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