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Optimal Topological Cycles and Their Application in Cardiac Trabeculae Restoration

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Book cover Information Processing in Medical Imaging (IPMI 2017)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 10265))

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Abstract

In cardiac image analysis, it is important yet challenging to reconstruct the trabeculae, namely, fine muscle columns whose ends are attached to the ventricular walls. To extract these fine structures, traditional image segmentation methods are insufficient. In this paper, we propose a novel method to jointly detect salient topological handles and compute the optimal representations of them. The detected handles are considered hypothetical trabeculae structures. They are further screened using a classifier and are then included in the final segmentation. We show in experiments the significance of our contribution compared with previous standard segmentation methods without topological priors, as well as with previous topological method in which non-optimal representations of topological handles are used.

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References

  1. Busaryev, O., Cabello, S., Chen, C., Dey, T.K., Wang, Y.: Annotating simplices with a homology basis and its applications. In: Fomin, F.V., Kaski, P. (eds.) SWAT 2012. LNCS, vol. 7357, pp. 189–200. Springer, Heidelberg (2012). doi:10.1007/978-3-642-31155-0_17

    Chapter  Google Scholar 

  2. Chen, C., Freedman, D.: Hardness results for homology localization. Discret. Comput. Geom. 45(3), 425–448 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  3. Chen, C., Freedman, D., Lampert, C.H.: Enforcing topological constraints in random field image segmentation. In: CVPR, pp. 2089–2096 (2011)

    Google Scholar 

  4. Chen, C., Kerber, M.: An output-sensitive algorithm for persistent homology. Comput. Geom. 46(4), 435–447 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  5. Cohen-Steiner, D., Edelsbrunner, H., Harer, J.: Stability of persistence diagrams. Discret. Comput. Geom. 37(1), 103–120 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  6. Dey, T.K., Fan, F., Wang, Y.: Computing topological persistence for simplicial maps. In: Proceedings of the Thirtieth Annual Symposium on Computational Geometry, p. 345. ACM (2014)

    Google Scholar 

  7. Edelsbrunner, H., Harer, J.: Computational Topology: An Introduction. American Mathematical Society, Providence (2010)

    MATH  Google Scholar 

  8. Ewing Jr., E.P.: Gross pathology of idiopathic cardiomyopathy – Wikipedia, the free encyclopedia (2016). Accessed 09 Dec 2016

    Google Scholar 

  9. Gao, M., Chen, C., Zhang, S., Qian, Z., Metaxas, D., Axel, L.: Segmenting the papillary muscles and the trabeculae from high resolution cardiac CT through Restoration of topological handles. In: Gee, J.C., Joshi, S., Pohl, K.M., Wells, W.M., Zöllei, L. (eds.) IPMI 2013. LNCS, vol. 7917, pp. 184–195. Springer, Heidelberg (2013). doi:10.1007/978-3-642-38868-2_16

    Chapter  Google Scholar 

  10. Kulp, S., Gao, M., Zhang, S., Qian, Z., Voros, S., Metaxas, D., Axel, L.: Using high resolution cardiac CT data to model and visualize patient-specific interactions between trabeculae and blood flow. In: Fichtinger, G., Martel, A., Peters, T. (eds.) MICCAI 2011. LNCS, vol. 6891, pp. 468–475. Springer, Heidelberg (2011). doi:10.1007/978-3-642-23623-5_59

    Chapter  Google Scholar 

  11. Li, Y., Ascoli, G., Mitra, P.P., Wang, Y.: Metrics for comparing neuronal tree shapes based on persistent homology. bioRxiv, p. 087551 (2016)

    Google Scholar 

  12. Munkres, J.R.: Elements of Algebraic Topology, vol. 2. Addison-Wesley, Menlo Park (1984)

    MATH  Google Scholar 

  13. Singh, N., Couture, H.D., Marron, J.S., Perou, C., Niethammer, M.: Topological descriptors of histology images. In: Wu, G., Zhang, D., Zhou, L. (eds.) MLMI 2014. LNCS, vol. 8679, pp. 231–239. Springer, Cham (2014). doi:10.1007/978-3-319-10581-9_29

    Google Scholar 

  14. Wong, E., Palande, S., Wang, B., Zielinski, B., Anderson, J., Fletcher, P.T.: Kernel partial least squares regression for relating functional brain network topology to clinical measures of behavior. In: 2016 IEEE 13th International Symposium on Biomedical Imaging (ISBI), pp. 1303–1306. IEEE (2016)

    Google Scholar 

  15. Yushkevich, P., Piven, J., Hazlett, H., Smith, R., Ho, S., Gee, J., Gerig, G.: User-guided 3D active contour segmentation of anatomical structures: significantly improved efficiency and reliability. Neuroimage 31(3), 1116–1128 (2006)

    Article  Google Scholar 

  16. Zhen, X., Zhang, H., Islam, A., Bhaduri, M., Chan, I., Li, S.: Direct and simultaneous estimation of cardiac four chamber volumes by multioutput sparse regression. Med. Image Anal. 36, 184–196 (2017)

    Article  Google Scholar 

  17. Zheng, Y., Barbu, A., Georgescu, B., Scheuering, M., Comaniciu, D.: Four-chamber heart modeling and automatic segmentation for 3D cardiac CT volumes using marginal space learning and steerable features. TMI 27(11), 1668–1681 (2008)

    Google Scholar 

  18. Zhu, S., Lee, T., Yuille, A.: Region competition: unifying snakes, region growing, energy/Bayes/MDL for multi-band image segmentation. In: ICCV, pp. 416–423, June 1995

    Google Scholar 

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Acknowledgment

The research of Chao Chen is partially supported by the grants NSF PSC-CUNY 69844-00 47.

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Correspondence to Chao Chen .

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Wu, P. et al. (2017). Optimal Topological Cycles and Their Application in Cardiac Trabeculae Restoration. In: Niethammer, M., et al. Information Processing in Medical Imaging. IPMI 2017. Lecture Notes in Computer Science(), vol 10265. Springer, Cham. https://doi.org/10.1007/978-3-319-59050-9_7

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  • DOI: https://doi.org/10.1007/978-3-319-59050-9_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-59049-3

  • Online ISBN: 978-3-319-59050-9

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