- Volume 19 Issue 1
DOI QR Code
A MODIFIED CAHN-HILLIARD EQUATION FOR 3D VOLUME RECONSTRUCTION FROM TWO PLANAR CROSS SECTIONS
- Lee, Seunggyu (Department of Mathematics, Korea University) ;
- Choi, Yongho (Department of Mathematics, Korea University) ;
- Lee, Doyoon (Seoul Science High School) ;
- Jo, Hong-Kwon (Seoul Science High School) ;
- Lee, Seunghyun (Seoul Science High School) ;
- Myung, Sunghyun (Seoul Science High School) ;
- Kim, Junseok (Department of Mathematics, Korea University)
- 투고 : 2014.12.19
- 심사 : 2015.02.23
- 발행 : 2015.03.25
In this paper, we present an implicit method for reconstructing a 3D solid model from two 2D cross section images. The proposed method is based on the Cahn-Hilliard model for the image inpainting. Image inpainting is the process of reconstructing lost parts of images based on information from neighboring areas. We treat the empty region between the two cross sections as inpainting region and use two cross sections as neighboring information. We initialize the empty region by the linear interpolation. We perform numerical experiments demonstrating that our proposed method can generate a smooth 3D solid model from two cross section data.
연구 과제 주관 기관 : National Research Foundation of Korea(NRF)
- J.F. Guo, Y.L. Cai, and Y.P. Wang, Morphology-based interpolation for 3D medical image reconstruction, Comput. Med. Imaging Graph., 19 (1995), 267-279. https://doi.org/10.1016/0895-6111(95)00007-D
- T.Y. Lee and C.H. Lin, Feature-guided shape-based image interpolation, IEEE Trans. Med. Imaging, 21 (2002), 1479-1489. https://doi.org/10.1109/TMI.2002.806574
- H. Fuchs, Z. M. Kedem, and S. P. Uselton, Optimal surface reconstruction from planar contours, Commun. ACM, 20 (1977), 693-702. https://doi.org/10.1145/359842.359846
- G. Herman and C. Coin, The use of 3D computer display in the study of disk disease, J. Comput. Assist. Tomogr., 4(4) (1980), 564-567. https://doi.org/10.1097/00004728-198008000-00036
- C.C. Liang, C.T. Chen, and W.C. Lin, Intensity interpolation for reconstructing 3-D medical images from serial cross-sections, Engineering in Medicine and Biology Society, Proceedings of the Annual International Conference of the IEEE, (1988), 1389-1390.
- C.C. Liang, C.T. Chen, and W.C. Lin, Intensity interpolation for branching in reconstructing threedimensional objects from serial cross-sections, Medical Imaging V: Image Processing. International Society for Optics and Photonics, (1991), 456-467.
- G.J. Grevera and J.K. Udupa, Shape-based interpolation of multidimensional grey-level images, IEEE Trans. Med. Imaging, 15 (1996), 881-892. https://doi.org/10.1109/42.544506
- G.T. Herman, J. Zheng, and C.A. Bucholtz, Shape-based interpolation, IEEE Comput. Graphics Apllicat., 12 (1992), 69-79.
- Y.H. Liu, Y.N. Sun, C.W. Mao, and C.J. Lin, Edge-shrinking interpolation for medical images, Comput. Vis. Graphics Image Processing, 21(2) (1997), 91-101.
- T.Y. Lee and W.H. Wang, Morphology-based three-dimensional interpolation, IEEE Trans. Med. Imag. 19 (2000), 711-721. https://doi.org/10.1109/42.875193
- J.W. Cahn, On Spinodal Decomposition, Acta Metall. Mater., 9(9) (1961), 795-801. https://doi.org/10.1016/0001-6160(61)90182-1
- A. Bertozzi, S. Esedoglu and A. Gillette, Inpainting of binary images using the Cahn-Hilliard equation, IEEE Trans. Image. Proc., 16 (2007), 285-291. https://doi.org/10.1109/TIP.2006.887728
- Y. Li, J. Shin, Y. Choi and J. Kim, Three-dimensional volume reconstruction from slice data using phase-field models, Comput. Vis. Image Und. DOI:10.1016/j.cviu.2015.02.001, 2015. https://doi.org/10.1016/j.cviu.2015.02.001
- D. Lee, J-Y. Huh, D. Jeong, J. Shin, A. Yun, and J. Kim, Physical, mathematical, and numerical derivations of the Cahn-Hilliard equation, Comput. Mater. Sci., 81 (2014), 216-225. https://doi.org/10.1016/j.commatsci.2013.08.027
- D. Jeong, Y. Li, H.G. Lee and J. Kim, Fast and automatic inpainting of binary images using a phase-field model, J. KSIAM, 13 (2009), 225-236.
- D. Eyre, An unconditionally stable one-step scheme for gradient systems, unpulished article, http://www.math.utah.edu/-eyre/research/methods/stable.ps, (1998).
- S. Lee, C. Lee, H.G. Lee, and J. Kim, Comparison of different numerical schemes for the Cahn-Hilliard equation, J. KSIAM, 17(3) (2013), 197-207.
- J.J. Eggleston, G.B. McFadden, and P.W. Voorhees, Phase-field model for highly anisotropic interfacial energy, Phys. D, 150 (2001), 91-103. https://doi.org/10.1016/S0167-2789(00)00222-0
- P. Yue, C. Zhou and J.J. Feng, Spontaneous shrinkage of drops and mass conservation in phase-field simulations, J. Comput. Phys., 223 (2007), 1-9. https://doi.org/10.1016/j.jcp.2006.11.020