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Propagation and Attribution of Uncertainty in Medical Imaging Pipelines

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Uncertainty for Safe Utilization of Machine Learning in Medical Imaging (UNSURE 2023)

Abstract

Uncertainty estimation, which provides a means of building explainable neural networks for medical imaging applications, have mostly been studied for single deep learning models that focus on a specific task. In this paper, we propose a method to propagate uncertainty through cascades of deep learning models in medical imaging pipelines. This allows us to aggregate the uncertainty in later stages of the pipeline and to obtain a joint uncertainty measure for the predictions of later models. Additionally, we can separately report contributions of the aleatoric, data-based, uncertainty of every component in the pipeline. We demonstrate the utility of our method on a realistic imaging pipeline that reconstructs undersampled brain and knee magnetic resonance (MR) images and subsequently predicts quantitative information from the images, such as the brain volume, or knee side or patient’s sex. We quantitatively show that the propagated uncertainty is correlated with input uncertainty and compare the proportions of contributions of pipeline stages to the joint uncertainty measure.

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References

  1. Abdelaziz, A.H., Watanabe, S., Hershey, J.R., Vincent, E., Kolossa, D.: Uncertainty propagation through deep neural networks. In: Annual Conference of the International Speech Communication Association, pp. 3561–3565 (2015)

    Google Scholar 

  2. Astudillo, R.F., Da Silva Neto, J.P.: Propagation of uncertainty through multilayer perceptrons for robust automatic speech recognition. Annual Conference of the International Speech Communication Association pp. 461–464 (2011)

    Google Scholar 

  3. Bibi, A., Alfadly, M., Ghanem, B.: Analytic expressions for probabilistic moments of PL-DNN with gaussian input. In: Computer Society Conference on Computer Vision and Pattern Recognition, pp. 9099–9107 (2018)

    Google Scholar 

  4. Blundell, C., Cornebise, J., Kavukcuoglu, K., Wierstra, D.: Weight uncertainty in neural network. In: International Conference on Machine Learning, pp. 1613–1622 (2015)

    Google Scholar 

  5. Dalca, A.V., Balakrishnan, G., Guttag, J., Sabuncu, M.R.: Unsupervised learning of probabilistic diffeomorphic registration for images and surfaces. Med. Image Anal. 57, 226–236 (2019)

    Article  Google Scholar 

  6. Feng, X., Li, T., Song, X., Zhu, H.: Bayesian scalar on image regression with nonignorable nonresponse. J. Am. Stat. Assoc. 115(532), 1574–1597 (2020)

    Article  MathSciNet  Google Scholar 

  7. Gal, Y., Ghahramani, Z.: Dropout as a Bayesian approximation: representing model uncertainty in deep learning. Int. Conf. Mach. Learn. 3, 1651–1660 (2016)

    Google Scholar 

  8. Gast, J., Roth, S.: Lightweight probabilistic deep networks. In: Computer Society Conference on Computer Vision and Pattern Recognition, pp. 3369–3378 (2018)

    Google Scholar 

  9. Ghosh, S., Delle Fave, F.M., Yedidia, J.: Assumed density filtering methods for learning Bayesian neural networks. In: Conference on Artificial Intelligence, pp. 1589–1595 (2016)

    Google Scholar 

  10. Ghoshal, B., Tucker, A., Sanghera, B., Lup Wong, W.: Estimating uncertainty in deep learning for reporting confidence to clinicians in medical image segmentation and diseases detection. Comput. Intell. 37(2), 701–734 (2021)

    Article  MathSciNet  Google Scholar 

  11. Jalal, A., Arvinte, M., Daras, G., Price, E., Dimakis, A.G., Tamir, J.: Robust compressed sensing MRI with deep generative priors. Adv. Neural. Inf. Process. Syst. 34, 14938–14954 (2021)

    Google Scholar 

  12. Ji, W., Ren, Z., Law, C.K.: Uncertainty propagation in deep neural network using active subspace. arXiv preprint (2019)

    Google Scholar 

  13. Ju, L., et al.: Improving medical images classification with label noise using dual-uncertainty estimation. Trans. Med. Imaging 41(6), 1533–1546 (2022)

    Article  Google Scholar 

  14. Kendall, A., Gal, Y.: What uncertainties do we need in Bayesian deep learning for computer vision? Neural Inf. Process. Syst. 30, 5575–5585 (2017)

    Google Scholar 

  15. Lakshminarayanan, B., Pritzel, A., Blundell, C.: Simple and scalable predictive uncertainty estimation using deep ensembles. Neural Inf. Process. Syst. 30, 1–12 (2017)

    Google Scholar 

  16. Laves, M.H., Ihler, S., Fast, J.F., Kahrs, L.A., Ortmaier, T.: Well-calibrated regression uncertainty in medical imaging with deep learning. In: Medical Imaging with Deep Learning, pp. 393–412 (2020)

