TY - JOUR
T1 - Surface embedding narrow volume reconstruction from unorganized points
AU - Li, Yibao
AU - Lee, Dongsun
AU - Lee, Chaeyoung
AU - Lee, Jihu
AU - Lee, Sanha
AU - Kim, Junseok
AU - Kim, Jisu
AU - Ahn, Shinwoo
N1 - Funding Information:
The corresponding author (J.S. Kim) was supported by Seoul Science High School R&E program. The second author (D. Lee) was supported by NRF (National Research Foundation of Korea) Grant funded by the Korean Government (NRF-2012-Fostering Core Leaders of the Future Basic Science Program). The authors are grateful to the anonymous referees for their constructive and valuable comments that improved significantly the quality of this paper.
PY - 2014/4
Y1 - 2014/4
N2 - In this paper, we present a novel fast and accurate numerical method for the surface embedding narrow volume reconstruction from unorganized points in R3. Though the level set method prevails in the image processing, it requires a redistancing procedure to maintain a desired shape of the level set function. On the other hand, our method is based on the Allen-Cahn equation, which has been applied in image segmentation due to its motion by mean curvature property. We modify the original Allen-Cahn equation by multiplying a control function to restrict the evolution within a narrow band around the given surface data set. To improve the numerical stability of our proposed model, we split the governing equation into linear and nonlinear terms and use an operator splitting technique. The linear equation is solved by the multigrid method which is a fast solver and the nonlinear equation is solved analytically. The unconditional stability of the proposed scheme is also proved. Various numerical results are presented to demonstrate the robustness and accuracy of the proposed method.
AB - In this paper, we present a novel fast and accurate numerical method for the surface embedding narrow volume reconstruction from unorganized points in R3. Though the level set method prevails in the image processing, it requires a redistancing procedure to maintain a desired shape of the level set function. On the other hand, our method is based on the Allen-Cahn equation, which has been applied in image segmentation due to its motion by mean curvature property. We modify the original Allen-Cahn equation by multiplying a control function to restrict the evolution within a narrow band around the given surface data set. To improve the numerical stability of our proposed model, we split the governing equation into linear and nonlinear terms and use an operator splitting technique. The linear equation is solved by the multigrid method which is a fast solver and the nonlinear equation is solved analytically. The unconditional stability of the proposed scheme is also proved. Various numerical results are presented to demonstrate the robustness and accuracy of the proposed method.
KW - Allen-Cahn equation
KW - Multigrid method
KW - Unconditional stability
KW - Unsigned distance function
KW - Volume reconstruction
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U2 - 10.1016/j.cviu.2014.02.002
DO - 10.1016/j.cviu.2014.02.002
M3 - Article
AN - SCOPUS:84897113302
SN - 1077-3142
VL - 121
SP - 100
EP - 107
JO - Computer Vision and Image Understanding
JF - Computer Vision and Image Understanding
ER -