Abstract
The anatomical landmarking on statistical shape models is widely used in structural and morphometric analyses. The current study focuses on leveraging geometric features to realize an automatic and reliable landmarking. The existing implementations usually rely on classical geometric features and data-driven learning methods. However, such designs often have limitations to specific shape types. Additionally, calculating the features as a standalone step increases the computational cost. In this paper, we propose a convolutional Bayesian model for anatomical landmarking on multi-dimensional shapes. The main idea is to embed the convolutional filtering in a stationary kernel so that the geometric features are efficiently captured and implicitly encoded into the prior knowledge of a Gaussian process. In this way, the posterior inference is geometrically meaningful without entangling with extra features. By using a Gaussian process regression framework and the active learning strategy, our method is flexible and efficient in extracting arbitrary numbers of landmarks. We demonstrate extensive applications on various publicly available datasets, including one brain imaging cohort and three skeletal anatomy datasets. Both the visual and numerical evaluations verify the effectiveness of our method in extracting significant landmarks.
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
Al-Aifari, R., Daubechies, I., Lipman, Y.: Continuous procrustes distance between two surfaces. Commun. Pure Appl. Math. 66(6), 934–964 (2013)
Aubry, M., Schlickewei, U., Cremers, D.: The wave kernel signature: a quantum mechanical approach to shape analysis. In: 2011 IEEE International Conference on Computer Vision Workshops (ICCV Workshops), pp. 1626–1633. IEEE (2011)
Berline, N., Getzler, E., Vergne, M.: Heat Kernels and Dirac Operators. Springer, Heidelberg (2003)
Bonaretti, S., Seiler, C., Boichon, C., Reyes, M., Büchler, P.: Image-based vs. mesh-based statistical appearance models of the human femur: implications for finite element simulations. Medical Eng. Phys. 36(12), 1626–1635 (2014)
Boyer, D.M., Lipman, Y., Clair, E.S., Puente, J., Patel, B.A., Funkhouser, T., Jernvall, J., Daubechies, I.: Algorithms to automatically quantify the geometric similarity of anatomical surfaces. Proc. Natl. Acad. Sci. 108(45), 18221–18226 (2011)
Bronstein, M.M., Bruna, J., LeCun, Y., Szlam, A., Vandergheynst, P.: Geometric deep learning: going beyond euclidean data. IEEE Signal Process. Mag. 34(4), 18–42 (2017)
Couette, S., White, J.: 3D geometric morphometrics and missing-data. can extant taxa give clues for the analysis of fossil primates? C.R. Palevol 9(6–7), 423–433 (2010)
Fan, Y., Lepore, N., Wang, Y.: Morphometric gaussian process for landmarking on grey matter tetrahedral models. In: 15th International Symposium on Medical Information Processing and Analysis, vol. 11330, p. 113300H. International Society for Optics and Photonics (2020)
Fan, Y., Wang, G., Leporé, N., Wang, Y.: A tetrahedron-based heat flux signature for cortical thickness morphometry analysis. Med. Image Comput. Comput. Assist. Interv. 11072, 420–428 (2018)
Gao, T., Kovalsky, S.Z., Boyer, D.M., Daubechies, I.: Gaussian process landmarking for three-dimensional geometric morphometrics. SIAM J. Math. Data Sci. 1(1), 237–267 (2019)
Gardner, J., Pleiss, G., Weinberger, K.Q., Bindel, D., Wilson, A.G.: Gpytorch: blackbox matrix-matrix gaussian process inference with GPU acceleration. In: Advances in Neural Information Processing Systems, pp. 7576–7586 (2018)
Guennebaud, G., Germann, M., Gross, M.: Dynamic sampling and rendering of algebraic point set surfaces. In: Computer Graphics Forum, vol. 27, pp. 653–662. Wiley Online Library (2008)
Huang, S.G., Lyu, I., Qiu, A., Chung, M.K.: Fast polynomial approximation of heat kernel convolution on manifolds and its application to brain sulcal and gyral graph pattern analysis. IEEE Trans. Med. Imaging 39(6), 2201–2212 (2020)
