Abstract
Statistical shape models (SSMs) are an established way to represent the anatomy of a population with various clinically relevant applications. However, they typically require domain expertise, and labor-intensive landmark annotations to construct. We address these shortcomings by proposing an unsupervised method that leverages deep geometric features and functional correspondences to simultaneously learn local and global shape structures across population anatomies. Our pipeline significantly improves unsupervised correspondence estimation for SSMs compared to baseline methods, even on highly irregular surface topologies. We demonstrate this for two different anatomical structures: the thyroid and a multi-chamber heart dataset. Furthermore, our method is robust enough to learn from noisy neural network predictions, potentially enabling scaling SSMs to larger patient populations without manual segmentation annotation. The code is publically available at:
Lennart Bastian and Alexander Baumann contributed equally to this work.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Adams, J., Bhalodia, R., Elhabian, S.: Uncertain-DeepSSM: from images to probabilistic shape models. In: Reuter, M., Wachinger, C., Lombaert, H., Paniagua, B., Goksel, O., Rekik, I. (eds.) ShapeMI 2020. LNCS, vol. 12474, pp. 57–72. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-61056-2_5
Adams, J., Elhabian, S.: From images to probabilistic anatomical shapes: a deep variational bottleneck approach. In: Wang, L., Dou, Q., Fletcher, P.T., Speidel, S., Li, S. (eds.) MICCAI 2022. LNCS, vol. 13432, pp. 474–484. Springer, Heidelberg (2022). https://doi.org/10.1007/978-3-031-16434-7_46
Adams, J., Khan, N., Morris, A., Elhabian, S.: Spatiotemporal cardiac statistical shape modeling: a data-driven approach. In: Camara, O., et al. (eds.) STACOM MICCAI 2022, vol. 13593, pp. 143–156. Springer, Heidelberg (2023). https://doi.org/10.1007/978-3-031-23443-9_14
Agrawal, P., Whitaker, R.T., Elhabian, S.Y.: Learning deep features for shape correspondence with domain invariance. arXiv preprint arXiv:2102.10493 (2021)
Aubry, M., Schlickewei, U., Cremers, D.: The wave kernel signature: a quantum mechanical approach to shape analysis. In: ICCV Workshops (2011)
Banerjee, A., Zacur, E., Choudhury, R.P., Grau, V.: Automated 3d whole-heart mesh reconstruction from 2d cine mr slices using statistical shape model. In: 2022 IEEE EMBS, pp. 1702–1706. IEEE (2022)
Bhalodia, R., Elhabian, S., Adams, J., Tao, W., Kavan, L., Whitaker, R.: Deepssm: a blueprint for image-to-shape deep learning models. arXiv preprint arXiv:2110.07152 (2021)
Bongratz, F., Rickmann, A.M., Pölsterl, S., Wachinger, C.: Vox2cortex: fast explicit reconstruction of cortical surfaces from 3d MRI scans with geometric deep neural networks. In: CVPR 2022, pp. 20773–20783 (2022)
Bronstein, M.M., Kokkinos, I.: Scale-invariant heat kernel signatures for non-rigid shape recognition. In: CVPR 2010, pp. 1704–1711. IEEE (2010)
Cao, D., Bernard, F.: Unsupervised deep multi-shape matching. In: Avidan, S., Brostow, G., Cisse, M., Farinella, G.M., Hassner, T. (eds.) ECCV 2022. LNCS, vol. 13663, pp. 55–71. Springer, Heidelberg (2022). https://doi.org/10.1007/978-3-031-20062-5_4
Cates, J., Elhabian, S., Whitaker, R.: ShapeWorks. In: Statistical Shape and Deformation Analysis, pp. 257–298. Elsevier (2017)
Cerrolaza, J.J., et al.: Computational anatomy for multi-organ analysis in medical imaging: a review. Med. Image Anal. 56, 44–67 (2019)
Cootes, T.F., Taylor, C.J., Cooper, D.H., Graham, J.: Training models of shape from sets of examples. In: BMVC92 (1992)
Cootes, T.F., Twining, C.J., Babalola, K.O., Taylor, C.J.: Diffeomorphic statistical shape models. Image Vision Comput. 26(3), 326–332 (2008)
Crane, K.: Discrete differential geometry: an applied introduction. Not. AMS Commun. 7, 1153–1159 (2018)
Davies, R.H.: Learning Shape: Optimal Models for Analysing Natural Variability. The University of Manchester (United Kingdom) (2002)
Donati, N., Sharma, A., Ovsjanikov, M.: Deep geometric functional maps: robust feature learning for shape correspondence. In: CVPR 2020, pp. 8592–8601 (2020)
Du, J., Zhang, S., Wu, G., Moura, J.M., Kar, S.: Topology adaptive graph convolutional networks. arXiv preprint arXiv:1710.10370 (2017)
Goparaju, A., Iyer, K., Bone, A., Hu, N., Henninger, H.B., et al.: Benchmarking off-the-shelf statistical shape modeling tools in clinical applications. Med. Image Anal. 76, 102271 (2022)
