A hierarchical curve-based approach to the analysis of manifold data

Vittert, L., Bowman, A. W. and Katina, S. (2019) A hierarchical curve-based approach to the analysis of manifold data. Annals of Applied Statistics, 13(4), pp. 2539-2563. (doi: 10.1214/19-AOAS1267)

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One of the data structures generated by medical imaging technology is high resolution point clouds representing anatomical surfaces. Stereophotogrammetry and laser scanning are two widely available sources of this kind of data. A standardised surface representation is required to provide a meaningful correspondence across different images as a basis for statistical analysis. Point locations with anatomical definitions, referred to as landmarks, have been the traditional approach. Landmarks can also be taken as the starting point for more general surface representations, often using templates which are warped on to an observed surface by matching landmark positions and subsequent local adjustment of the surface. The aim of the present paper is to provide a new approach which places anatomical curves at the heart of the surface representation and its analysis. Curves provide intermediate structures which capture the principal features of the manifold (surface) of interest through its ridges and valleys. As landmarks are often available these are used as anchoring points, but surface curvature information is the principal guide in estimating the curve locations. The surface patches between these curves are relatively flat and can be represented in a standardised manner by appropriate surface transects to give a complete surface model. This new approach does not require the use of a template, reference sample or any external information to guide the method and, when compared with a surface based approach, the estimation of curves is shown to have improved performance. In addition, examples involving applications to mussel shells and human faces show that the analysis of curve information can deliver more targeted and effective insight than the use of full surface information.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Bowman, Prof Adrian and Katina, Dr Stanislav and Vittert, Dr Liberty
Authors: Vittert, L., Bowman, A. W., and Katina, S.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Statistics
Journal Name:Annals of Applied Statistics
Publisher:Institute of Mathematical Statistics
ISSN (Online):1941-7330
Published Online:28 November 2019
Copyright Holders:Copyright © 2019 Institute of Mathematical Statistics
First Published:First published in Annals of Applied Statistics 13(4):2539-2563
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
477842The analysis of three-dimensional facial dysmorphologyAdrian BowmanWellcome Trust (WELLCOTR)086901/Z/08/ZM&S - STATISTICS