Premium
Functional data analysis and visualisation of three‐dimensional surface shape
Author(s) -
Katina Stanislav,
Vittert Liberty,
W. Bowman Adrian
Publication year - 2021
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.1111/rssc.12482
Subject(s) - context (archaeology) , surface (topology) , principal component analysis , computer science , focus (optics) , visualization , shape analysis (program analysis) , range (aeronautics) , set (abstract data type) , multivariate statistics , artificial intelligence , point (geometry) , data science , mathematics , geometry , machine learning , geography , optics , engineering , physics , static analysis , archaeology , programming language , aerospace engineering
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.