Abstract
In landmark localization, due to ambiguities in defining their exact position, landmark annotations may suffer from both large inter- and intra-observer variabilites, which result in uncertain annotations. Therefore, predicting a single coordinate for a landmark is not sufficient for modeling the distribution of possible landmark locations. We propose to learn the Gaussian covariances of target heatmaps, such that covariances for pointed heatmaps correspond to more certain landmarks and covariances for flat heatmaps to more uncertain or ambiguous landmarks. By fitting Gaussian functions to the predicted heatmaps, our method is able to obtain landmark location distributions, which model location uncertainties. We show on a dataset of left hand radiographs and on a dataset of lateral cephalograms that the predicted uncertainties correlate with the landmark error, as well as inter-observer variabilities.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Beichel, R., Bischof, H., Leberl, F., Sonka, M.: Robust active appearance models and their application to medical image analysis. IEEE Trans. Med. Imaging 24(9), 1151–1169 (2005)
Bier, B., et al.: Learning to detect anatomical landmarks of the pelvis in X-rays from arbitrary views. Int. J. Comput. Assist. Radiol. Surg. 14(9), 1463–1473 (2019)
Branch, M.A., Coleman, T.F., Li, Y.: A subspace, interior, and conjugate gradient method for large-scale bound-constrained minimization problems. SIAM J. Sci. Comput. 21(1), 1–23 (1999)
Chen, R., Ma, Y., Chen, N., Lee, D., Wang, W.: Cephalometric landmark detection by attentive feature pyramid fusion and regression-voting. In: Shen, D., et al. (eds.) MICCAI 2019. LNCS, vol. 11766, pp. 873–881. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-32248-9_97
Cootes, T.F., Ionita, M.C., Lindner, C., Sauer, P.: Robust and accurate shape model fitting using random forest regression voting. In: Fitzgibbon, A., Lazebnik, S., Perona, P., Sato, Y., Schmid, C. (eds.) ECCV 2012. LNCS, vol. 7578, pp. 278–291. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-33786-4_21
Gal, Y., Ghahramani, Z.: Dropout as a Bayesian approximation: representing model uncertainty in deep learning. In: Proceedings of the International Conference on Machine Learning, pp. 1050–1059 (2016)
Gertych, A., Zhang, A., Sayre, J., Pospiech-Kurkowska, S., Huang, H.: Bone age assessment of children using a digital hand atlas. Comput. Med. Imaging Graph. 31(4–5), 322–331 (2007)
Gunning, D., Stefik, M., Choi, J., Miller, T., Stumpf, S., Yang, G.Z.: XAI–explainable artificial intelligence. Sci. Robot. 4(37), eaay7120 (2019)
Heimann, T., Meinzer, H.P.: Statistical shape models for 3D medical image segmentation: a review. Med. Image Anal. 13(4), 543–563 (2009)
Ibragimov, B., Likar, B., Pernuš, F., Vrtovec, T.: Shape representation for efficient landmark-based segmentation in 3-D. IEEE Trans. Med. Imaging 33(4), 861–874 (2014)
Johnson, H.J., Christensen, G.E.: Consistent landmark and intensity-based image registration. IEEE Trans. Med. Imaging 21(5), 450–461 (2002)
Lindner, C., Bromiley, P.A., Ionita, M.C., Cootes, T.F.: Robust and accurate shape model matching using random forest regression-voting. IEEE Trans. Pattern Anal. Mach. Intell. 37(9), 1862–1874 (2015)
Lindner, C., Wang, C.W., Huang, C.T., Li, C.H., Chang, S.W., Cootes, T.F.: Fully automatic system for accurate localisation and analysis of cephalometric landmarks in lateral cephalograms. Sci. Rep. 6, 33581 (2016)
Nair, T., Precup, D., Arnold, D.L., Arbel, T.: Exploring uncertainty measures in deep networks for Multiple sclerosis lesion detection and segmentation. Med. Image Anal. 59, 101557 (2020)
Payer, C., Štern, D., Bischof, H., Urschler, M.: Regressing heatmaps for multiple landmark localization using CNNs. In: Ourselin, S., Joskowicz, L., Sabuncu, M.R., Unal, G., Wells, W. (eds.) MICCAI 2016. LNCS, vol. 9901, pp. 230–238. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-46723-8_27
Payer, C., Štern, D., Bischof, H., Urschler, M.: Integrating spatial configuration into heatmap regression based CNNs for landmark localization. Med. Image Anal. 54, 207–219 (2019)
Tompson, J., Jain, A., LeCun, Y., Bregler, C.: Joint training of a convolutional network and a graphical model for human pose estimation. In: Advances in Neural Information Processing Systems, pp. 1799–1807 (2014)
Urschler, M., Ebner, T., Štern, D.: Integrating geometric configuration and appearance information into a unified framework for anatomical landmark localization. Med. Image Anal. 43, 23–36 (2018)
Urschler, M., Zach, C., Ditt, H., Bischof, H.: Automatic point landmark matching for regularizing nonlinear intensity registration: application to thoracic CT images. In: Larsen, R., Nielsen, M., Sporring, J. (eds.) MICCAI 2006. LNCS, vol. 4191, pp. 710–717. Springer, Heidelberg (2006). https://doi.org/10.1007/11866763_87
Vrtovec, T., Pernuš, F., Likar, B.: A review of methods for quantitative evaluation of spinal curvature. Eur. Spine J. 18(5), 593–607 (2009)
Wang, C.W., et al.: A benchmark for comparison of dental radiography analysis algorithms. Med. Image Anal. 31, 63–76 (2016)
Wang, G., Li, W., Ourselin, S., Vercauteren, T.: Automatic brain tumor segmentation based on cascaded convolutional neural networks with uncertainty estimation. Front. Comput. Neurosci. 13, 56 (2019)
Wickstrøm, K., Kampffmeyer, M., Jenssen, R.: Uncertainty and interpretability in convolutional neural networks for semantic segmentation of colorectal polyps. Med. Image Anal. 60, 101619 (2020)
Yang, D., et al.: Automatic vertebra labeling in large-scale 3D CT using deep image-to-image network with message passing and sparsity regularization. In: Niethammer, M., et al. (eds.) IPMI 2017. LNCS, vol. 10265, pp. 633–644. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-59050-9_50
Zhang, A., Sayre, J.W., Vachon, L., Liu, B.J., Huang, H.K.: Racial differences in growth patterns of children assessed on the basis of bone age. Radiology 250(1), 228–235 (2009)
Zhong, Z., Li, J., Zhang, Z., Jiao, Z., Gao, X.: An attention-guided deep regression model for landmark detection in cephalograms. In: Shen, D., et al. (eds.) MICCAI 2019. LNCS, vol. 11769, pp. 540–548. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-32226-7_60
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
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Payer, C., Urschler, M., Bischof, H., Štern, D. (2020). Uncertainty Estimation in Landmark Localization Based on Gaussian Heatmaps. In: Sudre, C.H., et al. Uncertainty for Safe Utilization of Machine Learning in Medical Imaging, and Graphs in Biomedical Image Analysis. UNSURE GRAIL 2020 2020. Lecture Notes in Computer Science(), vol 12443. Springer, Cham. https://doi.org/10.1007/978-3-030-60365-6_5
Download citation
DOI: https://doi.org/10.1007/978-3-030-60365-6_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-60364-9
Online ISBN: 978-3-030-60365-6
eBook Packages: Computer ScienceComputer Science (R0)