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

VITTERT, Liberty, Adrian W. BOWMAN and Stanislav KATINA. A hierarchical curve-based approach to the analysis of manifold data. The Annals of Applied Statistics. Cleveland: The Institute of Mathematical Statistics, 2019, vol. 13, No 4, p. 2539-2563. ISSN 1932-6157. Available from: https://dx.doi.org/10.1214/19-AOAS1267.

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TY  - JOUR
ID  - 1585641
AU  - Vittert, Liberty - Bowman, Adrian W. - Katina, Stanislav
PY  - 2019
TI  - A hierarchical curve-based approach to the analysis of manifold data
JF  - The Annals of Applied Statistics
VL  - 13
IS  - 4
SP  - 2539-2563
EP  - 2539-2563
PB  - The Institute of Mathematical Statistics
SN  - 19326157
KW  - Anatomy
KW  - curves
KW  - manifold
KW  - p-splines
KW  - shape analysis
KW  - smoothing
KW  - three dimensional
UR  - https://projecteuclid.org/euclid.aoas/1574910054
L2  - https://projecteuclid.org/euclid.aoas/1574910054
N2  - 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.
ER  -

Basic information
Original name	A hierarchical curve-based approach to the analysis of manifold data
Authors	VITTERT, Liberty (840 United States of America), Adrian W. BOWMAN (826 United Kingdom of Great Britain and Northern Ireland) and Stanislav KATINA (703 Slovakia, guarantor, belonging to the institution).
Edition	The Annals of Applied Statistics, Cleveland, The Institute of Mathematical Statistics, 2019, 1932-6157.

Other information
Original language	English
Type of outcome	Article in a journal
Field of Study	10103 Statistics and probability
Country of publisher	United States of America
Confidentiality degree	is not subject to a state or trade secret
WWW	URL
Impact factor	Impact factor: 1.675
RIV identification code	RIV/00216224:14310/19:00111523
Organization unit	Faculty of Science
Doi	http://dx.doi.org/10.1214/19-AOAS1267
UT WoS	000509780500021
Keywords in English	Anatomy; curves; manifold; p-splines; shape analysis; smoothing; three dimensional
Tags	rivok
Tags	International impact, Reviewed
Changed by	Changed by: Mgr. Marie Šípková, DiS., učo 437722. Changed: 26/3/2020 15:56.

Abstract

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.

Links
MUNI/A/1503/2018, interní kód MU	Name: Matematické statistické modelování 3 (Acronym: MaStaMo3)
MUNI/A/1503/2018, interní kód MU	Investor: Masaryk University, Category A

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

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