Quantification and Visualization of Variation in Anatomical Trees

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


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.


Chronic Obstructive Pulmonary Disease Chronic Obstructive Pulmonary Disease Patient Tree Topology Geodesic Distance Quadratic Discriminant Analysis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



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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Copyright information

© Springer International Publishing Switzerland & The Association for Women in Mathematics 2015

Authors and Affiliations

  1. 1.University of California at DavisDavisUSA
  2. 2.Scientific Computing and Imaging InstituteUniversity of UtahSalt Lake CityUSA
  3. 3.Lungemedicinsk AfdelingHellerupDenmark
  4. 4.Department of Computer ScienceUniversity of CopenhagenCopenhagenDenmark
  5. 5.Erasmus MCRotterdamThe Netherlands
  6. 6.Department of Computer Science and EngineeringOhio State UniversityColumbusUSA
  7. 7.Department of Cardiothoracic Surgery, RigshospitaletUniversity of CopenhagenCopenhagenDenmark
  8. 8.National Security Technologies, LLC (A Department of Energy Contractor)Las VegasUSA
  9. 9.Department of Mathematics and Computer ScienceLehman College, City University of New YorkBronxUSA
  10. 10.School of Computing, Informatics, and Decision Systems EngineeringArizona State UniversityTucsonUSA
  11. 11.Department of MathematicsFlorida State UniversityTallahasseeUSA

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