IDEAS home Printed from https://ideas.repec.org/a/bla/jorssc/v70y2021i3p691-713.html
   My bibliography  Save this article

Functional data analysis and visualisation of three‐dimensional surface shape

Author

Listed:
  • Stanislav Katina
  • Liberty Vittert
  • Adrian W. Bowman

Abstract

The advent of high‐resolution imaging has made data on surface shape widespread. Methods for the analysis of shape based on landmarks are well established but high‐resolution data require a functional approach. The starting point is a systematic and consistent description of each surface shape and a method for creating this is described. Three innovative forms of analysis are then introduced. The first uses surface integration to address issues of registration, principal component analysis and the measurement of asymmetry, all in functional form. Computational issues are handled through discrete approximations to integrals, based in this case on appropriate surface area weighted sums. The second innovation is to focus on sub‐spaces where interesting behaviour such as group differences are exhibited, rather than on individual principal components. The third innovation concerns the comparison of individual shapes with a relevant control set, where the concept of a normal range is extended to the highly multivariate setting of surface shape. This has particularly strong applications to medical contexts where the assessment of individual patients is very important. All of these ideas are developed and illustrated in the important context of human facial shape, with a strong emphasis on the effective visual communication of effects of interest.

Suggested Citation

  • Stanislav Katina & Liberty Vittert & Adrian W. Bowman, 2021. "Functional data analysis and visualisation of three‐dimensional surface shape," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(3), pages 691-713, June.
    • Handle: RePEc:bla:jorssc:v:70:y:2021:i:3:p:691-713
    DOI: 10.1111/rssc.12482
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/rssc.12482
    Download Restriction: no
    File URL: https://libkey.io/10.1111/rssc.12482?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Mitchum T. Bock & Adrian W. Bowman, 2006. "On the measurement and analysis of asymmetry with applications to facial modelling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 55(1), pages 77-91, January.
    2. Zeileis, Achim & Hornik, Kurt & Murrell, Paul, 2009. "Escaping RGBland: Selecting colors for statistical graphics," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3259-3270, July.
    3. Jackson, Christopher H, 2008. "Displaying Uncertainty With Shading," The American Statistician, American Statistical Association, vol. 62(4), pages 340-347.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Carlo Romano Marcello Alessandro Santagiustina & Matteo Iacopini, 2020. "Visualizing and comparing distributions with half-disk density strips," Papers 2006.16063, arXiv.org.
    2. repec:jss:jstsof:32:i01 is not listed on IDEAS
    3. Jonas Schöley, 2021. "The centered ternary balance scheme: A technique to visualize surfaces of unbalanced three-part compositions," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 44(19), pages 443-458.
    4. Matthias Templ & Andreas Alfons & Peter Filzmoser, 2012. "Exploring incomplete data using visualization techniques," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 6(1), pages 29-47, April.
    5. Pilhöfer, Alexander & Unwin, Antony, 2013. "New Approaches in Visualization of Categorical Data: R Package extracat," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 53(i07).
    6. Emura, Takeshi & Lin, Yi-Shuan, 2013. "A comparison of normal approximation rules for attribute control charts," MPRA Paper 51029, University Library of Munich, Germany.
    7. MacDonald, Blake & Ranjan, Pritam & Chipman, Hugh, 2015. "GPfit: An R Package for Fitting a Gaussian Process Model to Deterministic Simulator Outputs," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 64(i12).
    8. Christopher H. Jackson & Linda D. Sharples & Simon G. Thompson, 2010. "Structural and parameter uncertainty in Bayesian cost‐effectiveness models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(2), pages 233-253, March.
    9. de Wreede, Liesbeth C. & Fiocco, Marta & Putter, Hein, 2011. "mstate: An R Package for the Analysis of Competing Risks and Multi-State Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 38(i07).
    10. Reto Stauffer & Georg J. Mayr & Markus Dabernig & Achim Zeileis, 2013. "Somewhere over the Rainbow: How to Make Effective Use of Colors in Meteorological Visualizations," Working Papers 2013-37, Faculty of Economics and Statistics, Universität Innsbruck.
    11. Ben Jann, 2023. "Color palettes for Stata graphics: An update," Stata Journal, StataCorp LP, vol. 23(2), pages 336-385, June.
    12. Muñoz-Mas, R. & Martínez-Capel, F. & Alcaraz-Hernández, J.D. & Mouton, A.M., 2015. "Can multilayer perceptron ensembles model the ecological niche of freshwater fish species?," Ecological Modelling, Elsevier, vol. 309, pages 72-81.
    13. Meyer, Sebastian & Held, Leonhard & Höhle, Michael, 2017. "Spatio-Temporal Analysis of Epidemic Phenomena Using the R Package surveillance," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 77(i11).
    14. Ben Jann, 2022. "ColrSpace: A Mata class for color management," University of Bern Social Sciences Working Papers 42, University of Bern, Department of Social Sciences, revised 03 Jun 2022.
    15. Anette Fasang & Marcel Raab, 2014. "Beyond Transmission: Intergenerational Patterns of Family Formation Among Middle-Class American Families," Demography, Springer;Population Association of America (PAA), vol. 51(5), pages 1703-1728, October.
    16. Alexina J. Mason & Manuel Gomes & James Carpenter & Richard Grieve, 2021. "Flexible Bayesian longitudinal models for cost‐effectiveness analyses with informative missing data," Health Economics, John Wiley & Sons, Ltd., vol. 30(12), pages 3138-3158, December.
    17. Andrew J K Conlan & Trevelyan J McKinley & Katerina Karolemeas & Ellen Brooks Pollock & Anthony V Goodchild & Andrew P Mitchell & Colin P D Birch & Richard S Clifton-Hadley & James L N Wood, 2012. "Estimating the Hidden Burden of Bovine Tuberculosis in Great Britain," PLOS Computational Biology, Public Library of Science, vol. 8(10), pages 1-14, October.
    18. Andrew J K Conlan & Ellen Brooks Pollock & Trevelyan J McKinley & Andrew P Mitchell & Gareth J Jones & Martin Vordermeier & James L N Wood, 2015. "Potential Benefits of Cattle Vaccination as a Supplementary Control for Bovine Tuberculosis," PLOS Computational Biology, Public Library of Science, vol. 11(2), pages 1-27, February.
    19. Shannon P McPherron, 2018. "Additional statistical and graphical methods for analyzing site formation processes using artifact orientations," PLOS ONE, Public Library of Science, vol. 13(1), pages 1-21, January.
    20. Tseng, George C., 2010. "Quantile map: Simultaneous visualization of patterns in many distributions with application to tandem mass spectrometry," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 1124-1137, April.
    21. repec:jss:jstsof:38:i07 is not listed on IDEAS
    22. Fox, John & Hong, Jangman, 2009. "Effect Displays in R for Multinomial and Proportional-Odds Logit Models: Extensions to the effects Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 32(i01).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:jorssc:v:70:y:2021:i:3:p:691-713. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/rssssea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.