Multimedia Tools and Applications

, Volume 74, Issue 1, pp 139–158 | Cite as

Interior structure transfer via harmonic 1-forms

  • Juncong Lin
  • Jiazhi XiaEmail author
  • Xing Gao
  • Minghong Liao
  • Ying He
  • Xianfeng Gu


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.


Volumetric parameterization Harmonic 1-form Interior structure transfer 



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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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Juncong Lin
    • 1
  • Jiazhi Xia
    • 2
    Email author
  • Xing Gao
    • 1
  • Minghong Liao
    • 1
  • Ying He
    • 3
  • Xianfeng Gu
    • 4
  1. 1.Software SchoolXiamen UniversityXiamenPeople’s Republic of China
  2. 2.School of Information Science and EngineeringCentral South UniversityChangshaPeople’s Republic of China
  3. 3.School of Computer EngineeringNanyang Technological UniversitySingaporeSingapore
  4. 4.Department of Computer ScienceStony Brook UniversityStony BrookUSA

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