Automatic Analysis of Brain Tumor from Magnetic Resonance Images based on Geometric Median Shift

In this paper, we propose an automated approach based on the geometric median shift algorithm over Riemannian manifolds, for the brain tumor detection and segmentation in magnetic resonance images (MRI). This approach is based on the geometric median, geodesic distance. We propose the median shift to overcome the limitation of mean which is not necessary a point in a set. The geodesic distance can describe data points distributed on a manifold, compared to the Euclidean distance, and produce efficient results for image analysis. Coupled with k-means algorithm, the proposed framework can cluster the brain image into tree regions (gray matter, white matter and cerebrospinal fluid) and abnormalities regions. We applied this approach to clustering the brain tissues and brain tumor segmentation, which is validated on a synthetic brain MRI. The obtained results using two datasets show the efficiency of the used algorithm validated qualitatively by the measurement of Dice Similarity Coefficient.