    Google Scholar 

  17. Mehta, R., et al.: Propagating uncertainty across cascaded medical imaging tasks for improved deep learning inference. Trans. Med. Imaging. 41, 360–373 (2021)

    Article  Google Scholar 

  18. Mehta, R., Christinck, T., Nair, T., Lemaitre, P., Arnold, D., Arbel, T.: Propagating uncertainty across cascaded medical imaging tasks for improved deep learning inference. UNSURE/CLIP Conjunct. MICCAI 2019, 23–32 (2019)

    Google Scholar 

  19. Monteiro, M., et al.: Stochastic segmentation networks: modelling spatially correlated aleatoric uncertainty. Neural Inf. Process. Syst. 33, 12756–12767 (2020)

    Google Scholar 

  20. Narnhofer, D., Effland, A., Kobler, E., Hammernik, K., Knoll, F., Pock, T.: Bayesian uncertainty estimation of learned variational MRI reconstruction. Trans. Med. Imaging 41(2), 279–291 (2022)

    Article  Google Scholar 

  21. Nix, D.A., Weigend, A.S.: Estimating the mean and variance of the target probability distribution. Int. Conf. Neural Netw. 1, 55–60 (1994)

    Google Scholar 

  22. Novoa, J., Fredes, J., Poblete, V., Yoma, N.B.: Uncertainty weighting and propagation in DNN-HMM-based speech recognition (2018)

    Google Scholar 

  23. Ozdemir, O., Woodward, B., Berlin, A.A.: Propagating uncertainty in multi-stage Bayesian convolutional neural networks with application to pulmonary nodule detection. arXiv preprint (2017)

    Google Scholar 

  24. Petersen, R.C., et al.: Alzheimer’s disease neuroimaging initiative (ADNI): clinical characterization. Neurology 74(3), 201–209 (2010)

    Article  Google Scholar 

  25. Postels, J., Ferroni, F., Coskun, H., Navab, N., Tombari, F.: Sampling-free epistemic uncertainty estimation using approximated variance propagation. In: International Conference on Computer Vision, pp. 2931–2940 (2019)

    Google Scholar 

  26. Schlemper, J., Caballero, J., Hajnal, J.V., Price, A.N., Rueckert, D.: A deep cascade of convolutional neural networks for dynamic MR image reconstruction. Trans. Med. Imaging 25(2), 491–503 (2018)

    Article  Google Scholar 

  27. Schlemper, J., et al.: Bayesian deep learning for accelerated MR image reconstruction. In: Knoll, F., Maier, A., Rueckert, D. (eds.) MLMIR 2018. LNCS, vol. 11074, pp. 64–71. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-00129-2_8

    Chapter  Google Scholar 

  28. Shaw, R., Sudre, C.H., Ourselin, S., Cardoso, M.J.: A heteroscedastic uncertainty model for decoupling sources of MRI image quality. In: Medical Imaging with Deep Learning, pp. 733–742 (2020)

    Google Scholar 

  29. Tanno, R., et al.: Bayesian image quality transfer with CNNs: Exploring uncertainty in dMRI super-resolution. CoRR (2017)

    Google Scholar 

  30. Titensky, J.S., Jananthan, H., Kepner, J.: Uncertainty propagation in deep neural networks using extended Kalman filtering. In: MIT Undergraduate Research Technology Conference (2018)

    Google Scholar 

  31. Tschandl, P., et al.: Human-computer collaboration for skin cancer recognition. Nat. Med. 26(8), 1229–1234 (2020)

    Article  Google Scholar 

  32. Wang, G., Li, W., Aertsen, M., Deprest, J., Ourselin, S., Vercauteren, T.: Aleatoric uncertainty estimation with test-time augmentation for medical image segmentation with convolutional neural networks. Neurocomputing 338, 34–45 (2019)

    Article  Google Scholar 

  33. Zbontar, J., et al.: fastMRI: An open dataset and benchmarks for accelerated MRI. arXiv preprint (2018)

    Google Scholar 

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Acknowledgments

This research has been funded by the German Federal Ministry of Education and Research under project “NUM 2.0” (FKZ: 01KX2121). Data collection and sharing for this project was funded by the Alzheimer’s Disease Neuroimaging Initiative (ADNI) (National Institutes of Health Grant U01 AG024904) and DOD ADNI (Department of Defense award number W81XWH-12-2-0012).

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Correspondence to Leonhard F. Feiner .

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Feiner, L.F. et al. (2023). Propagation and Attribution of Uncertainty in Medical Imaging Pipelines. In: Sudre, C.H., Baumgartner, C.F., Dalca, A., Mehta, R., Qin, C., Wells, W.M. (eds) Uncertainty for Safe Utilization of Machine Learning in Medical Imaging. UNSURE 2023. Lecture Notes in Computer Science, vol 14291. Springer, Cham. https://doi.org/10.1007/978-3-031-44336-7_1

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  • DOI: https://doi.org/10.1007/978-3-031-44336-7_1

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