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.
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References
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
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
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)
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
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
Commowick, O., Cervenansky, F., Ameli, R.: MSSEG challenge proceedings: multiple sclerosis lesions segmentation challenge using a data management and processing infrastructure (2016)
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)
Fawcett, T.: An introduction to ROC analysis. Pattern Recogn. Lett. 27(8), 861–874 (2006)
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)
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)
Kingma, D., Ba, J.: Adam: a method for stochastic optimization. arXiv preprint arXiv:1412.6980 (2014)
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)
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)
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)
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)
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
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)
Shelhamer, E., Long, J., Darrell, T.: Fully convolutional networks for semantic segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 39(4), 640–651 (2017)
Tversky, A.: Features of similarity. Psychol. Rev. 84(4), 327 (1977)
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)
Wachinger, C., Reuter, M., Klein, T.: DeepNAT: deep convolutional neural network for segmenting neuroanatomy. NeuroImage (2017)
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)
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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.
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Salehi, S.S.M., Erdogmus, D., Gholipour, A. (2017). Tversky Loss Function for Image Segmentation Using 3D Fully Convolutional Deep Networks. In: Wang, Q., Shi, Y., Suk, HI., Suzuki, K. (eds) Machine Learning in Medical Imaging. MLMI 2017. Lecture Notes in Computer Science(), vol 10541. Springer, Cham. https://doi.org/10.1007/978-3-319-67389-9_44
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DOI: https://doi.org/10.1007/978-3-319-67389-9_44
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