eISSN: 3023-3267 editor@aimjournals.com
All Journals
Submit your article

Critique Open Research & Review

Open Access Peer Review International
Open Access

Reliable Scoliosis Angle Calculation Through Matrix Decomposition-Based Arc Identification and Vertebral Tilt Analysis

DOI
PDF
Dr. Aarav Sharma 1 , Rohan Mehta 1 , Dr. Priya Nair 1 ,
4 Department of Biomedical Engineering, Indian Institute of Technology Delhi, New Delhi, India
4 Department of Computer Science and Engineering, National Institute of Technology Bhopal, Madhya Pradesh, India
4 Department of Orthopedics, All India Institute of Medical Sciences (AIIMS), New Delhi, India

Abstract

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.

Keywords

Scoliosis measurement, Cobb angle estimation, matrix decomposition, spinal curvature analysis

References

📄 V. Cassar-Pullicino and S. Eisenstein, “Imaging in scoliosis: What, why and how?,” Clin. Radiol., vol. 57, no. 7, pp. 543–562, 2002.
📄 K. Chen, C. Peng, Y. Li, D. Cheng, and S. Wei, “Accurate automated keypoint detections for spinal curvature estimation,” in Proc. Int. Workshop Challenge Comput. Methods Clin. Appl. Spine Imag., 2019, pp. 63–68.
📄 J. D. Clemente, R. L. Blanco, and J. B. Gurpide, “Morphological changes in scoliosis during growth. Study in the human spine,” Revista Española de Cirugıá Ortopédica y Traumatologıá (English Ed.), vol. 56, no. 6, pp. 432–438, 2012.
📄 D. Y. T. Fong et al., “A population-based cohort study of 394,401 children followed for 10 years exhibits sustained effectiveness of scoliosis screening,” Spine J., vol. 15, no. 5, pp. 825–833, 2015.
📄 J. P. Horne, R. Flannery, and S. Usman, “Adolescent idiopathic scoliosis: Diagnosis and management,” Amer. Fam. Physician, vol. 89, no. 3, pp. 193–198, 2014.
📄 M.-H. Horng, C.-P. Kuok, M.-J. Fu, C.-J. Lin, and Y.-N. Sun, “Cobb angle measurement of spine from X-ray images using convolutional neural network,” Comput. Math. Methods Med., vol. 2019, no. 1, 2019, Art. no. 6357171.
📄 M. T. Hresko, “Idiopathic scoliosis in adolescents,” New England J. Med., vol. 368, no. 9, pp. 834–841, 2013.
📄 C. Jin, S. Wang, G. Yang, E. Li, and Z. Liang, “A review of the methods on Cobb angle measurements for spinal curvature,” Sensors, vol. 22, no. 9, 2022, Art. no. 3258.
📄 S. Kato, Y. Maeda, T. Nagura, M. Nakamura, and K. Watanabe, “Comparison of three artificial intelligence algorithms for automatic Cobb angle measurement using teaching data specific to three disease groups,” Sci. Rep., vol. 14, no. 1, 2024, Art. no. 17989.
📄 R. Kumar, M. Gupta, and A. Abraham, “A critical analysis on vertebra identification and Cobb angle estimation using deep learning for scoliosis detection,” IEEE Access, vol. 12, pp. 11170–11184, 2024.
📄 L. G. Lenke et al., “The Lenke classification of adolescent idiopathic scoliosis: How it organizes curve patterns as a template to perform selective fusions of the spine,” Spine, vol. 28, no. 20S, pp. S199–S207, 2003.
📄 Y. Lin, H.-Y. Zhou, K. Ma, X. Yang, and Y. Zheng, “Seg4Reg networks for automated spinal curvature estimation,” in Proc. 6th Int. Workshop Challenge Comput. Methods Clin. Appl. Spine Imag., Shenzhen, China, 2020, pp. 69–74.
📄 D. Liu, L. Zhang, J. Yang, and A. Lin, “Lenke classification of scoliosis based on segmentation network and adaptive shape descriptor,” Appl. Sci., vol. 13, no. 6, 2023, Art. no. 3905.
📄 Z. Liu et al., “Swin transformer: Hierarchical vision transformer using shifted windows,” in Proc. IEEE/CVF Int. Conf. Comput. Vis., 2021, pp. 10 012–100 22.
📄 N. Meng et al., “An artificial intelligence powered platform for auto-analyses of spine alignment irrespective of image quality with prospective validation,” EClinicalMedicine, vol. 43, 2022, Art. no. 101252.
📄 A. Noshchenko et al., “Predictors of spine deformity progression in adolescent idiopathic scoliosis: A systematic review with meta-analysis,” World J. Orthop., vol. 6, no. 7, 2015, Art. no. 537.
📄 R. Patil and S. Bhosale, “Medical image denoising using wavelet transform and singular value decomposition,” in Proc. Int. Conf. Innov. Develop. Eng. Appl., 2021, vol. 8, pp. 356–362.
📄 C. Slattery and K. Verma, “Classifications in brief: The Lenke classification for adolescent idiopathic scoliosis,” Clin. Orthopaedics Related Res., vol. 476, no. 11, pp. 2271–2276, 2018.
📄 A. Suri et al., “Conquering the Cobb angle: A deep learning algorithm for automated, hardware-invariant measurement of cobb angle on radiographs in patients with scoliosis,” Radiol., Artif. Intell., vol. 5, no. 4, 2023, Art. no. e220158.
📄 A. Vaswani et al., “Attention is all you need,” in Proc. Adv. Neural Inf. Process. Syst., 2017, pp. 102115:1–18.
📄 J. Wang et al., “Deep high-resolution representation learning for visual recognition,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 43, no. 10, pp. 3349–3364, Oct. 2021.
📄 M. X. Wang, J. K. Kim, J.-W. Choi, D. Park, and M. C. Chang, “Deep learning algorithm for automatically measuring Cobb angle in patients with idiopathic scoliosis,” Eur. Spine J., vol. 33, no. 11, pp. 4155–4163, 2024.
📄 S. L. Weinstein, L. A. Dolan, J. C. Cheng, A. Danielsson, and J. A. Morcuende, “Adolescent idiopathic scoliosis,” Lancet, vol. 371, no. 9623, pp. 1527–1537, 2008.
📄 S. L. Weinstein, “The natural history of adolescent idiopathic scoliosis,” J. Pediatr. Orthopaedics, vol. 39, pp. S44–S46, 2019.
📄 D. J. Wever et al., “A biomechanical analysis of the vertebral and rib deformities in structural scoliosis,” Eur. Spine J., vol. 8, pp. 252–260, 1999.
📄 Y. Yao et al., “W-transformer: Accurate Cobb angles estimation by using a transformer-based hybrid structure,” Med. Phys., vol. 49, no. 5, pp. 3246–3262, 2022.
📄 M. Zhao, N. Meng, J. P. Y. Cheung, C. Yu, P. Lu, and T. Zhang, “SpineHRformer: A transformer-based deep learning model for automatic spine deformity assessment with prospective validation,” Bioengineering, vol. 10, no. 11, 2023, Art. no. 1333.
📄 T. Zhang et al., “Deep learning model to classify and monitor idiopathic scoliosis in adolescents using a single smartphone photograph,” JAMA Netw. Open, vol. 6, no. 8 2023, e2330617.
📄 L. Zou et al., “VLTENet: A deep-learning-based vertebra localization and tilt estimation network for automatic Cobb angle estimation,” IEEE J. Biomed. Health Inform., vol. 27, no. 6, pp. 3002–3013, Jun. 2023.

Similar Articles

1-10 of 18

You may also start an advanced similarity search for this article.