- Volume 40 Issue 4
DOI QR Code
Method of Fast Interpolation of B-Spline Volumes for Reconstructing the Heterogeneous Model of Bones from CT Images
CT 영상에서 뼈의 불균질 모델 생성을 위한 B-스플라인 볼륨의 빠른 보간 방법
- Received : 2016.01.07
- Accepted : 2016.03.02
- Published : 2016.04.01
It is known that it is expedient to represent the distribution of the properties of a bone with complex heterogeneity as B-spline volume functions. For B-spline-based representation, the pixel values of CT images are interpolated by B-spline volume functions. However, the CT images of a bone are three-dimensional and very large, and hence a large amount of memory and long computation time for the interpolation are required. In this study, a method for resolving these problems is proposed. In the proposed method, the B-spline volume interpolation problem is simplified by using the uniformity of pixel spacing of the image and the properties of B-spline basis functions. This results in a reduction in computation time and the amount of memory used. The proposed method was implemented and it was verified that the computation time and the amount of memory used were reduced.
B-spline Volume;CT Images;Heterogeneous Model;Interpolation;Reconstruction
- Kumar, V., Burns, D., Dutta, D. and Hoffmann, C., 1999, "A Framework for Object Modeling," Computer-Aided Design, Vol. 31, No. 9, pp. 541-556. https://doi.org/10.1016/S0010-4485(99)00051-2
- Watari, F., Kondo, H., Matsuo, S., Miyao, R., Yokoyama, A., Omori, M., Hirai, T., Tamura, Y., Uo, M., Ohara, N. and Kawasaki, T., 2003, "Development of Functionally Graded Implant and Dental Post for Bio-Medical Application," Materials Science Forum, Vol. 423-425, pp. 321-326. https://doi.org/10.4028/www.scientific.net/MSF.423-425.321
- Shackelford, J. F., 1999, Bioceramics: Applications of Ceramic and Glass Materials in Medicine, Trans Tech Publications.
- Pise, U. V., Bhatt, A. D., Srivastava, R. K. and Warkhedkar, R. M., 2009, "A B-Spline Based Heterogeneous Modeling and Analysis of Proximal Femur with Graded Element," Journal of Biomechanics, Vol. 42, No. 12, pp. 1981-1988. https://doi.org/10.1016/j.jbiomech.2009.05.019
- Warkhedkar, R. M. and Bhatt, A. D., 2009, "Material-Solid Modeling of Human Body: A Heterogeneous B-Spline Based Approach," Computer-Aided Design, Vol. 41, No. 8, pp. 586-597. https://doi.org/10.1016/j.cad.2008.10.016
- Kou, X. Y. and Tan, S. T., 2007, "Heterogeneous Object Modeling: A Review," Computer-Aided Design, Vol. 39, No. 4, pp. 284-301. https://doi.org/10.1016/j.cad.2006.12.007
- Chandru, V., Manohar, S. and Prakash, C. E., 1995, "Voxel-Based Modeling for Layered Manufacturing," IEEE Computer Graphics and Applications, Vol. 15, No. 6, pp. 42-47.
- Cho, J. R. and Ha, D. Y., 2002, "Optimal Tailoring of 2D Volume-Fraction Distributions for Heat-Resisting Functionally Graded Materials using FDM," Computer Methods in Applied Mechanics and Engineering, Vol. 191, No. 29-30, pp. 3195-3211. https://doi.org/10.1016/S0045-7825(02)00256-6
- Jackson, T. R., 2000, Analysis of Functionally Graded Material Object Representation Methods, Ph.D. thesis, Massachusetts Institute of Technology.
- Shin, K.-H. and Dutta, D., 2001, "Constructive Representation of Heterogeneous Objects," Journal of Computing and Information Science in Engineering, Vol. 1, No. 3, pp. 205-217. https://doi.org/10.1115/1.1403448
- Shin, K.-H., 2011, "Modeling of Time-Variant Heterogeneous Objects in Micro-System Packages," Journal of Mechanical Science and Technology, Vol. 25, No. 5, pp. 1119-1128. https://doi.org/10.1007/s12206-011-0227-0
- Adzhiev, V., Kartasheva, E., Kunii, T., Pasko, A. and Schmitt, B., 2003, "Hybrid Cellular-functional Modeling of Heterogeneous Objects," Journal of Computing and Information Sciences in Engineering, Vol. 2, No. 4, pp. 312-322.
