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Tversky Loss Function for Image Segmentation Using 3D Fully Convolutional Deep Networks

  • Seyed Sadegh Mohseni SalehiEmail author
  • Deniz Erdogmus
  • Ali Gholipour
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10541)

Abstract

Fully convolutional deep neural networks carry out excellent potential for fast and accurate image segmentation. One of the main challenges in training these networks is data imbalance, which is particularly problematic in medical imaging applications such as lesion segmentation where the number of lesion voxels is often much lower than the number of non-lesion voxels. Training with unbalanced data can lead to predictions that are severely biased towards high precision but low recall (sensitivity), which is undesired especially in medical applications where false negatives are much less tolerable than false positives. Several methods have been proposed to deal with this problem including balanced sampling, two step training, sample re-weighting, and similarity loss functions. In this paper, we propose a generalized loss function based on the Tversky index to address the issue of data imbalance and achieve much better trade-off between precision and recall in training 3D fully convolutional deep neural networks. Experimental results in multiple sclerosis lesion segmentation on magnetic resonance images show improved \(F_2\) score, Dice coefficient, and the area under the precision-recall curve in test data. Based on these results we suggest Tversky loss function as a generalized framework to effectively train deep neural networks.

Notes

Acknowledgements

This work was in part supported by the National Institutes of Health (NIH) under grant R01 EB018988. The content of this work is solely the responsibility of the authors and does not necessarily represent the official views of the NIH.

Supplementary material

454062_1_En_44_MOESM1_ESM.pdf (84 kb)
Supplementary material 1 (pdf 84 KB)

