Fast and efficient narrow volume reconstruction from scattered data

Yibao Li; Junseok Kim

doi:10.1016/j.patcog.2015.06.014

Fast and efficient narrow volume reconstruction from scattered data

Yibao Li, Junseok Kim

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

19 Citations (Scopus)

Abstract

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.

Original language	English
Article number	5459
Pages (from-to)	4057-4069
Number of pages	13
Journal	Pattern Recognition
Volume	48
Issue number	12
DOIs	https://doi.org/10.1016/j.patcog.2015.06.014
Publication status	Published - 2015 Dec 1

Bibliographical note

Funding 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.

Publisher Copyright:
© 2015 Elsevier Ltd.

Keywords

Allen-Cahn equation
Narrow band domain
Offset surface reconstruction
Unconditional stability
Unsigned distance function

ASJC Scopus subject areas

Software
Signal Processing
Computer Vision and Pattern Recognition
Artificial Intelligence

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10.1016/j.patcog.2015.06.014

Cite this

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title = "Fast and efficient narrow volume reconstruction from scattered data",

abstract = "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.",

keywords = "Allen-Cahn equation, Narrow band domain, Offset surface reconstruction, Unconditional stability, Unsigned distance function",

author = "Yibao Li and Junseok Kim",

note = "Funding 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. Publisher Copyright: {\textcopyright} 2015 Elsevier Ltd.",

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doi = "10.1016/j.patcog.2015.06.014",

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AU - Li, Yibao

AU - Kim, Junseok

N1 - Funding 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. Publisher Copyright: © 2015 Elsevier Ltd.

PY - 2015/12/1

Y1 - 2015/12/1

N2 - 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.

AB - 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.

KW - Allen-Cahn equation

KW - Narrow band domain

KW - Offset surface reconstruction

KW - Unconditional stability

KW - Unsigned distance function

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SN - 0031-3203

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JO - Pattern Recognition

JF - Pattern Recognition

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ER -

Fast and efficient narrow volume reconstruction from scattered data

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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