Physics, mathematics, and technology

2019 Issue №3

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Auto­matic System for Determining the Angles of Scoliotic Deformity of the Human Spine



Scoliosis is a common disease among children and adults. A standard method for assessing the severity of scoliosis is to measure the Cobb angle. However in some cases the Cobb angle may not be clinically indicative. More­over, the measurement process is fraught with errors caused by the subjectivi­ty of setting key points at the first measurement stage. The article describes the developed system for measuring the scoliosis angle, based on the use of ar­tificial convolutional neural networks and subsequent algorithmic processing. The objective of the developed program is to measure the angles of scoliotic de­formation of the spinal column.


1. Trobisch P., Suess O., Schwab F. Die idiopathische Skoliose // Dtsch Arztebl Int. 2010. Vol. 107(49). P. 875—84. doi: 10.3238/arztebl.2010.0875.

2. Cobb J. R. Outline for the Study of Scoliosis // Instr. Course Lect. 1948. Vol. 5. P. 261—275.

3. James J. Scoliosis. Edinburgh ; L., 1976.

4. Kim H., Kim H. K., Moon E. S. et al. Scoliosis Imaging: What Radiologists Should Know// Radiographics. 2010. Vol. 30, iss. 7. P. 1823—1842. URL: 10.1148/rg.307105061 (дата обращения: 15.06.2019).

5. Göçen S., Havitçioglu H. Effect of Rotation on Frontal Plane Deformity in Idio­pa­thic Scoliosis // Orthopedics. 2001. Vol. 24, iss. 3. P. 265—268.

6. Beauchamp M., Labelle H., Grimard G. et al. Diurnal Variation of Cobb Angle Measurement in Adolescent Idiopathic Scoliosis // Spine (Phila Pa 1976). 1993. Vol. 18 (12). P. 1581—1583.

7. Pruijs J. E., Hageman M. A., Keessen W. et al. Variation in Cobb Angle Measure­ments in Scoliosis // Skeletal Radiology. 1994. Vol. 23 (7). P. 517—520.

8. Morrissy R. T., Goldsmith G. S., Hall E. C. et al. Measurement of the Cobb Angle on Radiographs of Patients Who Have Scoliosis: Evaluation of Intrinsic Error // J Bone Joint Surg. Am. 1990. Vol. 72 (3). P. 320—327.

9. National Scoliosis Foundation : [сайт]. URL: showthread.php?6208-Cobb-Angle-Measurement (дата обращения: 17.06.2019).

10. Ronneberger O., Fischer P., Brox T. U-Net: Convolutional Networks for Bio­medical Image Segmentation // MICCAI 2015. arXiv:1505.04597v1 [cs.CV].

11. Yu F., Koltun V. Multi-Scale Context Aggregation by Dilated Convolutions // ICLR 2016. arXiv: 1511.07122v3 [cs.CV].

12. Iandola F., Han S., Moskewicz M. et al. SqueezeNet: AlexNet-level Accuracy with 50x Fewer Parameters and < 0.5MB Model Size // ICLR 2016. arXiv:1602. 07360v4 [cs.CV].

13. Ioffe S., Szegedy C. Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift // ICML. 2015. Vol. 37. P. 448—456. arXiv:1502. 03167v3 [cs.LG].

14. PyTorch: From Research to Production : [сайт]. URL: (дата обращения: 19.06.2019).

15. Kingma D., Ba J. Adam: A Method for Stochastic Optimization // The 3rd In­ternational Conference for Learning Representations, 2015. arXiv:1412.6980v9 [cs.LG].

16. Reddi S., Kale S., Kumar S. On the Convergence of Adam and Beyond // ICLR 2018. arXiv:1904.09237v1 [cs.LG].

17. Kadoury. S., Labdlc. H., Paragios. N. Spine Segmentation in Medical Images Us­ing Manifold Embeddings and Higher-Order MRFs // IEEE Trans. Med. Imaging. 2013. Vol. 32(7). P. 1227—1238.

