Abstract
In this paper, we present a novel flux-based method to robustly identify the vasculature structure in the angiography, where the curvilinear geometry is delineated by the higher-order tensor computed in the spherical frequency domain. We first modify the vesselness measurement derived from the oriented flux and introduce an antisymmetry measurement to generate the curvilinear responses. We then extend the responses to the cylindrical model and fit them into spherical harmonics transform to perform high-order tensor analysis, in which fiber orientation distribution function is utilized. A graphical framework based on the random walker is applied for vascular segmentation. It is experimentally demonstrated that the proposed method can achieve accurate and stable segmentation performance with various noise levels, demonstrating the proposed method can deliver reliable curvilinear structure responses.
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References
Zheng, Y., Tek, H., Funka-Lea, G.: Robust and accurate coronary artery centerline extraction in CTA by combining model-driven and data-driven approaches. In: Mori, K., Sakuma, I., Sato, Y., Barillot, C., Navab, N. (eds.) MICCAI 2013. LNCS, vol. 8151, pp. 74–81. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40760-4_10
Aylward, S.R., Bullitt, E.: Initialization, noise, singularities, and scale in height ridge traversal for tubular object centerline extraction. IEEE Trans. Med. Imaging 21(2), 61–75 (2002)
Cetin, S., Unal, G.: A higher-order tensor vessel tractography for segmentation of vascular structures. IEEE Trans. Med. Imaging 34(10), 2172–2185 (2015)
Descoteaux, M., Angelino, E., Fitzgibbons, S., Deriche, R.: Apparent diffusion coefficients from high angular resolution diffusion imaging: estimation and applications. Magn. Reson. Med. 56(2), 395–410 (2006)
Descoteaux, M., Deriche, R., Knosche, T.R., Anwander, A.: Deterministic and probabilistic tractography based on complex fibre orientation distributions. IEEE Trans. Med. Imaging 28(2), 269–286 (2009)
Frangi, A.F., Niessen, W.J., Vincken, K.L., Viergever, M.A.: Multiscale vessel enhancement filtering. In: Wells, W.M., Colchester, A., Delp, S. (eds.) MICCAI 1998. LNCS, vol. 1496, pp. 130–137. Springer, Heidelberg (1998). https://doi.org/10.1007/BFb0056195
Grady, L.: Random walks for image segmentation. IEEE Transaction on Pattern Analysis and Machine Intelligence 28(11), 1768–1783 (2006)
Hamarneh, G., Jassi, P.: Vascusynth: simulating vascular trees for generating volumetric image data with ground-truth segmentation and tree analysis. Compute. Med. Imaging Graph. 34(8), 605–616 (2010)
Jassi, P., Hamarneh, G.: Vascusynth: vascular tree synthesis software. Insight J. (2011)
Law, M.W.K., Chung, A.C.S.: Three dimensional curvilinear structure detection using optimally oriented flux. In: Forsyth, D., Torr, P., Zisserman, A. (eds.) ECCV 2008. LNCS, vol. 5305, pp. 368–382. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-88693-8_27
Merveille, O., Talbot, H., Najman, L., Passat, N.: Curvilinear structure analysis by ranking the orientation responses of path operators. IEEE Trans. Pattern Anal. Mach. Intell. 40(2), 304–317 (2018)
Moreno, R., Smedby, Ö.: Vesselness estimation through higher-order orientation tensors. In: 2016 IEEE 13th International Symposium on Biomedical Imaging (ISBI), pp. 1139–1142. IEEE (2016)
Moriconi, S., Zuluaga, M.A., Jäger, H.R., Nachev, P., Ourselin, S., Cardoso, M.J.: VTrails: inferring vessels with geodesic connectivity trees. In: Niethammer, M., Styner, M., Aylward, S., Zhu, H., Oguz, I., Yap, P.-T., Shen, D. (eds.) IPMI 2017. LNCS, vol. 10265, pp. 672–684. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-59050-9_53
Schultz, T.: Towards resolving fiber crossings with higher order tensor inpainting. In: Laidlaw, D., Vilanova, A. (eds.) New Developments in the Visualization and Processing of Tensor Fields. MATHVISUAL. Springer, Heidelberg (2012)
Vasilevskiy, A., Siddiqi, K.: Flux maximizing geometric flows. IEEE Trans. Pattern Anal. Mach. Intelligence 24(12), 1565–1578 (2002)
Wang, J., Chung, A.C.S.: High-order oriented cylindrical flux for curvilinear structure detection and vessel segmentation. In: Chung, A.C.S., Gee, J.C., Yushkevich, P.A., Bao, S. (eds.) IPMI 2019. LNCS, vol. 11492, pp. 479–491. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-20351-1_37
Zhang, Q., Chung, A.C.S.: 3D vessel segmentation using random walker with oriented flux analysis and direction coherence. In: Zheng, G., Liao, H., Jannin, P., Cattin, P., Lee, S.-L. (eds.) MIAR 2016. LNCS, vol. 9805, pp. 281–291. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-43775-0_25
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Wang, J., Chung, A.C.S. (2020). Higher-Order Flux with Spherical Harmonics Transform for Vascular Analysis. In: Martel, A.L., et al. Medical Image Computing and Computer Assisted Intervention – MICCAI 2020. MICCAI 2020. Lecture Notes in Computer Science(), vol 12266. Springer, Cham. https://doi.org/10.1007/978-3-030-59725-2_6
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DOI: https://doi.org/10.1007/978-3-030-59725-2_6
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