Parallel Adaptive Method for Selecting Points of Interest in Structures: Cranial Deformation
Método adaptativo paralelo para la selección de puntos de interés en estructuras: deformación craneal
Claudia García-Blanquel1, Amitava Majumdar2, and René Luna-García1
1 Centro de Investigación en Computación, IPN, Mexico City, Mexico. cgarciab10@sagitario.cic.ipn.mx, lunar@cic.ipn.mx
]]> 2 San Diego Supercomputer Center, University of California San Diego, La Jolla, CA 92037, USA. majumdar@sdsc.edu
Article received on 11/02/2013;
accepted on 11/08/2013.
Abstract
In this paper, we present a cranial deformation simulation by applying a stress model using the Finite Element Method (FEM). We determine the geometry of cranium by processing 134 Computed Tomography (CT) images. We implement an image segmentation algorithm to build a three-dimensional cranium structure. We simulate stress and propose the boundary conditions according to the final position of forces applied by a stereotactic frame fixed on the human head. We used probabilistic and adaptive methods to select points in the structure with the purpose of reducing the computational cost and computational error due to discretization problem. We implement the algorithms using parallel programming (PosixThread and MPI).
Keywords: HPC, parallel programming, FEM, adaptive method, cranial deformation.
Resumen
]]> En este trabajo, presentamos un modelo de deformación por esfuerzos para el cráneo humano usando el Método del Elemento Finito (FEM). Determinamos la geometría del cráneo a partir de 134 imágenes de tomografías computarizadas (CT) e implementamos un algoritmo para la segmentación de imágenes y construir una imagen tridimensional del cráneo. Simulamos los esfuerzos y proponemos las condiciones de frontera de acuerdo con la posición de la fuerza aplicada por un marco estereotáctico fijo sobre un cráneo humano. Aplicamos métodos probabilísticos y adaptativos para la selección de puntos en la estructura con la finalidad de reducir el costo computacional y el error de cálculo debido a la discretización del problema. Implementamos los algoritmos usando programación paralela (PosixThread y MPI).Palabras clave: HPC, programación paralela, FEM, método adaptivo, deformación craneal.
DESCARGAR ARTÍCULO EN FORMATO PDF
References
1. Wohlmuth, B.I. (2001). Discretization Methods and Iterative Solvers Based on Domain Decomposition. Berlin; New York: Springer. [ Links ]
2. Li, B. & Acton, S.T. (2007). Active Contour External Force using Vector Field Convolution for Image Segmentation. IEEE Transactions on Image Processing, 16(8), 2096-2106. [ Links ]
]]>3. Bolle, R.M. & Vemuri, B.C. (1991). On Three Dimensional Surface Reconstruction Methods. IEEE Transactions on Pattern Analysis and Machine Intelligence, 13(1), 1-13. [ Links ]
4. C. García Bauza, V. Cifuentes (2010), "Método del punto proximal para la reconstrucción automática de geometría de lechos", Mecánica computacional. [ Links ]
5. Gelfand, N., Mitra, N.J., Guibas, L.J., & Pottmann, H. (2005). Robust global registration. Third Eurographics Symposium on Geometry Processing, Vienna, Austria, Article No. 197. [ Links ]
6. Hu, J. & Hua, J. (2009). Salient spectral geometric features for shape matching and retrieval. The Visual Computer: International Journal of Computer Graphics, 25(5-7), 667-675. [ Links ]
7. Hoffmann, C.M. (1989). Geometric and Solid Modeling: an introduction. San Mateo, Calif.: Morgan Kauffmann. [ Links ]
]]>8. Nieto, J.J., Minor, A., Álvarez, J., Alonso, M.A., & Algorri, M.E. (2005). Análisis de esfuerzos de compresión en el cráneo humano por medio del método del elemento finito. Revista Mexicana de Ingeniería Biomédica, 26(1), 16-21. [ Links ]
9. Lee, C.H., Varshney, A., & Jacobs, D.W. (2005). Mesh saliency. 32nd International Conference on Computer Graphics and Interactive Techniques (SIGGRAPH 2005), Los Angeles, CA, 659-666. [ Links ]
10. Li, B. & Acton, S.T. (2007). Active Contour External Force Using Vector Field Convolution for Image Segmentation. IEEE Transactions on Image Processing, 16(8), 2096-2106. [ Links ]
11. Root(2013). Retrieved from http://root.cern.ch/drupal/. [ Links ]
12. Tierny, J., Vandeborre, J.P., & Daoudi, M. (2008). Enhancing 3D mesh topological skeletons with discrete contour constrictions. The Visual Computer: International Journal of Computer Graphics, 24(3), 155-172. [ Links ]
]]>13. Wriggers, P. & Boersma, A. (1998). A parallel algebraic multigrid solver for problems in solid mechanics discretized by Finite elements. Computers & Structures, 69(1), 129-137. [ Links ]
14. Venere M. y Dari E. (2012). Análisis comparativo de algoritmos para obtener triangulaciones Delaunay. Mecánica Computacional, 10, 491-506. [ Links ]
15. Gropp, W., Lusk, E., & Skjellem, A. (1999). Using MPI, Portable Parallel Programming Whit the Message-Passing Interface (2nd ed.). Cambridge, Mass.: MIT Press. [ Links ]
16. Willinger, R., Kang, H.S., & Diaw, B. (1999). Three-dimensional human head finite-element model validation against two experimental impacts. Annals of Biomedical Engineering, 27(3), 403-410. [ Links ]
17. Xu, C. & Prince, J.L. (1998). Snakes, shapes, and gradient vector flow. IEEE Transactions on Image Processing, 7(3), 359-369. [ Links ]
]]>18. Katz, S., Leifman, G., & Tal, A. (2005). Mesh segmentation using feature point and core extraction. The visual Computer, 21(8-10), 649658. [ Links ]
19. McInerney, T. & Terzoupoulos, D. (1999). Topology adaptive deformable surfaces for medical image volume segmentation. IEEE Transactions on Medical Imaging, 18(10), 840-850. [ Links ]
20. McInerney, T. & Terzoupoulos, D. (1996). Deformable models in medical image analysis: A survey. Medical Image Analysis, 1(2), 91-108. [ Links ]
21. Cootes, T.F., Edwards, G.J., & Taylor. C.J. (2001). Active appearance models. IEEE Transactions on Pattern Analysis and Machine Intelligence, 23(6), 681-685. [ Links ]
]]>