Abstract
We present a method for 3D image segmentation based on the Lagrangian approach. The segmentation model is a 3D analogue of the geodesic active contour model [1] and it contains an additional tangential movement term that allows us to control the quality of the mesh during the evolution process. The model is discretized by the finite volume approach. Segmentation of zebrafish cell images is shown to illustrate the performance of the method.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Caselles, V., Kimmel, R., Sapiro, G.: Geodesic active contours. Int. J. Comput. Vision 22, 61–79 (1997)
Dziuk, G., Elliott, C.: Finite elements on evolving surfaces. IMA J. Numer. Anal. 27, 262–292 (2007)
Mantegazza, C.: Lecture Notes on Mean Curvature Flow. Springer, Berlin (2011)
Meyer, M., Desbrun, M., Schroeder, P., Barr, A.: Discrete differential geometry operators for triangulated 2manifolds. Vis. Math. III, 35–57 (2003)
Mikula, K., Peyrieras, N., Remesikova, M., Stasova, O.: Segmentation of 3d cell membrane images by pde methods and its applications. Comput. Biol. Med. 41(6), 326–339 (2011)
Mikula, K., Remesikova, M., Sarkoci, P., Sevcovic, D.: Surface evolution with tangential redistribution of points (2013) (submitted)
Acknowledgments
This work was supported by the grants APVV-0184-10 and VEGA 1/1137/12.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Mikula, K., Remešíková, M. (2014). 3D Lagrangian Segmentation with Simultaneous Mesh Adjustment. In: Fuhrmann, J., Ohlberger, M., Rohde, C. (eds) Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems. Springer Proceedings in Mathematics & Statistics, vol 78. Springer, Cham. https://doi.org/10.1007/978-3-319-05591-6_68
Download citation
DOI: https://doi.org/10.1007/978-3-319-05591-6_68
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-05590-9
Online ISBN: 978-3-319-05591-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)