Curve Matching with Applications in Medical Imaging

Martin Bauer; Martins  Bruveris; Philipp  Harms; Jakob Møller-Andersen

Curve Matching with Applications in Medical Imaging

Martin Bauer
, Martins Bruveris
, Philipp Harms
, Jakob Møller-Andersen

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

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Abstract

In the recent years, Riemannian shape analysis of curves and surfaces has found several applications in medical image analysis. In this paper we present a numerical discretization of second order Sobolev metrics on the space of regular curves in Euclidean space. This class of metrics has several desirable mathematical properties. We propose numerical solutions for the initial and boundary value problems of _nding geodesics. These two methods are combined in a Riemannian gradientbased optimization scheme to compute the Karcher mean. We apply this to a study of the shape variation in HeLa cell nuclei and cycles of cardiac deformations, by computing means and principal modes of variations.

Original language	English
Title of host publication	Proceedings of the 5th MICCAI Workshop on Mathematical Foundations of Computational Anatomy (MFCA 2015)
Publication date	2015
Pages	83-94
Publication status	Published - 2015
Event	5th MICCAI Workshop on Mathematical Foundations of Computational Anatomy (MFCA 2015) - Munich, Germany Duration: 9 Oct 2015 → … Conference number: 5 http://www-sop.inria.fr/asclepios/events/MFCA15/

Workshop

Workshop	5th MICCAI Workshop on Mathematical Foundations of Computational Anatomy (MFCA 2015)
Number	5
Country/Territory	Germany
City	Munich
Period	09/10/2015 → …
Other	In conjunction with MICCAI 2015.
Internet address	http://www-sop.inria.fr/asclepios/events/MFCA15/

Bibliographical note

The proceedings of the workshop are available as a collection of open archive papers.

Keywords

Curve matching
Sobolev metrics
Riemannian shape analysis
Discrete geodesics
Minimizing geodesics

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@inproceedings{cd13dc314a7f4e4db17d94fdecb4a34e,

title = "Curve Matching with Applications in Medical Imaging",

abstract = "In the recent years, Riemannian shape analysis of curves and surfaces has found several applications in medical image analysis. In this paper we present a numerical discretization of second order Sobolev metrics on the space of regular curves in Euclidean space. This class of metrics has several desirable mathematical properties. We propose numerical solutions for the initial and boundary value problems of \_nding geodesics. These two methods are combined in a Riemannian gradientbased optimization scheme to compute the Karcher mean. We apply this to a study of the shape variation in HeLa cell nuclei and cycles of cardiac deformations, by computing means and principal modes of variations.",

keywords = "Curve matching, Sobolev metrics, Riemannian shape analysis, Discrete geodesics, Minimizing geodesics",

author = "Martin Bauer and Martins Bruveris and Philipp Harms and Jakob M{\o}ller-Andersen",

note = "The proceedings of the workshop are available as a collection of open archive papers.; 5th MICCAI Workshop on Mathematical Foundations of Computational Anatomy (MFCA 2015), MFCA ; Conference date: 09-10-2015",

year = "2015",

language = "English",

pages = "83--94",

booktitle = "Proceedings of the 5th MICCAI Workshop on Mathematical Foundations of Computational Anatomy (MFCA 2015)",

url = "http://www-sop.inria.fr/asclepios/events/MFCA15/",

}

Bauer, M, Bruveris, M, Harms, P & Møller-Andersen, J 2015, Curve Matching with Applications in Medical Imaging. in Proceedings of the 5th MICCAI Workshop on Mathematical Foundations of Computational Anatomy (MFCA 2015). pp. 83-94, 5th MICCAI Workshop on Mathematical Foundations of Computational Anatomy (MFCA 2015), Munich, Germany, 09/10/2015. <http://www-sop.inria.fr/asclepios/events/MFCA15/MFCA15_Proceedings.pdf>

TY - GEN

T1 - Curve Matching with Applications in Medical Imaging

AU - Bauer, Martin

AU - Bruveris, Martins

AU - Harms, Philipp

AU - Møller-Andersen, Jakob

N1 - Conference code: 5

PY - 2015

Y1 - 2015

N2 - In the recent years, Riemannian shape analysis of curves and surfaces has found several applications in medical image analysis. In this paper we present a numerical discretization of second order Sobolev metrics on the space of regular curves in Euclidean space. This class of metrics has several desirable mathematical properties. We propose numerical solutions for the initial and boundary value problems of _nding geodesics. These two methods are combined in a Riemannian gradientbased optimization scheme to compute the Karcher mean. We apply this to a study of the shape variation in HeLa cell nuclei and cycles of cardiac deformations, by computing means and principal modes of variations.

AB - In the recent years, Riemannian shape analysis of curves and surfaces has found several applications in medical image analysis. In this paper we present a numerical discretization of second order Sobolev metrics on the space of regular curves in Euclidean space. This class of metrics has several desirable mathematical properties. We propose numerical solutions for the initial and boundary value problems of _nding geodesics. These two methods are combined in a Riemannian gradientbased optimization scheme to compute the Karcher mean. We apply this to a study of the shape variation in HeLa cell nuclei and cycles of cardiac deformations, by computing means and principal modes of variations.

KW - Curve matching

KW - Sobolev metrics

KW - Riemannian shape analysis

KW - Discrete geodesics

KW - Minimizing geodesics

M3 - Article in proceedings

SP - 83

EP - 94

BT - Proceedings of the 5th MICCAI Workshop on Mathematical Foundations of Computational Anatomy (MFCA 2015)

T2 - 5th MICCAI Workshop on Mathematical Foundations of Computational Anatomy (MFCA 2015)

Y2 - 9 October 2015

ER -

Curve Matching with Applications in Medical Imaging

Abstract

Workshop

Bibliographical note

Keywords

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