Jack Jr., C.R., et al.: The alzheimer’s disease neuroimaging initiative (ADNI): MRI methods. J. Mag. Resonance Imaging Off. J. Int. Soc. Magnet. Resonance Med. 27(4), 685–691 (2008)
Kondor, R.I., Lafferty, J.: Diffusion kernels on graphs and other discrete structures. In: Proceedings of the 19th International Conference on Machine Learning, vol. 2002, pp. 315–322 (2002)
Lee, C.H., Varshney, A., Jacobs, D.W.: Mesh saliency. ACM Trans. graphics (TOG) 24(3), 659–666 (2005)
Lipman, Y.: Bounded distortion mapping spaces for triangular meshes. ACM Trans. Graphics (TOG) 31(4), 1–13 (2012)
Mueller, S.G., et al.: The alzheimer’s disease neuroimaging initiative. Neuroimaging Clin. 15(4), 869–877 (2005)
Øksendal, B.: Stochastic Differential Equations. U. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-642-14394-6
Pini, L., et al.: Brain atrophy in alzheimer’s disease and aging. Ageing Res. Rev. 30, 25–48 (2016)
Salhi, A., Burdin, V., Brochard, S., Mutsvangwa, T.E., Borotikar, B.: Clinical relevance of augmented statistical shape model of the scapula in the glenoid region. Med. Eng. Phys. 76, 88–94 (2020)
Särkkä, S.: Linear operators and stochastic partial differential equations in gaussian process regression. In: Honkela, T., Duch, W., Girolami, M., Kaski, S. (eds.) ICANN 2011. LNCS, vol. 6792, pp. 151–158. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-21738-8_20
Seim, H., Kainmueller, D., Heller, M., Zachow, S., Hege, H.C.: Automatic extraction of anatomical landmarks from medical image data: an evaluation of different methods. In: 2009 IEEE International Symposium on Biomedical Imaging: From Nano to Macro, pp. 538–541. IEEE (2009)
Si, H.: Tetgen, a delaunay-based quality tetrahedral mesh generator. ACM Trans. Math. Softw. (TOMS) 41(2), 1–36 (2015)
Stein, M.L.: A kernel approximation to the kriging predictor of a spatial process. Ann. Inst. Stat. Math. 43(1), 61–75 (1991)
Wang, G., Wang, Y., Initiative, A.D.N., et al.: Towards a holistic cortical thickness descriptor: heat kernel-based grey matter morphology signatures. Neuroimage 147, 360–380 (2017)
Williams, C.K., Rasmussen, C.E.: Gaussian Processes for Machine Learning, vol. 2. MIT press, Cambridge (2006)
Wilson, A., Adams, R.: Gaussian process kernels for pattern discovery and extrapolation. In: International Conference on Machine Learning, pp. 1067–1075 (2013)
Wilson, A.G.: Covariance kernels for fast automatic pattern discovery and extrapolation with Gaussian processes. Ph.D. thesis, University of Cambridge (2014)
Wu, Z., et al.: Intrinsic patch-based cortical anatomical parcellation using graph convolutional neural network on surface manifold. Med Image Comput Comput Assist Interv 11766, 492–500 (2019)
Xie, W., et al.: Statistical model-based segmentation of the proximal femur in digital antero-posterior (AP) pelvic radiographs. Int. J. Comput. Assist. Radiol. Surg. 9(2), 165–176 (2014)
Zhang, J., Liu, M., Shen, D.: Detecting anatomical landmarks from limited medical imaging data using two-stage task-oriented deep neural networks. IEEE Trans. Image Process. 26(10), 4753–4764 (2017)
Zheng, G., Gollmer, S., Schumann, S., Dong, X., Feilkas, T., Gonzülez Ballester, M.A.: A 2D/3D correspondence building method for reconstruction of a patient-specific 3D bone surface model using point distribution models and calibrated X-ray images. Med. Image Anal. 13(6), 883–899 (2009)
Acknowledgements
This work is supported in part by NIH (RF1AG051710 and R01EB025032) and Arizona Alzheimer Consortium.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Fan, Y., Wang, Y. (2020). Convolutional Bayesian Models for Anatomical Landmarking on Multi-dimensional Shapes. In: Martel, A.L., et al. Medical Image Computing and Computer Assisted Intervention – MICCAI 2020. MICCAI 2020. Lecture Notes in Computer Science(), vol 12264. Springer, Cham. https://doi.org/10.1007/978-3-030-59719-1_76
Download citation
DOI: https://doi.org/10.1007/978-3-030-59719-1_76
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-59718-4
Online ISBN: 978-3-030-59719-1
eBook Packages: Computer ScienceComputer Science (R0)