- Biswas, A., Shapiro, V. and Tsukanov, I., 2004, "Heterogeneous Material Modeling with Distance Field," Computer Aided Geometric Design, Vol. 21, No. 3, pp. 215-242. https://doi.org/10.1016/j.cagd.2003.08.002
- Siu, Y. K. and Tan, S. T., 2002, "Source-Based Heterogeneous Solid Modeling," Computer Aided Geometric Design, Vol. 34, No. 1, pp. 41-55. https://doi.org/10.1016/S0010-4485(01)00046-X
- Samanta, K. and Koc, B., 2005, "Feature-Based Design and Material Blending for Freeform Heterogeneous Object Modeling," Computer Aided Geometric Design, Vol. 37, No. 3, pp. 287-305. https://doi.org/10.1016/j.cad.2004.03.005
- Yang, P. and Qian, X., 2007, "A B-Spline-Based Approach to Heterogeneous Objects Design and Analysis," Computer-Aided Design, Vol. 39, No. 2, pp. 95-111. https://doi.org/10.1016/j.cad.2006.10.005
- Huang, J., Fadel, M. G., Blouin, V. Y. and Grujicic, M., 2002, "Bi-Objective Optimization Design of Functionally Gradient Materials," Materials and Design, Vol. 23, No. 7, pp. 657-666. https://doi.org/10.1016/S0261-3069(02)00048-1
- Piegl, L. and Tiller, W., 1997, The NURBS Book, Springer-Verlag, New York.
- Park, H., 2001, "An Approximate Lofting Approach for B-Spline Surface Fitting to Functional Surfaces," International Journal of Advanced Manufacturing Technology, Vol. 18, No. 7, pp 474-482. https://doi.org/10.1007/s0017010180474
- Park, H., 2003, "Lofted B-Spline Surface Interpolation by Linearly Constrained Energy Minimization," Computer-Aided Design, Vol. 35, No. 14, pp. 1261-1268. https://doi.org/10.1016/S0010-4485(03)00040-X
- Park, S., 2009, "A Rational B-Spline Hypervolume for Multidimensional Multivariate Modeling," Journal of Mechanical Science and Technology, Vol. 23, No. 7, pp. 1967-1981. https://doi.org/10.1007/s12206-009-0513-2
- Martin, T., Cohen, E. and Kirby, R. M., 2009, "Volumetric Parameterization and Trivariate B-Spline Fitting Using Harmonic Functions," Computer-Aided Geometric Design, Vol. 26, No. 6, pp. 648-664. https://doi.org/10.1016/j.cagd.2008.09.008
- Unser, M., Aldroubi, A. and Eden, M., 1991, "Fast B-Spline Transforms for Continuous Image Representation and Interpolation," IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 13, No. 3, pp. 277-285. https://doi.org/10.1109/34.75515
- Thevenaz, P., Blu, T. and Unser, M., "Interpolation Revisited," IEEE Transactions on Medical Imaging, Vol. 19, No. 7, pp. 739-758. https://doi.org/10.1109/42.875199
- Rho, J. Y., Hobatho, M. C. and Ashman, R. B., 1995, "Relations of Mechanical Properties to Density and CT Numbers in Human Bone," Medical Engineering and Physics, Vo. 17, No. 5, pp. 347-355. https://doi.org/10.1016/1350-4533(95)97314-F
- Wirtz, D. C., Schiffers, N., Pandorf, T., Radermacher, K., Weichert, D. and Forst, R., 2000, "Critical Evaluation of Known Bone Material Properties to Realize Anisotropic FE-Simulation of the Proximal Femur," Journal of Biomechanics, Vol. 33, No. 10, 1325-1330. https://doi.org/10.1016/S0021-9290(00)00069-5
- Visible Korean Homepage, http://vkh3.kisti.re.kr/.
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