Abstract
Many segmentation tasks for biomedical images can be modeled as the minimization of an energy function and solved by a class of max-flow and min-cut optimization algorithms. However, the segmentation accuracy is sensitive to the contrasting of semantic features of different segmenting objects, as the traditional energy function usually uses hand-crafted features in their energy functions. To address these limitations, we propose to incorporate end-to-end trainable neural network features into the energy functions. Our deep neural network features are extracted from the down-sampling and up-sampling layers with skip-connections of a U-net. In the inference stage, the learned features are fed into the energy functions. And the segmentations are solved in a primal-dual form by ADMM solvers. In the training stage, we train our neural networks by optimizing the energy function in the primal form with regularizations on the min-cut and flow-conservation functions, which are derived from the optimal conditions in the dual form. We evaluate our methods, both qualitatively and quantitatively, in a brain tumor segmentation task. As the energy minimization model achieves a balance on sensitivity and smooth boundaries, we would show how our segmentation contours evolve actively through iterations as ensemble references for doctor diagnosis.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Chan, T.F., Esedoglu, S., Nikolova, M.: Algorithms for finding global minimizers of image segmentation and denoising models. SIAM J. Appl. Math. 66(5), 1632–1648 (2006)
Chan, T.F., Vese, L.A.: Active contours without edges. IEEE Trans. Image Process. 10(2), 266–277 (2001)
Chen, L., Wu, Y., DSouza, A.M., Abidin, A.Z., Wismüller, A., Xu, C.: MRI tumor segmentation with densely connected 3D CNN. In: Medical Imaging 2018: Image Processing, vol. 10574, p. 105741F. International Society for Optics and Photonics (2018)
Cohen, L.D.: On active contour models and balloons. CVGIP Image Underst. 53(2), 211–218 (1991)
Dey, R., Hong, Y.: CompNet: complementary segmentation network for brain MRI extraction. In: Frangi, A.F., Schnabel, J.A., Davatzikos, C., Alberola-López, C., Fichtinger, G. (eds.) MICCAI 2018. LNCS, vol. 11072, pp. 628–636. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-00931-1_72
Ganaye, P.-A., Sdika, M., Benoit-Cattin, H.: Semi-supervised learning for segmentation under semantic constraint. In: Frangi, A.F., Schnabel, J.A., Davatzikos, C., Alberola-López, C., Fichtinger, G. (eds.) MICCAI 2018. LNCS, vol. 11072, pp. 595–602. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-00931-1_68
Greig, D.M., Porteous, B.T., Seheult, A.H.: Exact maximum a posteriori estimation for binary images. J. Roy. Stat. Soc.: Ser. B (Methodol.) 51(2), 271–279 (1989)
Kamnitsas, K., Chen, L., Ledig, C., Rueckert, D., Glocker, B.: Multi-scale 3D CNNs for segmentation of brain lesions in multi-modal MRI. In: Proceeding of Isles Challenge, MICCAI (2015)
Kamnitsas, K., et al.: Efficient multi-scale 3D CNN with fully connected CRF for accurate brain lesion segmentation. Med. Image Anal. 36, 61–78 (2017)
Karimaghaloo, Z., Arnold, D.L., Arbel, T.: Adaptive multi-level conditional random fields for detection and segmentation of small enhanced pathology in medical images. Med. Image Anal. 27, 17–30 (2016)
Kass, M., Witkin, A., Terzopoulos, D.: Snakes: active contour models. Int. J. Comput. Vis. 1(4), 321–331 (1988)
Le, T.H.N., Gummadi, R., Savvides, M.: Deep recurrent level set for segmenting brain tumors. In: Frangi, A.F., Schnabel, J.A., Davatzikos, C., Alberola-López, C., Fichtinger, G. (eds.) MICCAI 2018. LNCS, vol. 11072, pp. 646–653. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-00931-1_74
Mangasarian, O.L.: Nonlinear Programming. SIAM (1994)
Menze, B.H., et al.: The multimodal brain tumor image segmentation benchmark (BRATS). IEEE Trans. Med. Imaging 34(10), 1993–2024 (2014)
Qin, Y., et al.: Autofocus layer for semantic segmentation. In: Frangi, A.F., Schnabel, J.A., Davatzikos, C., Alberola-López, C., Fichtinger, G. (eds.) MICCAI 2018. LNCS, vol. 11072, pp. 603–611. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-00931-1_69
Spitzer, H., Kiwitz, K., Amunts, K., Harmeling, S., Dickscheid, T.: Improving cytoarchitectonic segmentation of human brain areas with self-supervised Siamese networks. In: Frangi, A.F., Schnabel, J.A., Davatzikos, C., Alberola-López, C., Fichtinger, G. (eds.) MICCAI 2018. LNCS, vol. 11072, pp. 663–671. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-00931-1_76
Yuan, J., Bae, E., Tai, X.-C.: A study on continuous max-flow and min-cut approaches. In: 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp. 2217–2224. IEEE (2010)
Zhou, C., Ding, C., Lu, Z., Wang, X., Tao, D.: One-pass multi-task convolutional neural networks for efficient brain tumor segmentation. In: Frangi, A.F., Schnabel, J.A., Davatzikos, C., Alberola-López, C., Fichtinger, G. (eds.) MICCAI 2018. LNCS, vol. 11072, pp. 637–645. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-00931-1_73
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Shen, Y., Ji, Z., Gao, M. (2020). An End-to-End Learnable Flow Regularized Model for Brain Tumor Segmentation. In: Liu, M., Yan, P., Lian, C., Cao, X. (eds) Machine Learning in Medical Imaging. MLMI 2020. Lecture Notes in Computer Science(), vol 12436. Springer, Cham. https://doi.org/10.1007/978-3-030-59861-7_54
Download citation
DOI: https://doi.org/10.1007/978-3-030-59861-7_54
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-59860-0
Online ISBN: 978-3-030-59861-7
eBook Packages: Computer ScienceComputer Science (R0)