| Summary: | Brain tumors are abnormal cell growth in the brain tissues that can be cancerous or not. In any case, they could be a very aggressive disease that should be detected as early as possible. Usually, magnetic resonance imaging (MRI) is the main tool commonly adopted by neurologists and radiologists to identify and classify any possible anomalies present in the brain anatomy. In the present work, an automatic unsupervised method called Z2-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula>, based on the use of adaptive finite-elements and suitable pre-processing and post-processing techniques, is introduced. The adaptive process, driven by a Zienkiewicz-Zhu type error estimator (Z2), is carried out on isotropic triangulations, while the given input images are pre-processed via nonlinear transformations (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula> corrections) to enhance the ability of the error estimator to detect any relevant anomaly. The proposed methodology is able to automatically classify whether a given MR image represents a healthy or a diseased brain and, in this latter case, is able to locate the tumor area, which can be easily delineated by removing any redundancy with post-processing techniques based on morphological transformations. The method is tested on a freely available dataset achieving 0.846 of accuracy and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>F</mi><mn>1</mn></msub></semantics></math></inline-formula> score equal to 0.88.
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