Abstract
Despite recent progress of deep learning-based medical image segmentation techniques, fully automatic results often fail to meet clinically acceptable accuracy, especially when topological constraints should be observed, e.g., closed surfaces. Although modern image segmentation methods show promising results when evaluated based on conventional metrics such as the Dice score or Intersection-over-Union, these metrics do not reflect the correctness of a segmentation in terms of a required topological genus. Existing approaches estimate and constrain the topological structure via persistent homology (PH). However, these methods are not computationally efficient as calculating PH is not differentiable. To overcome this problem, we propose a novel approach for topological constraints based on the multi-scale Euler Characteristic (EC). To mitigate computational complexity, we propose a fast formulation for the EC that can inform the learning process of arbitrary segmentation networks via topological violation maps. Topological performance is further facilitated through a corrective convolutional network block. Our experiments on two datasets show that our method can significantly improve topological correctness.
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References
Byrne, N., Clough, J.R., Valverde, I., Montana, G., King, A.P.: A persistent homology-based topological loss for CNN-based multiclass segmentation of CMR. IEEE Trans. Med. Imaging 42(1), 3–14 (2022)
Clough, J.R., Byrne, N., Oksuz, I., Zimmer, V.A., Schnabel, J.A., King, A.P.: A topological loss function for deep-learning based image segmentation using persistent homology. IEEE Trans. Pattern Anal. Mach. Intell. 44(12), 8766–8778 (2020)
Clough, J.R., Oksuz, I., Byrne, N., Schnabel, J.A., King, A.P.: Explicit topological priors for deep-learning based image segmentation using persistent homology. In: Chung, A.C.S., Gee, J.C., Yushkevich, P.A., Bao, S. (eds.) IPMI 2019. LNCS, vol. 11492, pp. 16–28. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-20351-1_2
Dale, A.M., Fischl, B., Sereno, M.I.: Cortical surface-based analysis: I. segmentation and surface reconstruction. Neuroimage 9(2), 179–194 (1999)
de Dumast, P., Kebiri, H., Atat, C., Dunet, V., Koob, M., Cuadra, M.B.: Segmentation of the cortical plate in fetal brain MRI with a topological loss. In: Sudre, C.H., et al. (eds.) UNSURE/PIPPI -2021. LNCS, vol. 12959, pp. 200–209. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-87735-4_19
Funke, J., et al.: Large scale image segmentation with structured loss based deep learning for connectome reconstruction. IEEE Trans. Pattern Anal. Mach. Intell. 41(7), 1669–1680 (2018)
Gray, S.B.: Local properties of binary images in two dimensions. IEEE Trans. Comput. 100(5), 551–561 (1971)
Hu, X.: Structure-aware image segmentation with homotopy warping. Adv. Neural. Inf. Process. Syst. 35, 24046–24059 (2022)
Hu, X., Li, F., Samaras, D., Chen, C.: Topology-preserving deep image segmentation. In: Advances in Neural Information Processing Systems 32 (2019)
Kainz, B., et al.: Fast volume reconstruction from motion corrupted stacks of 2D slices. IEEE Trans. Med. Imaging 34(9), 1901–1913 (2015)
Kaji, S., Sudo, T., Ahara, K.: Cubical Ripser: software for computing persistent homology of image and volume data. arXiv:2005.12692 (2020)
Kervadec, H., Bouchtiba, J., Desrosiers, C., Granger, E., Dolz, J., Ayed, I.B.: Boundary loss for highly unbalanced segmentation. In: International Conference on Medical Imaging with Deep Learning, pp. 285–296. PMLR (2019)
Kuklisova-Murgasova, M., Quaghebeur, G., Rutherford, M.A., Hajnal, J.V., Schnabel, J.A.: Reconstruction of fetal brain MRI with intensity matching and complete outlier removal. Med. Image Anal. 16(8), 1550–1564 (2012)
Lee, M.C.H., Petersen, K., Pawlowski, N., Glocker, B., Schaap, M.: Tetris: Template transformer networks for image segmentation with shape priors. IEEE Trans. Med. Imaging 38(11), 2596–2606 (2019)
Li, L., et al.: Fetal cortex segmentation with topology and thickness loss constraints. In: Baxter, J.S.H., et al. (eds.) Ethical and Philosophical Issues in Medical Imaging, Multimodal Learning and Fusion Across Scales for Clinical Decision Support, and Topological Data Analysis for Biomedical Imaging. EPIMI ML-CDS TDA4BiomedicalImaging 2022. LNCS, vol. 13755. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-23223-7_11
Maier-Hein, L., Menze, B., et al.: Metrics reloaded: pitfalls and recommendations for image analysis validation. arXiv. org (2206.01653) (2022)
Makropoulos, A.: The developing human connectome project: a minimal processing pipeline for neonatal cortical surface reconstruction. Neuroimage 173, 88–112 (2018)
Maria, C., Boissonnat, J.-D., Glisse, M., Yvinec, M.: The Gudhi library: simplicial complexes and persistent homology. In: Hong, H., Yap, C. (eds.) ICMS 2014. LNCS, vol. 8592, pp. 167–174. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-44199-2_28
McInerney, T., Terzopoulos, D.: Deformable models in medical image analysis: a survey. Med. Image Anal. 1(2), 91–108 (1996)
Oktay, O., et al.: Anatomically constrained neural networks (acnns): application to cardiac image enhancement and segmentation. IEEE Trans. Med. Imag. 37(2), 384–395 (2017)
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). https://doi.org/10.1007/978-3-319-24574-4_28
Shit, S., et al.: clDice-a novel topology-preserving loss function for tubular structure segmentation. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 16560–16569 (2021)
Stucki, N., Paetzold, J.C., Shit, S., Menze, B., Bauer, U.: Topologically faithful image segmentation via induced matching of persistence barcodes. arXiv preprint arXiv:2211.15272 (2022)
Stucki, N., Paetzold, J.C., Shit, S., Menze, B., Bauer, U.: Topologically faithful image segmentation via induced matching of persistence barcodes. In: International Conference on Machine Learning, pp. 32698–32727. PMLR (2023)
Wilcoxon, F.: Individual comparisons by ranking methods. In: Kotz, S., Johnson, N.L. (eds.) Breakthroughs in Statistics. Springer Series in Statistics. Springer, NY (1992). https://doi.org/10.1007/978-1-4612-4380-9_16
Yao, B., He, L., Kang, S., Chao, Y., Zhao, X.: A novel bit-quad-based Euler number computing algorithm. Springerplus 4, 1–16 (2015)
Acknowledgements
This project is supported by Lee Family Scholarship from Imperial College London. HPC resources are provided by the Erlangen National High Performance Computing Center (NHR@FAU) of the Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) under the NHR project b143dc. NHR funding is provided by federal and Bavarian state authorities. NHR@FAU hardware is partially funded by the German Research Foundation (DFG) - 440719683. Support was also received by the ERC - project MIA-NORMAL 101083647 and DFG KA 5801/2-1, INST 90/1351-1.
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Li, L. et al. (2023). Robust Segmentation via Topology Violation Detection and Feature Synthesis. In: Greenspan, H., et al. Medical Image Computing and Computer Assisted Intervention – MICCAI 2023. MICCAI 2023. Lecture Notes in Computer Science, vol 14223. Springer, Cham. https://doi.org/10.1007/978-3-031-43901-8_7
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