Gutiérrez-Becker, B., Wachinger, C.: Learning a conditional generative model for anatomical shape analysis. In: Chung, A.C.S., Gee, J.C., Yushkevich, P.A., Bao, S. (eds.) IPMI 2019. LNCS, vol. 11492, pp. 505–516. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-20351-1_39
Heimann, T., Meinzer, H.P.: Statistical shape models for 3D medical image segmentation: a review. Med. Image Anal. 13(4), 543–563 (2009)
Henderson, E.G., Green, A.F., van Herk, M., Vasquez Osorio, E.M.: Automatic identification of segmentation errors for radiotherapy using geometric learning. In: Wang, L., Dou, Q., Fletcher, P.T., Speidel, S., Li, S. (eds.) MICCAI 2022. LNCS, vol. 13435, pp. 319–329. Springer, Heidelberg (2022). https://doi.org/10.1007/978-3-031-16443-9_31
Kazi, A., et al.: InceptionGCN: receptive field aware graph convolutional network for disease prediction. In: Chung, A.C.S., Gee, J.C., Yushkevich, P.A., Bao, S. (eds.) IPMI 2019. LNCS, vol. 11492, pp. 73–85. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-20351-1_6
Klatzow, J., Dalmasso, G., Martínez-Abadías, N., Sharpe, J., Uhlmann, V.: \(\upmu \)Match: 3D shape correspondence for biological image data, vol. 4 (2022)
Krönke, M., Eilers, C., Dimova, D., Köhler, M., Buschner, G., et al.: Tracked 3d ultrasound and deep neural network-based thyroid segmentation reduce interobserver variability in thyroid volumetry. Plos One 17(7) (2022)
Litany, O., Remez, T., Rodola, E., Bronstein, A., Bronstein, M.: Deep functional maps: structured prediction for dense shape correspondence. In: ICCV, pp. 5659–5667 (2017)
Lorensen, W.E., Cline, H.E.: Marching cubes: a high resolution 3d surface construction algorithm. ACM Siggraph Comput. Graph. 21(4), 163–169 (1987)
Lüdke, D., Amiranashvili, T., Ambellan, F., Ezhov, I., Menze, B.H., Zachow, S.: Landmark-free statistical shape modeling via neural flow deformations. In: Wang, L., Dou, Q., Fletcher, P.T., Speidel, S., Li, S. (eds.) MICCAI 2022. LNCS, vol. 13432, pp. 453–463. Springer, Heidelberg (2022). https://doi.org/10.1007/978-3-031-16434-7_44
Ovsjanikov, M., Ben-Chen, M., Solomon, J., Butscher, A., Guibas, L.: Functional maps: a flexible representation of maps between shapes. ACM ToG 31(4) (2012)
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
Roufosse, J.M., Sharma, A., Ovsjanikov, M.: Unsupervised deep learning for structured shape matching. In: ICCV (2019)
Saleh, M., Dehghani, S., Busam, B., Navab, N., Tombari, F.: Graphite: graph-induced feature extraction for point cloud registration. In: 2020 3DV, pp. 241–251. IEEE (2020)
Saleh, M., Wu, S.C., Cosmo, L., Navab, N., Busam, B., Tombari, F.: Bending graphs: hierarchical shape matching using gated optimal transport. In: CVPR 2022, pp. 11757–11767 (2022)
Sharma, A., Ovsjanikov, M.: Weakly supervised deep functional maps for shape matching. NeurIPS 33, 19264–19275 (2020)
Tobon-Gomez, C., et al.: Benchmark for algorithms segmenting the left atrium from 3d ct and mri datasets. IEEE Trans. Med. Imaging 34(7), 1460–1473 (2015)
Tombari, F., Salti, S., Di Stefano, L.: Unique signatures of histograms for local surface description. In: Daniilidis, K., Maragos, P., Paragios, N. (eds.) ECCV 2010. LNCS, vol. 6313, pp. 356–369. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15558-1_26
Vestner, M., Litman, R., Rodola, E., Bronstein, A., Cremers, D.: Product manifold filter: non-rigid shape correspondence via kernel density estimation in the product space. In: CVPR (2017)
Wang, Y., Sun, Y., Liu, Z., Sarma, S.E., Bronstein, M.M., Solomon, J.M.: Dynamic graph cnn for learning on point clouds. Acm ToG 38(5), 1–12 (2019)
Zhang, L., et al.: Disentangling human error from ground truth in segmentation of medical images. NeurIPS 33, 15750–15762 (2020)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
1 Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Bastian, L. et al. (2023). S3M: Scalable Statistical Shape Modeling Through Unsupervised Correspondences. In: Greenspan, H., et al. Medical Image Computing and Computer Assisted Intervention – MICCAI 2023. MICCAI 2023. Lecture Notes in Computer Science, vol 14229. Springer, Cham. https://doi.org/10.1007/978-3-031-43999-5_44
Download citation
DOI: https://doi.org/10.1007/978-3-031-43999-5_44
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-43998-8
Online ISBN: 978-3-031-43999-5
eBook Packages: Computer ScienceComputer Science (R0)
