Accurate surface reconstruction in 3D using two-dimensional parallel cross sections평행한 2차원 단면 정보를 이용한 정확한 3차원 표면 복구

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Images obtained from MRI or CT scanner are two-dimensional and parallel. In some cases, we need to reconstruct a surface from contours on 2-D cross-section images. For example, currently, Magnetic Resonance Electrical Impedance Tomography (MREIT) recovers conductivity of tissues by solving two-dimensional forward problems. However, for more accurate conductivity reconstruction, it is required to solve three-dimensional forward problems and create a surface which encloses a 3-D volume as computational domain. In addition, 3-D reconstruction of the blood vessel or the organ is necessary in computational biology. We consider two requirements for the surface reconstruction. First, it is required that the reconstructed surface satisfies the accuracy of surface reconstruction, which means that the surface exactly passes through each given contour on parallel planes. Secondly, the surface should be smooth enough because blood vessels or organs of the human body are smooth. In addition, since the contours are usually obtained by image segmentation methods based on the level set method, we assume that the contours are given by the level set functions. To the best of our knowledge, there are no methods to satisfy both requirements in present. In this dissertation, we propose a new surface energy based on gradient of the surface normal vector for the smoothness of the reconstructed surface. This energy is a simpler form which keeps the role of the energy based on the total curvature. The new surface energy enforces the surface to be flat and $C^2$ continuous. Also, we propose a methodology to impose constraints to match the given contours to the reconstructed surface exactly based on the level set function with the Heaviside function. With the new surface energy and the new methodology for constraints, we define an energy minimization problem with constrains. Because the Euler-Lagrange equation of the minimization problem is nonlinear fourth order problem, we introduce...
Lee, Chang-Ockresearcher이창옥
한국과학기술원 : 수리과학과,
Issue Date
591786/325007  / 020085024

학위논문(박사) - 한국과학기술원 : 수리과학과, 2014.8, [ iv, 29p ]


Surface reconstruction; 45도 회전 불변 방법; Augmented Lagrangian method; 표면 법선 벡터의 경사도; 표면 복구; Gradient of surface normal vector; Augmented Lagrangian method

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