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We present a novel 3-D deformable model-based approach for accurate, robust, and automated tissue segmentation of brain MRI data of single as well as multiple magnetic resonance sequences. The main contribution of this study is that we employ an edge-based geodesic active contour for the segmentation task by integrating both image edge geometry and voxel statistical homogeneity into a novel hybrid geometric-statistical feature to regularize contour convergence and extract complex anatomical structures. We validate the accuracy of the segmentation results on simulated brain MRI scans of both single T1-weighted and multiple T1/T2/PD-weighted sequences. We also demonstrate the robustness of the proposed method when applied to clinical brain MRI scans. When compared to a current state-of-the-art region-based level-set segmentation formulation, our white matter and gray matter segmentation resulted in significantly higher accuracy levels with a mean improvement in Dice similarity indexes of 8.55% (p<0.0001) and 10.18% (p<0.0001), respectively.