Accurate measurement of spinal curvature is essential for diagnosis, monitoring, and treatment planning of adolescent idiopathic scoliosis. The Cobb angle remains the clinical gold standard for evaluating spinal deformity; however, manual measurement is time-consuming and prone to inter-observer variability. Recent advances in medical image analysis, artificial intelligence, and computational geometry have enabled automated approaches for spinal curvature estimation, yet many existing methods rely heavily on deep learning models requiring large datasets, complex training procedures, and high computational cost. This study proposes a reliable scoliosis angle calculation framework based on matrix decomposition-driven arc identification combined with vertebral tilt analysis to achieve precise, interpretable, and computationally efficient curvature estimation.

The proposed approach integrates singular value decomposition-based curve extraction, geometric arc modeling, and vertebral orientation quantification to compute the spinal curvature angle without dependence on extensive neural network training. The method first performs structural feature extraction from radiographic images using matrix decomposition to isolate dominant curvature patterns. Subsequently, arc fitting techniques are applied to identify the global spinal curve, while local vertebral tilt estimation is used to refine angular measurements. This hybrid strategy enables both global and local curvature representation, improving robustness against noise, imaging artifacts, and incomplete vertebral visibility.

A comparative analysis with existing automated and deep learning-based methods demonstrates that the proposed technique provides competitive accuracy while maintaining higher interpretability and lower computational complexity. The framework is particularly suitable for clinical environments where reliability, reproducibility, and transparency are critical. The study also discusses the theoretical basis of matrix decomposition in medical image geometry, the biomechanical relevance of vertebral wedging and tilt, and the limitations of purely data-driven approaches.

The results indicate that combining mathematical decomposition with anatomical feature analysis can produce stable and clinically meaningful scoliosis angle estimation. This research contributes a methodological alternative to purely neural network-based systems and highlights the importance of integrating geometric modeling with biomedical knowledge for reliable spinal deformity assessment.