Abstract
We propose a parameter efficient Bayesian layer for hierarchical convolutional Gaussian Processes that incorporates Gaussian Processes operating in Wasserstein-2 space to reliably propagate uncertainty. This directly replaces convolving Gaussian Processes with a distance-preserving affine operator on distributions. Our experiments on brain tissue-segmentation show that the resulting architecture approaches the performance of well-established deterministic segmentation algorithms (U-Net), which has never been achieved with previous hierarchical Gaussian Processes. Moreover, by applying the same segmentation model to out-of-distribution data (i.e., images with pathology such as brain tumors), we show that our uncertainty estimates result in out-of-distribution detection that outperforms the capabilities of previous Bayesian networks and reconstruction-based approaches that learn normative distributions.
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
References
Alfaro-Almagro, F., et al.: Image processing and quality control for the first 10,000 brain imaging datasets from UK Biobank. Neuroimage 166, 400–424 (2018)
van Amersfoort, J., Smith, L., Teh, Y.W., Gal, Y.: Simple and scalable epistemic uncertainty estimation using a single deep deterministic neural network. arXiv preprint arXiv:2003.02037 (2020)
Bakas, S., et al.: Advancing the cancer genome atlas Glioma MRI collections with expert segmentation labels and radiomic features. Sci. Data 4, 170117 (2017)
Blomqvist, K., Kaski, S., Heinonen, M.: Deep convolutional gaussian processes. arXiv preprint arXiv:1810.03052 (2018)
Chen, X., Pawlowski, N., Glocker, B., Konukoglu, E.: Unsupervised lesion detection with locally Gaussian approximation. In: Suk, H.-I., Liu, M., Yan, P., Lian, C. (eds.) MLMI 2019. LNCS, vol. 11861, pp. 355–363. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-32692-0_41
Franchi, G., Bursuc, A., Aldea, E., Dubuisson, S., Bloch, I.: One versus all for deep neural network incertitude (OVNNI) quantification. preprint arXiv:2006.00954 (2020)
Guo, C., Pleiss, G., Sun, Y., Weinberger, K.Q.: On calibration of modern neural networks. arXiv preprint arXiv:1706.04599 (2017)
Hensman, J., Fusi, N., Lawrence, N.D.: Gaussian processes for big data. arXiv preprint arXiv:1309.6835 (2013)
McClure, P., et al.: Knowing what you know in brain segmentation using Bayesian deep neural networks. Front. Neuroinform. 13, 67 (2019)
Monteiro, M., et al.: Stochastic segmentation networks: modelling spatially correlated aleatoric uncertainty. arXiv preprint arXiv:2006.06015 (2020)
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)
Padhy, S., Nado, Z., Ren, J., Liu, J., Snoek, J., Lakshminarayanan, B.: Revisiting One-vs-All classifiers for predictive uncertainty and out-of-distribution detection in neural networks. arXiv preprint arXiv:2007.05134 (2020)
Popescu, S., Sharp, D., Cole, J., Glocker, B.: Hierarchical Gaussian processes with Wasserstein-2 Kernels. arXiv preprint arXiv:2010.14877 (2020)
Wilson, A.G., Izmailov, P.: Bayesian deep learning and a probabilistic perspective of generalization. arXiv preprint arXiv:2002.08791 (2020)
Zhou, S.K., et al.: A review of deep learning in medical imaging: image traits, technology trends, case studies with progress highlights, and future promises. arXiv preprint arXiv:2008.09104 (2020)
Acknowledgements
SGP is funded by an EPSRC Centre for Doctoral Training studentship award to Imperial College London. KK is funded by the UKRI London Medical Imaging & Artificial Intelligence Centre for Value Based Healthcare.
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
© 2021 Springer Nature Switzerland AG
About this paper
Cite this paper
Popescu, S.G., Sharp, D.J., Cole, J.H., Kamnitsas, K., Glocker, B. (2021). Distributional Gaussian Process Layers for Outlier Detection in Image Segmentation. In: Feragen, A., Sommer, S., Schnabel, J., Nielsen, M. (eds) Information Processing in Medical Imaging. IPMI 2021. Lecture Notes in Computer Science(), vol 12729. Springer, Cham. https://doi.org/10.1007/978-3-030-78191-0_32
Download citation
DOI: https://doi.org/10.1007/978-3-030-78191-0_32
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-78190-3
Online ISBN: 978-3-030-78191-0
eBook Packages: Computer ScienceComputer Science (R0)