Skip to main content

Graph Convolutional Network with Probabilistic Spatial Regression: Application to Craniofacial Landmark Detection from 3D Photogrammetry

  • Conference paper
  • First Online:
Medical Image Computing and Computer Assisted Intervention – MICCAI 2022 (MICCAI 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13433))

Abstract

Quantitative evaluation of pediatric craniofacial anomalies relies on the accurate identification of anatomical landmarks and structures. While segmentation and landmark detection methods in standard clinical images are available in the literature, image-based methods are not directly applicable to 3D photogrammetry because of its unstructured nature consisting in variable numbers of vertices and polygons. In this work, we propose a graph-based convolutional neural network based on Chebyshev polynomials that exploits vertex coordinates, polygonal connectivity, and surface normal vectors to extract multi-resolution spatial features from the 3D photographs. We then aggregate them using a novel weighting scheme that accounts for local spatial resolution variability in the data. We also propose a new trainable regression scheme based on the probabilistic distances between each original vertex and the anatomical landmarks to calculate coordinates from the aggregated spatial features. This approach allows calculating accurate landmark coordinates without assuming correspondences with specific vertices in the original mesh. Our method achieved state-of-the-art landmark detection errors.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Trainor, P.A., Richtsmeier, J.T.: Facing up to the challenges of advancing craniofacial research. Am. J. Med. Genet. A 167(7), 1451–1454 (2015). https://doi.org/10.1002/ajmg.a.37065

    Article  Google Scholar 

  2. Wang, J.Y., Dorafshar, A.H., Liu, A., Groves, M.L., Ahn, E.S.: The metopic index: an anthropometric index for the quantitative assessment of trigonocephaly from metopic synostosis. J. Neurosurg. Pediatr. 18(3), 275–280 (2016). https://doi.org/10.3171/2016.2.PEDS15524

    Article  Google Scholar 

  3. Mathijssen, I.M.J.: Updated guideline on treatment and management of craniosynostosis. J. Craniofac. Surg. 32(1), 371–450 (2021). https://doi.org/10.1097/SCS.0000000000007035

    Article  Google Scholar 

  4. Schweitzer, T., Böhm, H., Meyer-Marcotty, P., Collmann, H., Ernestus, R.-I., Krauß, J.: Avoiding CT scans in children with single-suture craniosynostosis. Childs Nerv. Syst. 28(7), 1077–1082 (2012). https://doi.org/10.1007/s00381-012-1721-0

    Article  Google Scholar 

  5. Tanikawa, C., Akcam, M.O., Takada, K.: Quantifying faces three-dimensionally in orthodontic practice. J. Cranio-Maxillofac. Surg. 47(6), 867–875 (2019). https://doi.org/10.1016/j.jcms.2019.02.012

    Article  Google Scholar 

  6. Porras, A.R., et al.: Quantification of head shape from three-dimensional photography for presurgical and postsurgical evaluation of craniosynostosis. Plast. Reconstr. Surg. 144(6), 1051e–1060e (2019). https://doi.org/10.1097/PRS.0000000000006260

    Article  Google Scholar 

  7. Cho, M.-J., et al.: Quantifying normal craniofacial form and baseline craniofacial asymmetry in the pediatric population. Plast. Reconstr. Surg. 141(3), 380e–387e (2018). https://doi.org/10.1097/PRS.0000000000004114

    Article  Google Scholar 

  8. Ma, Q., et al.: Automatic 3D landmarking model using patch-based deep neural networks for CT image of oral and maxillofacial surgery. Int. J. Med. Robot. 16(3), e2093 (2020). https://doi.org/10.1002/rcs.2093

    Article  Google Scholar 

  9. Torosdagli, N., Liberton, D.K., Verma, P., Sincan, M., Lee, J.S., Bagci, U.: Deep geodesic learning for segmentation and anatomical landmarking. IEEE Trans. Med. Imaging 38(4), 919–931 (2019). https://doi.org/10.1109/TMI.2018.2875814

    Article  Google Scholar 

  10. Song, Y., Qiao, X., Iwamoto, Y., Chen, Y.: Automatic cephalometric landmark detection on x-ray images using a deep-learning method. Appl. Sci. 10(7), 2547 (2020). https://doi.org/10.3390/app10072547

    Article  Google Scholar 

  11. Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. ArXiv160902907 Cs Stat (2017). Accessed 21 Feb 2022. http://arxiv.org/abs/1609.02907

  12. Defferrard, M., Bresson, X., Vandergheynst, P.: Convolutional neural networks on graphs with fast localized spectral filtering. ArXiv160609375 Cs Stat (2017). Accessed 08 Dec 2021. http://arxiv.org/abs/1606.09375

  13. Soberanis-Mukul, R.D., Navab, N., Albarqouni, S.: An uncertainty-driven GCN refinement strategy for organ segmentation. Machine Learning for Biomedical Imaging MELBA (2020). arXiv:2012.03352

  14. Wolterink, J.M., Leiner, T., Išgum, I.: Graph convolutional networks for coronary artery segmentation in cardiac CT angiography. In: Zhang, D., Zhou, L., Jie, B., Liu, M. (eds.) GLMI 2019. LNCS, vol. 11849, pp. 62–69. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-35817-4_8

