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4D space–time Delaunay meshing for medical images

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Abstract

In this paper, we present a Delaunay refinement algorithm for 4-dimensional (\(\hbox {3D}+t\)) segmented images. The output mesh is proved to consist of sliver-free simplices. Assuming that the hyper-surface is a closed smooth manifold, we also guarantee faithful geometric and topological approximation. We implement and demonstrate the effectiveness of our method on publicly available segmented cardiac images. Finally, we devise a tightly coupled parallelization technique to boost the performance of our 4-dimensional mesher, thereby taking advantage of the multi-core and many-core platforms already available in the market.

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Acknowledgments

The authors would like to thank Dr. Marek Behr, RWTH Aachen University, for the constructive discussions, and the anonymous reviewers for their comments and insight that helped the presentation of this paper. This work is supported in part by NSF grants: CCF-1139864, CCF-1136538, CSI-1136536 and CCF-1439079 and by the John Simon Guggenheim Foundation and the Richard T. Cheng Endowment.

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  1. Computer Science Department, College of William and Mary, Virginia, USA

    Panagiotis Foteinos

  2. Computer Science Department, Old Dominion University, Virginia, USA

    Nikos Chrisochoides

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  1. Panagiotis Foteinos
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Correspondence to Panagiotis Foteinos.

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Foteinos, P., Chrisochoides, N. 4D space–time Delaunay meshing for medical images. Engineering with Computers 31, 499–511 (2015). https://doi.org/10.1007/s00366-014-0380-z

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