References

  1. 1.
    Boyd, K., Eng, K.H., Page, C.D.: Area under the precision-recall curve: point estimates and confidence intervals. In: Blockeel, H., Kersting, K., Nijssen, S., Železný, F. (eds.) ECML PKDD 2013. LNCS, vol. 8190, pp. 451–466. Springer, Heidelberg (2013). doi: 10.1007/978-3-642-40994-3_29 CrossRefGoogle Scholar
  2. 2.
    Brosch, T., Yoo, Y., Tang, L.Y.W., Li, D.K.B., Traboulsee, A., Tam, R.: Deep convolutional encoder networks for multiple sclerosis lesion segmentation. In: Navab, N., Hornegger, J., Wells, W.M., Frangi, A.F. (eds.) MICCAI 2015. LNCS, vol. 9351, pp. 3–11. Springer, Cham (2015). doi: 10.1007/978-3-319-24574-4_1 CrossRefGoogle Scholar
  3. 3.
    Chen, H., Dou, Q., Yu, L., Qin, J., Heng, P.A.: VoxResNet: deep voxelwise residual networks for brain segmentation from 3D MR images. NeuroImage (2017)Google Scholar
  4. 4.
    Çiçek, Ö., Abdulkadir, A., Lienkamp, S.S., Brox, T., Ronneberger, O.: 3D U-Net: learning dense volumetric segmentation from sparse annotation. In: Ourselin, S., Joskowicz, L., Sabuncu, M.R., Unal, G., Wells, W. (eds.) MICCAI 2016. LNCS, vol. 9901, pp. 424–432. Springer, Cham (2016). doi: 10.1007/978-3-319-46723-8_49 CrossRefGoogle Scholar
  5. 5.
    Cireşan, D.C., Giusti, A., Gambardella, L.M., Schmidhuber, J.: Mitosis detection in breast cancer histology images with deep neural networks. In: Mori, K., Sakuma, I., Sato, Y., Barillot, C., Navab, N. (eds.) MICCAI 2013. LNCS, vol. 8150, pp. 411–418. Springer, Heidelberg (2013). doi: 10.1007/978-3-642-40763-5_51 CrossRefGoogle Scholar
  6. 6.
    Commowick, O., Cervenansky, F., Ameli, R.: MSSEG challenge proceedings: multiple sclerosis lesions segmentation challenge using a data management and processing infrastructure (2016)Google Scholar
  7. 7.
    Davis, J., Goadrich, M.: The relationship between precision-recall and ROC curves. In: Proceedings of the 23rd International Conference on Machine Learning, pp. 233–240. ACM (2006)Google Scholar
  8. 8.
    Fawcett, T.: An introduction to ROC analysis. Pattern Recogn. Lett. 27(8), 861–874 (2006)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Havaei, M., Davy, A., Warde-Farley, D., Biard, A., Courville, A., Bengio, Y., Pal, C., Jodoin, P.M., Larochelle, H.: Brain tumor segmentation with deep neural networks. Med. Image Anal. 35, 18–31 (2017)CrossRefGoogle Scholar
  10. 10.
    Kamnitsas, K., Ledig, C., Newcombe, V., Simpson, J., Kane, A., Menon, D., Rueckert, D., Glocker, B.: Efficient multi-scale 3D CNN with fully connected CRF for accurate brain lesion segmentation. Med. Image Anal. 36, 61–78 (2017)CrossRefGoogle Scholar
  11. 11.
    Kingma, D., Ba, J.: Adam: a method for stochastic optimization. arXiv preprint arXiv:1412.6980 (2014)
  12. 12.
    Long, J., Shelhamer, E., Darrell, T.: Fully convolutional networks for semantic segmentation. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 3431–3440 (2015)Google Scholar
  13. 13.
    Milletari, F., Navab, N., Ahmadi, S.A.: V-net: fully convolutional neural networks for volumetric medical image segmentation. In: 2016 Fourth International Conference on 3D Vision (3DV), pp. 565–571. IEEE (2016)Google Scholar
  14. 14.
    Moeskops, P., Viergever, M.A., Mendrik, A.M., de Vries, L.S., Benders, M.J., Išgum, I.: Automatic segmentation of MR brain images with a convolutional neural network. IEEE Trans. Med. Imaging 35(5), 1252–1261 (2016)CrossRefGoogle Scholar
  15. 15.
    Pereira, S., Pinto, A., Alves, V., Silva, C.A.: Brain tumor segmentation using convolutional neural networks in MRI images. IEEE Trans. Med. Imaging 35(5), 1240–1251 (2016)CrossRefGoogle Scholar
  16. 16.
    Ronneberger, O., Fischer, P., Brox, T.: U-Net: convolutional networks for biomedical image segmentation. In: Navab, N., Hornegger, J., Wells, W.M., Frangi, A.F. (eds.) MICCAI 2015. LNCS, vol. 9351, pp. 234–241. Springer, Cham (2015). doi: 10.1007/978-3-319-24574-4_28 CrossRefGoogle Scholar
  17. 17.
    Salehi, S.S.M., Erdogmus, D., Gholipour, A.: Auto-context convolutional neural network (Auto-Net) for brain extraction in magnetic resonance imaging. IEEE Trans. Med. Imaging (2017)Google Scholar
  18. 18.
    Shelhamer, E., Long, J., Darrell, T.: Fully convolutional networks for semantic segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 39(4), 640–651 (2017)CrossRefGoogle Scholar
  19. 19.
    Tversky, A.: Features of similarity. Psychol. Rev. 84(4), 327 (1977)CrossRefGoogle Scholar
  20. 20.
    Valverde, S., Cabezas, M., Roura, E., González-Villà, S., Pareto, D., Vilanova, J.C., Ramió-Torrentà, L., Rovira, À., Oliver, A., Lladó, X.: Improving automated multiple sclerosis lesion segmentation with a cascaded 3D convolutional neural network approach. NeuroImage 155, 159–168 (2017)CrossRefGoogle Scholar
  21. 21.
    Wachinger, C., Reuter, M., Klein, T.: DeepNAT: deep convolutional neural network for segmenting neuroanatomy. NeuroImage (2017)Google Scholar
  22. 22.
    Zhang, W., Li, R., Deng, H., Wang, L., Lin, W., Ji, S., Shen, D.: Deep convolutional neural networks for multi-modality isointense infant brain image segmentation. NeuroImage 108, 214–224 (2015)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Seyed Sadegh Mohseni Salehi
    • 1
    • 2
    Email author
  • Deniz Erdogmus
    • 1
  • Ali Gholipour
    • 2
  1. 1.Electrical and Computer Engineering DepartmentNortheastern UniversityBostonUSA
  2. 2.Radiology DepartmentBoston Children’s Hospital and Harvard Medical SchoolBostonUSA

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