Abstract
There is major interest within the bio-engineering community in developing accurate and non-invasive means for visualizing, modeling and analyzing bone micro-structures. Bones are composed of hierarchical bio-composite materials characterized by complex multi-scale structural geometry. The process of reconstructing a volumetric bone model is usually based upon CT/MRI scanned images. Meshes generated by current commercial CAD systems cannot be used for further modeling or analysis. Moreover, recently developed methods are only capable of capturing the micro-structure for small volumes (biopsy samples). This paper examines the problem of re-meshing a 3D computerized model of bone micro-structure. The proposed method is based on the following phases: defining sub-meshes of the original model in a grid-based structure, remeshing each sub-mesh using the neural network (NN) method, and merging the sub-meshes into a global mesh. Applying the NN method to micro-structures proved to be quite time consuming. Therefore, a parallel, grid-based approach was applied, yielding a simpler structure in each grid cell. The performance of this method is analyzed, and the method is demonstrated on real bone micro-structures. Furthermore, the method may be used as the basis for generating a multi-resolution bone geometric model.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Weiner S, Wagner H D. The material bone: Structure-mechanical function relations. Annual Review of Materials Science, Aug. 1998, 28: 271–298.
Holdstein Y, Fischer A. 3D surface reconstruction using meshing growing neural gas. The Visual Computer, 2008, Special Edition, 24(4): 295–302.
Amenta N, Bern M. Surface Reconstruction by Voronoi Filtering. ACM Press. 1998, pp.39–48.
Boissonnat J D. Representing 2D and 3D shapes with the Delaunay triangulation. In Proc. ICPR84, Montreal, Canada, 1984, pp.745–748.
Hoppe H, DeRose T, Duchamp T, McDonald J, Stuetzle W. Surface Reconstruction from Unorganized Points. ACM Press, 1992, pp.71–78.
Lorensen W E, Cline H E. Marching cubes: A high resolution 3D surface construction algorithm. ACM SIGGRAPH Computer Graphics, 1987, 21(4): 163–169.
Azernikov S, Fischer A. Efficient surface reconstruction method for distributed CAD. Computer Aided Design J., 2004, 36(9): 799–808.
Barhak J, Fischer A. Adaptive reconstruction of freeform objects with 3D SOM neural network grids. Computer & Graphics, 2002, 26(5): 745–751.
Fritzke B. A Growing Neural Gas Network Learns Topologies. Advances in Neural Information Processing Systems 7. Cambridge: MIT Press, MA, 1995.
Martinetz T, Schulten K. A Neural-Gas Network Learns Topologies. Artificial Neural Networks, Kohonen T, Makisara K, Simula O, Kangas J (eds.), Elsevier, 1991, pp.397–402.
Fritzke B. Growing cell structures – A self-organizing network for unsupervised and supervised learning. Neural Networks, 1994, 7(9): 1441–1460.
Kohonen T. Self-organized formation of topologically correct feature maps. Biological Cybernetics, 1982, 43(1): 59–69.
Hoppe H, DeRose T, Duchamp T, McDonald J, Stuetzle W. Mesh optimization. In Proc. Int. Conf. Computer Graphics and Interactive Techniques, Anaheim, USA, Aug. 2–6, 1993, pp.19–26.
Eck M, DeRose T, Duchamp T, Hoppe H, Lounsbery M, Stuetzle W. Multiresolution analysis of arbitrary meshes. In Proc. Int. Conf. Computer Graphics and Interactive Techniques, Los Angeles, USA, Aug. 6–11, 1995, pp.173–182.
Lee A, Sweldens W, Schrder P, Coswar L, Dobkin D. MAPS: Multiresolution adaptive parameterization of surfaces. In Proc. SlGGRAPH 98, Orlando, USA, July 19–24, 1998, pp.95–104.
Alliez P, Meyer M, Desburn M. Interactivc geometry remeshing. ACM Transaction on Graphics, 2002, 21(3): 347–354.
Alliez P, De Verdierc E C, Devillers O, Isenburg M. Isotropic surface remeshing. In Proc. SMI 2003, Seoul, Korea, May 12–15, 2003, p.49.
Álvarez R, Noguera J V, Tortosa L, Zamora A. A mesh optimization algorithm based on neural networks. Journal of Information Sciences, 2007, 177(23): 5347–5364.
Woodwark J. Blends in geometric modeling. In Proc. the Mathematics of Surfaces II., Cardiff, UK, 1987, pp.255–297.
Sears K, Middleditch A. Blend surfaces for set-theoretic volume modeling systems. Computer Graphics, 1985, 19(3): 161–170.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zaideman, O., Fischer, A. Geometric Bone Modeling: From Macro to Micro Structures. J. Comput. Sci. Technol. 25, 614–622 (2010). https://doi.org/10.1007/s11390-010-9350-0
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11390-010-9350-0