Abstract
Porous media segmentation is a nontrivial and often quite inaccurate process, due to the highly irregular structure of the segmentation phases and the huge interaction among them. In this paper we perform a 2-class segmentation of a gray-scale 3D image under the restriction that the number of voxels within the phases are a priori fixed. Two parallel algorithms, based on the graph 2-Laplacian model [1] are proposed, implemented, and numerically tested.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Kang, S.H., Shafei, B., Steidl, G.: Supervised and transductive multi-class segmentation using \(p\)-Laplacians and RKHS methods. J. Vis. Commun. Image Represent. 25(5), 1136–1148 (2014)
Shi, J., Szalam, J.: Normalized cuts and image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 22(8), 888–905 (2000)
von Luxburg, U.: A tutorial on spectral clustering. Stat. Comput. 17(4), 395–416 (2007)
Law, N.Y., Lee, H.K., Ng, M.K., Yip, A.M.: A semisupervised segmentation model for collections of images. IEEE Trans. Image Process. 21(6), 2955–2968 (2012)
Natarajan, B.K.: Sparse approximate solutions to linear systems. SIAM J. Comput. 24(2), 227–234 (1995)
Amghibech, S.: Eigenvalues of the discrete \(p\)-Laplacian for graphs. Ars Comb. 67, 283–302 (2003)
Bühler, T., Hein, M.: Spectral clustering based on the graph \(p\)-Laplacian. In: Proceedings of the 26th Annual International Conference on Machine Learning, pp. 81–88 (2009)
Axelsson, A.: Iterative Solution Methods. Cambridge University Press, Cambridge (1994)
Beller, G., Burkhart, M., Felsenberg, D., Gowin, W., Hege, H.-C., Koller, B., Prohaska, S., Saparin, P., Thomsen, J.: Vertebral Body Data Set ESA29-99-L3. http://bone3d.zib.de/data/2005/ESA29-99-L3/
Teuber, T., Steidl, G., Chan, R.H.: Minimization and parameter estimation for seminorm regularization models with I-divergence constraints. Inverse Prob. 29, 1–28 (2013)
Dagum, L., Menon, R.: OpenMP: an industry-standard API for shared-memory programming. IEEE Comput. Sci. Eng. 5(1), 46–55 (1998)
Acknowledgements
The research is partly supported by the project AComIn “Advanced Computing for Innovation”, grant 316087, funded by the FP7 Capacity Program.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Georgiev, I., Harizanov, S., Vutov, Y. (2015). Supervised 2-Phase Segmentation of Porous Media with Known Porosity. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2015. Lecture Notes in Computer Science(), vol 9374. Springer, Cham. https://doi.org/10.1007/978-3-319-26520-9_38
Download citation
DOI: https://doi.org/10.1007/978-3-319-26520-9_38
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-26519-3
Online ISBN: 978-3-319-26520-9
eBook Packages: Computer ScienceComputer Science (R0)