We describe a fast and efficient numerical algorithm for the process of three-dimensional narrow volume reconstruction from scattered data in three dimensions. The present study is an extension of previous research [Li et al., Surface embedding narrow volume reconstruction from unorganized points, Comput. Vis. Image Underst. 121 (2014) 100-107]. In the previous work, we modified the original Allen-Cahn equation by multiplying a control function to restrict the evolution within a narrow band around the given surface data set. The key idea of the present work is to perform the computations only on a narrow band around the given surface data set. In this way, we can significantly reduce the storage memory and CPU time. The proposed numerical method, based on operator splitting techniques, can employ a large time step size and exhibits unconditional stability. We perform a number of numerical experiments in order to demonstrate the efficiency of this method.
Bibliographical noteFunding Information:
Y.B. Li was supported by the Fundamental Research Funds for the Central Universities , China (No. XJJ2015068 ) and supported by China Postdoctoral Science Foundation (No. 2015M572541 ). The corresponding author (J.S. Kim) was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) ( NRF-2014R1A2A2A01003683 ). The authors are grateful to the reviewers whose valuable suggestions and comments significantly improved the quality of this paper.
© 2015 Elsevier Ltd.
- Allen-Cahn equation
- Narrow band domain
- Offset surface reconstruction
- Unconditional stability
- Unsigned distance function
ASJC Scopus subject areas
- Signal Processing
- Computer Vision and Pattern Recognition
- Artificial Intelligence