Volume 13, Issue 4
Improved 3D Surface Reconstruction via the Method of Fundamental Solutions

Hui Zheng, Feng Wang, C. S. Chen, M. Lei & Yong Wang

Numer. Math. Theor. Meth. Appl., 13 (2020), pp. 973-985.

Published online: 2020-06

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  • Abstract

A new mathematical model of the modified bi-Helmholtz equation is proposed for the reconstruction of 3D implicit surfaces using the method of fundamental solutions. In the algorithm, we also show how to properly determine the parameter so that the spurious surface can be avoided. The main attraction of the proposed method is its simplicity. Four examples for the surface reconstruction are presented to validate the proposed numerical model.

  • Keywords

Method of fundamental solutions, implicit surface, modified bi-Helmholtz equation, computer graphics, image reconstruction.

  • AMS Subject Headings

65N35, 65N99

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-13-973, author = {Hui Zheng , and Feng Wang , and C. S. Chen , and M. Lei , and Yong Wang , }, title = {Improved 3D Surface Reconstruction via the Method of Fundamental Solutions}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2020}, volume = {13}, number = {4}, pages = {973--985}, abstract = {

A new mathematical model of the modified bi-Helmholtz equation is proposed for the reconstruction of 3D implicit surfaces using the method of fundamental solutions. In the algorithm, we also show how to properly determine the parameter so that the spurious surface can be avoided. The main attraction of the proposed method is its simplicity. Four examples for the surface reconstruction are presented to validate the proposed numerical model.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2019-0192}, url = {http://global-sci.org/intro/article_detail/nmtma/16962.html} }
TY - JOUR T1 - Improved 3D Surface Reconstruction via the Method of Fundamental Solutions AU - Hui Zheng , AU - Feng Wang , AU - C. S. Chen , AU - M. Lei , AU - Yong Wang , JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 973 EP - 985 PY - 2020 DA - 2020/06 SN - 13 DO - http://doi.org/10.4208/nmtma.OA-2019-0192 UR - https://global-sci.org/intro/article_detail/nmtma/16962.html KW - Method of fundamental solutions, implicit surface, modified bi-Helmholtz equation, computer graphics, image reconstruction. AB -

A new mathematical model of the modified bi-Helmholtz equation is proposed for the reconstruction of 3D implicit surfaces using the method of fundamental solutions. In the algorithm, we also show how to properly determine the parameter so that the spurious surface can be avoided. The main attraction of the proposed method is its simplicity. Four examples for the surface reconstruction are presented to validate the proposed numerical model.

Hui Zheng, Feng Wang, C. S. Chen, M. Lei & Yong Wang. (2020). Improved 3D Surface Reconstruction via the Method of Fundamental Solutions. Numerical Mathematics: Theory, Methods and Applications. 13 (4). 973-985. doi:10.4208/nmtma.OA-2019-0192
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