7 for the white and grey matter and 0.45 for the cerebrospinal fluid. Furthermore, it also provides good results for high-resolution MR images provided by the NuclearMedicine Service of the "Virgen de las Nieves" Hospital (Granada, Spain).