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Challenges and Advances in Image-Based Geometric Modeling and Mesh Generation

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Image-Based Geometric Modeling and Mesh Generation

Part of the book series: Lecture Notes in Computational Vision and Biomechanics ((LNCVB,volume 3))

Abstract

Image-based geometric modeling and mesh generation play a critical role in computational medicine and biology. This paper presents challenges and advances in this area along with a comprehensive computational framework for analysis-suitable geometric modeling and mesh generation, which integrates image processing, geometric modeling, mesh generation and quality improvement with multi-scale analysis at molecular, cellular, tissue and organ scales. The input imaging data are passed through an image-processing module where the image quality is improved. The improved images are then fed to an in-house meshing software, LBIE-Mesher (Level-set Boundary Interior and Exterior Mesher), to construct 2D or 3D finite element meshes. Given geometry or atomic resolution data in the Protein Data Bank (PDB), we first construct volumetric density map using a signed distance function or a summation of Gaussian Kernel functions, and then use LBIE-Mesher to generate various kinds of meshes. Furthermore, the constructed unstructured meshes can be used as control meshes to construct high-order elements such as volumetric T-splines. In addition, a skeleton-based sweeping method is used to generate hexahedral control meshes and solid NURBS (Non-Uniform Rational B-Spline) or cubic Hermite for cardiovascular system. Different from other existing methods, the presented framework supports five important features: multiscale geometric modeling, automatic mesh generation for heterogeneous domains, all-hexahedral mesh generation with sharp feature preservation, robust quality improvement for non-manifold meshes, and high-order element construction.

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Acknowledgements

The author would like to thank her students, J. Ma, J. Qian and W. Wang, for generating pictures for this paper. This research was supported in part by the ONR-YIP award N00014-10-1-0698, an ONR grant N00014-08-1-0653, an AFOSR grant FA9550-11-1-0346, a NSF/DoD-MRSEC seed grant, a UPMC-HTI gift grant, a SINTEF gift grant from Norway, and a UCSD-subaward.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA, 15213, USA

    Yongjie Zhang

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  1. Yongjie Zhang
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Correspondence to Yongjie Zhang .

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Editors and Affiliations

  1. Department of Mechanical Engineering, Carnegie Mellon University, Forbes Avenue 5000, Pittsburgh, 15213, Pennsylvania, USA

    Yongjie (Jessica) Zhang

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Zhang, Y. (2013). Challenges and Advances in Image-Based Geometric Modeling and Mesh Generation. In: Zhang, Y. (eds) Image-Based Geometric Modeling and Mesh Generation. Lecture Notes in Computational Vision and Biomechanics, vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4255-0_1

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  • DOI: https://doi.org/10.1007/978-94-007-4255-0_1

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-4254-3

  • Online ISBN: 978-94-007-4255-0

  • eBook Packages: EngineeringEngineering (R0)

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