Functional data analysis and visualisation of three-dimensional surface shape

Katina, S., Vittert, L. and Bowman, A. W. (2021) Functional data analysis and visualisation of three-dimensional surface shape. Journal of the Royal Statistical Society: Series C (Applied Statistics), 70(3), pp. 691-713. (doi: 10.1111/rssc.12482) (PMCID:PMC8518487)

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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.

Item Type:Articles
Additional Information:The early stages of the research carried out by Adrian Bowman and Stanislav Katina was supported by a Wellcome Trust grant (WT086901MA) to the Face3D research consortium (, under whose auspices the facial data were collected.
Glasgow Author(s) Enlighten ID:Katina, Dr Stanislav and Bowman, Prof Adrian and Vittert, Dr Liberty
Authors: Katina, S., Vittert, L., and Bowman, A. W.
College/School:College of Science and Engineering > School of Mathematics and Statistics
Journal Name:Journal of the Royal Statistical Society: Series C (Applied Statistics)
ISSN (Online):1467-9876
Published Online:06 May 2021
Copyright Holders:Copyright © 2021 The Authors
First Published:First published in Journal of the Royal Statistical Society: Series C (Applied Statistics) 70(3): 691-713
Publisher Policy:Reproduced under a Creative Commons License

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
190175The analysis of three-dimensional facial dysmorphologyAdrian BowmanWellcome Trust (WELLCOTR)086901/Z/08/ZM&S - Statistics