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Interior structure transfer via harmonic 1-forms

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Abstract

As a natural extension of surface parameterizaiton, volumetric parameterization is becoming more and more popular and exhibiting great advantages in several applications such as medical image analysis, hexahedral meshing etc. This paper presents an efficient volume parameterization algorithm based on harmonic 1-form. Our new algorithm computes three harmonic 1-forms, which can be treated as three vector fields, such that both the divergence and circulation of them are zero. By integrating the three harmonic 1-forms over the entire volumes, we can bijectively map the volume to a cuboid domain. We demonstrate the power of the technique by introducing a new application, to transfer the interior structure during the morphing of two given shapes.

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Acknowledgements

This work was supported by AcRF 69/07, Singapore NRF Interactive Digital Media R&D Program under research grant NRF2008IDM-IDM004-006, the National Natural Science Foundation of China (No.61202142), Joint Funds of the Ministry of Education of China and China Mobile(MCM20122081), the Open Project Program of the State Key Lab of CAD&CG Zhejiang University(Grant No. A1205) and the Fundamental Research Funds for the Central Universities(No.2010121070). Jiazhi Xia is partially supported by the freedom explore Program of Central South University(NO.2012QNZT058) and Doctoral Fund of Ministry of Education of China(NO. 20120162120019).

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Authors and Affiliations

  1. Software School, Xiamen University, Xiamen, People’s Republic of China

    Juncong Lin, Xing Gao & Minghong Liao

  2. School of Information Science and Engineering, Central South University, Changsha, Hunan, People’s Republic of China

    Jiazhi Xia

  3. School of Computer Engineering, Nanyang Technological University, Singapore, Singapore

    Ying He

  4. Department of Computer Science, Stony Brook University, Stony Brook, NY, 11790, USA

    Xianfeng Gu

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  1. Juncong Lin
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  2. Jiazhi Xia
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  3. Xing Gao
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  4. Minghong Liao
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  5. Ying He
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  6. Xianfeng Gu
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Correspondence to Jiazhi Xia.

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Lin, J., Xia, J., Gao, X. et al. Interior structure transfer via harmonic 1-forms. Multimed Tools Appl 74, 139–158 (2015). https://doi.org/10.1007/s11042-013-1508-7

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  • DOI: https://doi.org/10.1007/s11042-013-1508-7

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