Automatic assessment of brain regions in an MR image has emerged as a pivotal tool in advancing diagnosis and continual monitoring of neurological disorders through different phases of life. Nevertheless, current solutions often exhibit specificity to particular age groups, thereby constraining their utility in observing brain development from infancy to late adulthood. In our research, we introduce a novel approach for segmenting and classifying neonatal brain images. Our methodology capitalizes on minimum spanning tree (MST) segmentation employing the Manhattan distance, complemented by a shrunken centroid classifier empowered by the Brier score. This fusion enhances the accuracy of tissue classification, effectively addressing the complexities inherent in age-specific segmentation. Moreover, we propose a novel threshold estimation method utilizing the Brier score, further refining the classification process. The proposed approach yields a competitive Dice similarity index of 0.88 and a Jaccard index of 0.95. This approach marks a significant step toward neonatal brain tissue segmentation, showcasing the efficacy of our proposed methodology in comparison to the latest cutting-edge methods.