Weighted Functional Boxplot with Application to Statistical Atlas Construction

  • Yi Hong
  • Brad Davis
  • J. S. Marron
  • Roland Kwitt
  • Marc Niethammer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8151)


Atlas-building from population data is widely used in medical imaging. However, the emphasis of atlas-building approaches is typically to compute a mean / median shape or image based on population data. In this work, we focus on the statistical characterization of the population data, once spatial alignment has been achieved. We introduce and propose the use of the weighted functional boxplot. This allows the generalization of concepts such as the median, percentiles, or outliers to spaces where the data objects are functions, shapes, or images, and allows spatio-temporal atlas-building based on kernel regression. In our experiments, we demonstrate the utility of the approach to construct statistical atlases for pediatric upper airways and corpora callosa revealing their growth patterns. Furthermore, we show how such atlas information can be used to assess the effect of airway surgery in children.


Corpus Callosum Kernel Regression Subglottic Stenosis Spatial Alignment Airway Surgery 
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.


  1. 1.
    Aljabar, P., Heckemann, R., Hammers, A., Hajnal, J., Rueckert, D.: Multi-atlas based segmentation of brain images: Atlas selection and its effect on accuracy. NeuroImage 46, 726–739 (2009)CrossRefGoogle Scholar
  2. 2.
    Davis, B.C., Fletcher, P.T., Bullitt, E., Joshi, S.: Population shape regression from random design data. International Journal of Computer Vision 90(2), 255–266 (2010)CrossRefGoogle Scholar
  3. 3.
    Fletcher, P., Venkatasubramanian, S., Joshi, S.: The geometric median on Riemannian manifolds with application to robust atlas estimation. NeuroImage 45(suppl. 1), S143–S152 (2009)Google Scholar
  4. 4.
    Fletcher, T.: Geodesic regression on Riemannian manifolds. In: 3rd MICCAI Workshop on Mathematical Foundations of Computational Anatomy, pp. 75–86 (2011)Google Scholar
  5. 5.
    Gerber, S., Tasdizen, T., Fletcher, P.T., Joshi, S., Whitaker, R.: Manifold modeling for brain population analysis. Medical Image Analysis 14(5), 643–653 (2010)CrossRefGoogle Scholar
  6. 6.
    Hong, Y., Niethammer, M., Andruejol, J., Kimbel, J., Pitkin, E., Superfine, R., Davis, S., Zdanski, C., Davis, B.: A pediatric airway atlas and its application in subglottic stenosis. In: International Symposium on Biomedical Imaging: From Nano to Macro, pp. 1194–1197 (2013)Google Scholar
  7. 7.
    Joshi, S., Davis, B., Jomier, M.: Unbiased diffeomorphic atlas construction for computational anatomy. Neuroimage 23(suppl. 1), S151–S160 (2004)Google Scholar
  8. 8.
    Liu, R., Parelius, J., Singh, K.: Multivariate analysis by data depth: descriptive statistics, graphics and inference. The Annals of Statistics 27, 783–858 (1999)MathSciNetzbMATHGoogle Scholar
  9. 9.
    López-Pintado, S., Romo, J.: On the concept of depth for functional data. Journal of the American Statistical Association 104, 718–734 (2009)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Marron, J., Nolan, D.: Canonical kernels for density estimation. Statistics and Probability Letters 7, 195–199 (1988)CrossRefMathSciNetzbMATHGoogle Scholar
  11. 11.
    Ramsay, J., Silverman, B.: Functional Data Analysis. Springer (2005)Google Scholar
  12. 12.
    Sun, Y., Genton, M.: Functional boxplots. Journal of Computational and Graphical Statistics 20, 316–334 (2011)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Yi Hong
    • 1
  • Brad Davis
    • 3
  • J. S. Marron
    • 1
  • Roland Kwitt
    • 3
  • Marc Niethammer
    • 1
    • 2
  1. 1.University of North Carolina (UNC) at Chapel HillUSA
  2. 2.Biomedical Research Imaging CenterUNC-Chapel HillUSA
  3. 3.Kitware, Inc.CarrboroUSA

Personalised recommendations