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Quantification and Visualization of Variation in Anatomical Trees

  • Conference paper
Research in Shape Modeling

Part of the book series: Association for Women in Mathematics Series ((AWMS,volume 1))

Abstract

This paper presents two approaches to quantifying and visualizing variation in datasets of trees. The first approach localizes subtrees in which significant population differences are found through hypothesis testing and sparse classifiers on subtree features. The second approach visualizes the global metric structure of datasets through low-distortion embedding into hyperbolic planes in the style of multidimensional scaling. A case study is made on a dataset of airway trees in relation to Chronic Obstructive Pulmonary Disease.

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Acknowledgements

This work was supported by NSF IIS 111766; MO was supported through a Fields-Ontario Postdoctoral Fellowship; AF was supported by the Danish Council for Independent Research | Technology and Production. MH works for National Security Technologies, LLC, under Contract No. DE-AC52-06NA25946 with the U.S. Department of Energy/National Nuclear Security Administration, DOE/NV/25946--2016.

We thank the organizers, Kathryn Leonard and Luminita Vese, and the sponsors of the collaboration workshop Women in Shape (WiSh): Modeling Boundaries of Objects in 2- and 3- Dimensions that was held at the Institute for Pure and Applied Mathematics (IPAM) at UCLA July 15-19 2013, where the collaboration leading to this paper was established.

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Authors and Affiliations

  1. University of California at Davis, Davis, CA, USA

    Nina Amenta

  2. Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, UT, USA

    Manasi Datar

  3. Lungemedicinsk Afdeling, Gentofte Hospital, Hellerup, Denmark

    Asger Dirksen

  4. Department of Computer Science, University of Copenhagen, Copenhagen, Denmark

    Marleen de Bruijne, Aasa Feragen & Jens Petersen

  5. Erasmus MC, Rotterdam, The Netherlands

    Marleen de Bruijne

  6. Department of Computer Science and Engineering, Ohio State University, Columbus, OH, USA

    Xiaoyin Ge

  7. Department of Cardiothoracic Surgery, Rigshospitalet, University of Copenhagen, Copenhagen, Denmark

    Jesper Holst Pedersen

  8. National Security Technologies, LLC (A Department of Energy Contractor), Las Vegas, NV, USA

    Marylesa Howard

  9. Department of Mathematics and Computer Science, Lehman College, City University of New York, Bronx, NY, USA

    Megan Owen

  10. School of Computing, Informatics, and Decision Systems Engineering, Arizona State University, Tucson, AZ, USA

    Jie Shi

  11. Department of Mathematics, Florida State University, Tallahassee, FL, USA

    Qiuping Xu

Authors
  1. Nina Amenta
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  2. Manasi Datar
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  4. Marleen de Bruijne
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  5. Aasa Feragen
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  6. Xiaoyin Ge
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  7. Jesper Holst Pedersen
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  8. Marylesa Howard
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  9. Megan Owen
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  10. Jens Petersen
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  11. Jie Shi
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  12. Qiuping Xu
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Corresponding authors

Correspondence to Aasa Feragen or Megan Owen .

Editor information

Editors and Affiliations

  1. Department of Mathematics, California State University Channel Islands, Camarillo, California, USA

    Kathryn Leonard

  2. Department of Computer Engineering, Middle East Technical University, Ankara, Ankara, Turkey

    Sibel Tari

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Amenta, N. et al. (2015). Quantification and Visualization of Variation in Anatomical Trees. In: Leonard, K., Tari, S. (eds) Research in Shape Modeling. Association for Women in Mathematics Series, vol 1. Springer, Cham. https://doi.org/10.1007/978-3-319-16348-2_5

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