Abstract
In this paper, a variational tetrahedral meshing approach is used to adapt a tetrahedral mesh to the underlying CT volumetric data so that image edges are well approximated in the mesh. Afterwards, tetrahedra in the mesh are classified into regions whose image characteristics are similar. Three different clustering schemes are proposed to classify tetrahedra, while the clustering scheme viewing the mesh as an undirected graph achieved best results.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Spanel, M., Krsek, P., Stancl, V.: Vector Segmentation of Volumetric Image Data: Tetrahedral Meshing Constrained by Image Edges. In: Proceedings of the 3rd International Joint Converence on Computer Vision, Imaging and Computer Graphics Theaory and Applications, pp. 134–138 (2010)
George, P.-L., Borouchaki, H.: Delaunay Triangulation and Meshing: Application to Finite Elements, 413 pages, (1998)
Labelle, F., Shewchuk, J.R.: Isosurface stuffing: fast tetrahedral meshes with good dihedral angles. ACM Trans. Graph. 26(3), 57 (2007)
Zhang, Y., Bajaj, C., Sohn, B.-S.: Adaptive and quality 3D meshing from imaging data. In: Proceedings of the Eighth ACM Symposium on Solid Modeling and Applications, pp. 286–291 (2003)
Alliez, P., Cohen-Steiner, D., Yvinec, M., Desbrun, M.: Variational tetrahedral meshing. ACM Trans. Graph. 24(3), 617–625 (2005)
Fabbri, R., Costa, L., da, F., Torelli, J.C., Bruno, O.M.: 2D Euclidean Distance Transform Algorithms: A Comparative Survey. ACM Computing Surveys 40(1), 1–44 (2008)
Du, Q., Emelianenko, M., Ju, L.: Convergence of the lloyd algorithm for computing centroidal voronoi tessellations. SIAM J. Numer. Anal. 44(1), 102–119 (2006)
Fehr, J., Burkhardt, H.: 3d rotation invariant local binary patterns. Pattern Recognition 29, 1–4 (2008)
Pham, D.L., Prince, J.L.: Adaptive fuzzy segmentation of magnetic resonance images. IEEE Transactions on Medical Imaging 18 (1999)
Ng, S.K., McLachlan, G.J.: On some variants of the em algorithm for fitting mixture models. Austrian Journal of Statistics 23, 143–161 (2003)
Boykov, Y., Kolmogorov, V.: An experimental comparison of min-cut/max-flow algorithms for energy minimization in vision. IEEE Transactions on Pattern Analysis and Machine Intelligence 26(9), 1124–1137 (2004)
Kurita, T.: An efficient agglomerative clustering algorithm for region growing. In: Proc. of IAPR Workshop on Machine Vision Applications, pp. 210–213 (1991)
Lorensen, W.E., Cline, H.E.: Marching cubes: A high resolution 3d surface construction algorithm. SIGGRAPH Comput. Graph. 21(4), 163–169 (1987)
Botsch, M., Pauly, M., Rossl, C., Bischoff, S., Kobbelt, L.: Geometric modeling based on triangle meshes. In: SIGGRAPH Course Notes (2006)
Taubin, G.: Geometric signal processing on polygonal meshes (2000)
Vollmer, J., Mencl, R., Mller, H.: Improved laplacian smoothing of noisy surface meshes. In: Computer Graphics Forum, vol. 18, pp. 131–138. Blackwell Publishing, Malden (1999)
Garland, M., Heckbert, P.S.: Surface simplification using quadric error metrics. In: SIGGRAPH 1997: Proceedings of the 24th annual conference on Computer graphics and interactive techniques, pp. 209–216 (1997)
Hildebrandt, K., Polthier, K.: Constraint-based fairing of surface meshes. In: Proc. of the Fifth Eurographics Symposium on Geometry Processing, pp. 203–212 (2007)
Cignoni, P., Rocchini, C., Scopigno, R.: Metro: measuring error on simplified surfaces. Computer Graphics Forum 17, 167–174 (1998)
Tournois, J., Srinivasan, R., Alliez, P.: Perturbing slivers in 3d delaunay meshes. In: Proceedings of the 18th International Meshing Roundtable, pp. 157–173 (2009)
Veksler, O.: Gcmex – matlab wrapper for graph cuts multi-label energy minimization (2010)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Španěl, M., Kršek, P., Švub, M., Štancl, V. (2011). Tetrahedral Meshing of Volumetric Medical Images Respecting Image Edges. In: Real, P., Diaz-Pernil, D., Molina-Abril, H., Berciano, A., Kropatsch, W. (eds) Computer Analysis of Images and Patterns. CAIP 2011. Lecture Notes in Computer Science, vol 6854. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23672-3_20
Download citation
DOI: https://doi.org/10.1007/978-3-642-23672-3_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23671-6
Online ISBN: 978-3-642-23672-3
eBook Packages: Computer ScienceComputer Science (R0)