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Diffeomorphic Shape Matching by Operator Splitting in 3D Cardiology Imaging

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Abstract

We develop an operator splitting approach to solve diffeomorphic matching problems for sequences of surfaces in three-dimensional space. The goal is to smoothly match, at very fast rate, finite sequences of observed 3D-snapshots extracted from movies recording the smooth dynamic deformations of “soft” surfaces. We have implemented our algorithms in a proprietary software installed at The Methodist Hospital (Cardiology) to monitor mitral valve strain through computer analysis of noninvasive patients echocardiographies.

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Acknowledgements

This work was partly supported by the National Science Foundation through the grants DMS-1854853, DMS-2009923, and DMS-2012825. The research work of Dr. P. Zhang was supported for 3 years by The Methodist Hospital Research Institute (Cardiology Department). Any opinions, findings, and conclusions or recommendations expressed herein are those of the authors and do not necessarily reflect the views of the NSF. This work was completed in part with resources provided by the Research Computing Data Core at the University of Houston.

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Authors and Affiliations

  1. Department of Mathematics, University of Houston, Houston, TX, USA

    Peng Zhang, Andreas Mang, Jiwen He & Robert Azencott

  2. Houston Methodist, Houston, TX, USA

    K. Carlos El-Tallawi & William A. Zoghbi

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  1. Peng Zhang
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  2. Andreas Mang
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  3. Jiwen He
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  4. Robert Azencott
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  5. K. Carlos El-Tallawi
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  6. William A. Zoghbi
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Correspondence to Robert Azencott.

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Zhang, P., Mang, A., He, J. et al. Diffeomorphic Shape Matching by Operator Splitting in 3D Cardiology Imaging. J Optim Theory Appl 188, 143–168 (2021). https://doi.org/10.1007/s10957-020-01789-5

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