<p>This paper presents a structured and novel deep learning framework for biomedical image segmentation that integrates complex geometric mapping, hybrid deep learning architectures, and probabilistic optimization. The proposed framework consists of three essential components: a triangulation-based structural mapper, a hybrid U-Net + + backbone enhanced with Transformer layers, and a Stein Variational Gradient Descent (SVGD) optimization layer. The triangulation module directly projects input images onto geometrically structured meshes, enabling precise preservation of fine boundaries. The hybrid segmentation core captures both pixel-level local features and global contextual information, resulting in improved ability of the model to generalize across diverse patient datasets. The SVGD layer performs particle-based posterior estimation to optimize segmentation parameters, which reduces overfitting and enhances model robustness. We evaluate our framework against several state-of-the-art segmentation models, including TransUNet, Mixed Transformer U-Net, Attention U-Net, U-Net++, and Bayesian U-Net. Experimental results demonstrate that the proposed method consistently outperforms existing approaches without increasing computational costs. Our model achieves a Dice Similarity Coefficient (DSC) of 0.93, Intersection over Union (IoU) of 0.89, and Boundary F1 Score of 0.88, thus providing an interpretable, scalable, and highly effective solution for biomedical image segmentation.</p>