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Functional data analysis and visualisation of three‐dimensional surface shape

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  • 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
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    References listed on IDEAS

    as
    1. Jackson, Christopher H, 2008. "Displaying Uncertainty With Shading," The American Statistician, American Statistical Association, vol. 62(4), pages 340-347.
    2. 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.
    3. 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.
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