Application of Modified Subjective Surface Method to 3D Cell Membrane Image Segmentation
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Abstract
In this paper, we study $3$D cell membrane image segmentation where the segmented surface is reconstructed by the use of $3$D digital cell membrane image information and information that is obtained from thresholded $3$D image in a local domain. The segmentation method is based on evolution of surface that is governed by a nonlinear PDE, the modified subjective surface equation. A semi-implicit finite volume scheme was used for the numerical discretization of the proposed model. The method was applied to real data representing $3$D microscopy images of cell membrane within the zebrafish pectoral fin.
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How to Cite
Uba, M., Mikula, K., Krivá, Z., Hanh, N., Savy, T., Kardash, E., & Peyriéras, N.
(2020).
Application of Modified Subjective Surface Method to 3D Cell Membrane Image Segmentation.
Proceedings Of The Conference Algoritmy, , 51 - 60.
Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/1552/814
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References
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[8] K. Mikula and M. Remešı́ková, Finite volume schemes for the generalized subjective surface equation in image segmentation, Kybernetika, Vol. 45, No. 4 (2009) pp. 646-656.
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[11] A. Sarti, R. Malladi and J. A. Sethian, Subjective Surfaces: A Geometric Model for Boundary Completion, International Journal of Computer Vision, Vol. 46 Num. 3, pp. 201-221, 2002.
[12] M. O. Uba, K. Mikula, Z. Krivá, H. Nguyen, T. Savy, E. Kardash, N. Peyriéras, 3D Cell Image Segmentation by Modified Subjective Surface Method, Tatra Mountains Mathematical Publications, (2020) 75, 147-162. doi: 10.2478/tmmp-2020-0010.
[13] L. Vincent and P. Soille, Watersheds in Digital Spaces: an Efficient Algorithm Based on Immersion Simulations, IEEE Transactions on Pattern Analysis and Machine Intelligence, 13(6):583–598, 1991.
[14] C. Zanella, M. Campana, B. Rizzi, C. Melani, G.Sanguinetti, P. Bourgine, K. Mikula, N.Peyriéras, A.Sarti, Cells Segmentation from 3-D Confocal Images of Early Zebrafish Embryogenesis, IEEE Transactions on Image Processing, Vol.19, No.3 (2010) pp. 770-781.
[2] A. P. Dhawan, Image Segmentation, in Medical Image Analysis, IEEE, 2011, pp.229-264, doi:10.1002/9780470918548.ch10.
[3] L. C. Evans and J. Spruck, Motion of level sets by mean curvature I, J. Differential Geom., 33 (1991), 635–681. doi:10.4310/jdg/1214446559.
[4] A. X. Falcao, J. K. Udupa, S. Samarasekera, S. Sharma, B. E. Hirsch, and R. de Alencar Lofufo, User-steered image segmentation paradigms: Live-wire and live-lane, Graphics Models and Image Processing, 60(4):223–260, 1998.
[5] E. Faure, T. Savy, B. Rizzi, C. Melani, O. Drblı́ková, D. Fabregès, R. Špir, M. Hammons, R. Čunderlı́k, G. Recher, B. Lombardot, L. Duloquin, I. Colin, J. Kollár, S. Desnoulez, P. Affaticati, B. Maury, A. Boyreau, J. Nief, P. Calvat, P. Vernier, M. Frain, G. Lutfalla, Y. Kergosien, P. Suret, M. Remešı́ková, R. Doursat, A. Sarti, K. Mikula, N. Peyriéras, P. Bourgine, An algorithmic workflow for the automated processing of 3D+time microscopy imaging of developing organisms and reconstruction of their cell lineage, Nature Communications, 7 (2016), 8674.
[6] M. Kass, A.Witkin, and D. Terzopoulos, Snakes: active contour models, International Journal of Computer Vision, 1(4):321-331, 1988.
[7] K. Mikula, N. Peyriéras, M. Remešı́ková and O.Stašová Segmentation of 3D cell membrane images by PDE methods and its applications, Computers in Biology and Medicine, Vol. 41, No. 6 (2011) pp. 326-339.
[8] K. Mikula and M. Remešı́ková, Finite volume schemes for the generalized subjective surface equation in image segmentation, Kybernetika, Vol. 45, No. 4 (2009) pp. 646-656.
[9] P. Perona and J. Malik,Scale-space and edge detection using anisotropic diffusion, IEEE Transactions on Pattern Analysis and Machine Intelligence, 12 (1990), 629–639. doi:10.1109/34.56205.
[10] A. Sarti, R. Malladi and J. A. Sethian, Subjective Surfaces: A Method for Completing Missing Boundaries, PNAS, Vol. 12, Num. 97, pp. 6258-6263, 2000.
[11] A. Sarti, R. Malladi and J. A. Sethian, Subjective Surfaces: A Geometric Model for Boundary Completion, International Journal of Computer Vision, Vol. 46 Num. 3, pp. 201-221, 2002.
[12] M. O. Uba, K. Mikula, Z. Krivá, H. Nguyen, T. Savy, E. Kardash, N. Peyriéras, 3D Cell Image Segmentation by Modified Subjective Surface Method, Tatra Mountains Mathematical Publications, (2020) 75, 147-162. doi: 10.2478/tmmp-2020-0010.
[13] L. Vincent and P. Soille, Watersheds in Digital Spaces: an Efficient Algorithm Based on Immersion Simulations, IEEE Transactions on Pattern Analysis and Machine Intelligence, 13(6):583–598, 1991.
[14] C. Zanella, M. Campana, B. Rizzi, C. Melani, G.Sanguinetti, P. Bourgine, K. Mikula, N.Peyriéras, A.Sarti, Cells Segmentation from 3-D Confocal Images of Early Zebrafish Embryogenesis, IEEE Transactions on Image Processing, Vol.19, No.3 (2010) pp. 770-781.