18. Forsberg. D. Atlas-Based Segmentation of the Thoracic and Lumbar Vertebrae // Proceedings of 2nd MICCAI Workshop on Computational Methods and Clinical Ap­plications for Spine Imaging CSI2014. 2015. Vol. 20. P. 215—220.

19. Cootes T., Taylor C., Cooper D., J. Graham. Active Shape Models — Their Train­ing and Application // CVIU. 1995. Vol. 61, iss. 1. P. 38—59.

20. Cootes T., Edwards G., Taylor C. Active Appearance Models // IEEE Trans. Pattern Anal. Mach. IntelI. 2001. Vol. 23, iss. 6. P. 681—685.

21. Aslan M. S., Ali. A., Chen D. et al. 3D Vertebrae Segmentation Using Graph Cuts with Shape Prior Constraints. // IEEE International Conference on Image Pro­cessing. Hong Kong, 2010. P. 2193—2196. doi: 10.1109/ICIP.2010.5652849.

22. Rousson M., Paragios N. Prior Knowledge, Level Set Representations and Vis­ual Grouping // Int. J Comput. Vis. 2008. Vol. 76. P. 231—243.

23. Yookwan W., Chinnasarn K., Jantarakongkul B. Region of Interest of Human Lumbar Spine Segmentation Using Geometric Triangular Analysis // IWAIT 2018. doi: 10.1109/IWAIT.2018.8369775.

24. Whitehead W., Moran S., Gaonkar B. et al. L. A deep learning approach to spine segmentation using a feed-forward chain of pixel-wise convolutional networks // ISBI 2018. Washington, 2018. P. 868—871. doi: 10.1109 ISBL2018.8363709.

25. Li Y., Liang W., Zhang Y. et al. Automatic Lumbar Vertebrae Detection Based on Feature Fusion Deep Learning for Partial Occluded C-arm X-ray Images // EMBC 2016. Orlando, 2016. P. 640—650. doi: 10.1109/EMBC.2016.7590785.

26. Baka N., Leenstra S., van Walsum T. Ultrasound Aided Vertebral Level Locali­zation for Lumbar Surgery // IEEE T-MI. 2017. Vol. 36, iss. 10. P. 2138—2147. doi: 10.1109/TMI.2017.2738612.

27. Ma J., Lu L., Zhan Y. et al. Hierarchical Segmentation and Identification of Thoracic Vertebra Using Learning-Based Edge Detection and Coarse-to-Fine De­formable Model // Proceedings of MICCAI. 2010. P. 19—27.

28. Rehman F., Irtiza S., Shah A. et al. A Novel Framework to Segment Out Cervi­cal Vertebrae // IEEE 2019. doi: 10.1109/C-CODE.2019.8680994.

29. Lu J.-T., Pedemonte S., Bizzo B. et al. Deep Spine: Automated Lumbar Vertebral Segmentation, Disc-Level Designation, and Spinal Stenosis Grading Using Deep Learning // MLHC 2018. arXiv:1807.10215v1 [cs.CV].

30. Choi R., Watanabe K., Jinguji H. et al. CNN-based Spine and Cobb Angle Esti­mator Using Moire Images // IIEEJ Trans. 2017. Vol 5, iss. 2. P. 135—144. URL: (дата обращения: 15.06.2019).

31. Horng M.-H., Kuok C.-P., Fu M.-L. et al. Cobb Angle Measurement of Spine from X-Ray Images Using Convolutional Neural Network // Comput. Math. Me­thods Med. 2019. Vol. 2019. 6357171. URL: (да­та обращения: 19.06.2019).

32. Forsberg D., Lundström C., Andersson M. et al. Fully Automatic Measurements of Axial Vertebral Rotation for Assessment of Spinal Deformity in Idiopathic Scolio­sis // Phys Med Biol. 2013. Vol. 58, iss. 6. P. 1775—1787. doi: 10.1088/0031-9155/ 58/6/1775.