    Chapter  Google Scholar 

  15. Parisot, S., et al.: Spectral graph convolutions for population-based disease prediction. In: Descoteaux, M., Maier-Hein, L., Franz, A., Jannin, P., Collins, D.L., Duchesne, S. (eds.) MICCAI 2017. LNCS, vol. 10435, pp. 177–185. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-66179-7_21

    Chapter  Google Scholar 

  16. Qi, C.R., Su, H., Mo, K., Guibas, L.J.: PointNet: deep learning on point sets for 3D classification and segmentation. ArXiv161200593 Cs (2017). Accessed 12 Oct 2021. http://arxiv.org/abs/1612.00593

  17. Li, Y., Bu, R., Sun, M., Wu, W., Di, X., Chen, B.: PointCNN: convolution on $\mathcal{X}$-transformed points. ArXiv180107791 Cs (2018). Accessed 21 Feb 2022. http://arxiv.org/abs/1801.07791

  18. Qi, C.R., Yi, L., Su, H., Guibas, L.J.: PointNet++: deep hierarchical feature learning on point sets in a metric space. ArXiv170602413 Cs (2017). Accessed 25 Oct 2021. http://arxiv.org/abs/1706.02413

  19. Guo, Y., Wang, H., Hu, Q., Liu, H., Liu, L., Bennamoun, M.: Deep learning for 3D point clouds: a survey. IEEE Trans. Pattern Anal. Mach. Intell. 43(12), 4338–4364 (2021). https://doi.org/10.1109/TPAMI.2020.3005434

    Article  Google Scholar 

  20. Caple, J., Stephan, C.N.: A standardized nomenclature for craniofacial and facial anthropometry. Int. J. Legal Med. 130(3), 863–879 (2015). https://doi.org/10.1007/s00414-015-1292-1

    Article  Google Scholar 

  21. Garland, M., Heckbert, P.S.: Surface simplification using quadric error metrics. In: Proceedings of the 24th Annual Conference on Computer Graphics and Interactive Techniques - SIGGRAPH 1997, pp. 209–216 (1997). https://doi.org/10.1145/258734.258849

  22. Cai, T., Luo, S., Xu, K., He, D., Liu, T.-Y., Wang, L.: GraphNorm: a principled approach to accelerating graph neural network training. ArXiv200903294 Cs Math Stat (2021). Accessed 17 Feb 2022. http://arxiv.org/abs/2009.03294

  23. Li, W., et al.: Structured landmark detection via topology-adapting deep graph learning. In: Vedaldi, A., Bischof, H., Brox, T., Frahm, J.-M. (eds.) ECCV 2020. LNCS, vol. 12354, pp. 266–283. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-58545-7_16

    Chapter  Google Scholar 

  24. Reddi, S.J., Kale, S., Kumar, S.: On the convergence of Adam and beyond. ArXiv190409237 Cs Math Stat (2019). Accessed 24 Feb 2022. http://arxiv.org/abs/1904.09237

  25. Fey, M., Lenssen, J.E.: Fast graph representation learning with PyTorch geometric. ArXiv190302428 Cs Stat (2019). Accessed 15 Dec 2021. http://arxiv.org/abs/1903.02428

  26. Bookstein, F.L.: “Landmarks,” in Morphometric Tools for Landmark Data: Geometry and Biology, pp. 55–87. Cambridge University Press, Cambridge (1992)

    Book  Google Scholar 

  27. Yue, W., Yin, D., Li, C., Wang, G., Xu, T.: Automated 2-D cephalometric analysis on X-ray images by a model-based approach. IEEE Trans. Biomed. Eng. 53(8), 1615–1623 (2006). https://doi.org/10.1109/TBME.2006.876638

  28. Torres, H.R., et al.: Anthropometric landmark detection in 3D head surfaces using a deep learning approach. IEEE J. Biomed. Health Inform. 25(7), 2643–2654 (2021). https://doi.org/10.1109/JBHI.2020.3035888

    Article  Google Scholar 

  29. García-Mato, D., et al.: Effectiveness of automatic planning of fronto-orbital advancement for the surgical correction of metopic craniosynostosis. Plast. Reconstr. Surg. - Glob. Open 9(11), e3937 (2021). https://doi.org/10.1097/GOX.0000000000003937

    Article  Google Scholar 

Download references

Acknowledgements

CE is supported by the National Library of Medicine (NLM) under project number T15LM009451. ARP was supported by the National Institute of Dental & Craniofacial Research of the National Institutes of Health under Award Number R00DE027993. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Connor Elkhill .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Elkhill, C., LeBeau, S., French, B., Porras, A.R. (2022). Graph Convolutional Network with Probabilistic Spatial Regression: Application to Craniofacial Landmark Detection from 3D Photogrammetry. In: Wang, L., Dou, Q., Fletcher, P.T., Speidel, S., Li, S. (eds) Medical Image Computing and Computer Assisted Intervention – MICCAI 2022. MICCAI 2022. Lecture Notes in Computer Science, vol 13433. Springer, Cham. https://doi.org/10.1007/978-3-031-16437-8_55

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-16437-8_55

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-16436-1

  • Online ISBN: 978-3-031-16437-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics