Breast segmentation has a critical role for objective pre and postoperative aesthetic evaluation but challenged by limited data (privacy concerns), class imbalance, and anatomical variability. As a response to the noted obstacles, we introduce an encoder–decoder framework with a Segment Anything Model (SAM) backbone, enhanced with synthetic depth maps and a multiterm loss combining weighted crossentropy, convexity, and depth alignment constraints. Evaluated on a 120patient dataset split into 70% training, 10% validation, and 20% testing, our approach achieves a balanced test dice score of 98.75%—a 4.5% improvement over prior methods—with dice of 95.5% (breast) and 89.2% (nipple). Ablations show depth injection reduces noise and focuses on anatomical regions, yielding dice gains of 0.47% (body) and 1.04% (breast). Geometric alignment increases convexity by almost 3% up to 99.86%, enhancing geometric plausibility of the nipple masks. Lastly, crossdataset evaluation on CINDERELLA samples demonstrates robust generalization, with small performance gain primarily attributable to differences in annotation styles.