Large Deformation Diffeomorphic Metric Mappings -- Theory, Numerics, and Applications

Thomas Polzin

Large Deformation Diffeomorphic Metric Mappings -- Theory, Numerics, and Applications

Thomas Polzin

Abstract

n dieser Dissertation werden drei diffeomorphe Bildregistrierungsmethoden vorgestellt.Diese sind „Large Deformation Diffeomorphic Metric Mapping“-(LDDMM)-Methoden,die mittels der Theorie der optimalen Steuerung hergeleitet wurden. Für die Umsetzungwurde ein „Discretize-then-Optimize“-Ansatz genutzt. Zunächst wird in der vorliegen-den Arbeit ein Überblick über die theoretischen Grundlagen von LDDMM gegeben.Hierbei werden die zwei großen Klassen von Algorithmen vorgestellt: Relaxations-und Shooting-Verfahren. Anschließend wird die Verbindung zum Forschungsfeld deroptimalen Steuerung analysiert und die Relaxations- und Shooting-Methoden, die indieser Arbeit zur Registrierung genutzt werden, werden entwickelt. Ein besondererFokus der Arbeit liegt auf der Diskretisierung der Methoden und der Lösung desrestringierten numerischen Optimierungsproblems. Dies umfasst auch die konsistenteLösung der auftretenden partiellen Differenzialgleichungen (wie z. B. Transport- undKontinuitätsgleichungen), die die Nebenbedingungen des Optimierungsproblems sind.Da hochdimensionale Probleme gelöst werden sollen, werden Runge-Kutta-Verfahrenvierter Ordnung verwendet, die einen guten Kompromiss zwischen einer schnellenBerechnung und kleinen Approximationsfehlern darstellen.Zentrale Bestandteile der entwickelten Methoden sind ein frei wählbares differenzier-bares Distanzmaß, die Speicherplatz-effiziente Diskretisierung von Geschwindigkeitsfel-dern und Transformationen sowie die Erzeugung von diffeomorphen Transformationenauch im Diskreten. Registrierungen von Computertomografie-(CT-)Daten der Lunge,die häufig durch große Deformationen und Pathologien gekennzeichnet sind, demons-trieren, dass die präsentierten Algorithmen so präzise wie aktuell publizierte Verfahrensind: Mit einem durchschnittlichen Landmarkenfehler von 0.96 mm wird das zweit-beste aller veröffentlichten Ergebnisse für die DIR-Lab-COPD-Datensätze erreicht.Die Effektivität der speziell entwickelten Diskretisierung wird durch eine Reduktionder benötigten Arbeitsspeichermenge um 95 % bestätigt. Während andere LDDMM-Algorithmen Laufzeiten von mehr als einer Stunde auf schnellen Computer-Clustern fürdie Registrierung von zwei Lungen-CT-Aufnahmen benötigen, dauert die in dieser Ar-beit vorgestellte Regisrierung ca. 20 Minuten auf einem Standard-Desktop-Computer.Die in dieser Dissertation vorgestellten Algorithmen sind für eine große Bandbreite vonklinischen Anwendungen für diffeomorphe Lungen-CT-Registrierung anwendbar, wiez. B. bildbasierte Lungenfunktionstests, Registrierung von Follow-up-Daten, Strahlen-therapie und Stadieneinteilung von COPD. Durch die flexible Wahl des Distanzmaßeskönnen die Methoden an viele weitere Datentypen und Anwendungen angepasst werden.

Originalsprache	Englisch
Qualifikation	Doctorate
Gradverleihende Hochschule
Betreuer/-in / Berater/-in	Modersitzki, Jan, Betreuerin Keller, Karsten, Betreuerin
Publikationsstatus	Veröffentlicht - 07.06.2018
Extern publiziert	Ja

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@phdthesis{282b824cd50c4cf4b2e580582a52e725,

title = "Large Deformation Diffeomorphic Metric Mappings -- Theory, Numerics, and Applications",

abstract = "In this thesis three diffeomorphic image registration methods are proposed. ADiscretize-then-Optimize approach is used to derive these methods from optimalcontrol formulations in the Large Deformation Diffeomorphic Metric Mapping (LD-DMM) framework. We give a condensed overview of the theoretical background ofLDDMM and discuss the two major groups of algorithms: relaxation and shootingapproaches. Afterwards, we examine the connection to optimal control and derivethe relaxation and shooting models that are used for registration in this work. Aparticular focus of this dissertation is the discretization of the proposed models andthe solution of the constrained numerical optimization problem. The latter includesthe consistent solution of the arising partial differential equations (like transport andcontinuity equations) that are the constraints of the optimization problem. As we dealwith large-scale problems, explicit fourth-order Runge-Kutta methods are employed,which offer a good compromise between fast computation and small errors.Key elements of the proposed techniques are the flexible choice of arbitrary differ-entiable distance measures, the memory-efficient discretization of velocity fields andtransformations as well as the generation of diffeomorphic transformations in thediscrete setting. Experiments on computed tomography (CT) data of the lungs (com-prising large deformations and pathologies) demonstrate that our algorithms achievestate-of-the-art accuracy: The second-best of all published results on the DIR-Labchronic obstructive pulmonary disease (COPD) datasets is achieved with an averagelandmark distance after registration of 0.96 mm. Furthermore, the effectiveness of ourtailored discretization is confirmed by a reduction of memory consumption by 95 %and run times that are superior to those of related LDDMM methods. While otherauthors report run times of more than one hour for their LDDMM algorithms whenregistering two lung CT scans on powerful computer clusters, our registration takesabout 20 minutes on a standard desktop computer.The proposed methods are suitable for a wide range of clinical applications for diffeo-morphic lung CT registration like lung ventilation estimation, follow-up registration,radiotherapy, and COPD staging. Due to the flexible choice of distance measures ourmethods can be properly adapted to other data types and applications.",

author = "Thomas Polzin",

year = "2018",

month = jun,

day = "7",

language = "English",

}

TY - BOOK

T1 - Large Deformation Diffeomorphic Metric Mappings -- Theory, Numerics, and Applications

AU - Polzin, Thomas

PY - 2018/6/7

Y1 - 2018/6/7

N2 - In this thesis three diffeomorphic image registration methods are proposed. ADiscretize-then-Optimize approach is used to derive these methods from optimalcontrol formulations in the Large Deformation Diffeomorphic Metric Mapping (LD-DMM) framework. We give a condensed overview of the theoretical background ofLDDMM and discuss the two major groups of algorithms: relaxation and shootingapproaches. Afterwards, we examine the connection to optimal control and derivethe relaxation and shooting models that are used for registration in this work. Aparticular focus of this dissertation is the discretization of the proposed models andthe solution of the constrained numerical optimization problem. The latter includesthe consistent solution of the arising partial differential equations (like transport andcontinuity equations) that are the constraints of the optimization problem. As we dealwith large-scale problems, explicit fourth-order Runge-Kutta methods are employed,which offer a good compromise between fast computation and small errors.Key elements of the proposed techniques are the flexible choice of arbitrary differ-entiable distance measures, the memory-efficient discretization of velocity fields andtransformations as well as the generation of diffeomorphic transformations in thediscrete setting. Experiments on computed tomography (CT) data of the lungs (com-prising large deformations and pathologies) demonstrate that our algorithms achievestate-of-the-art accuracy: The second-best of all published results on the DIR-Labchronic obstructive pulmonary disease (COPD) datasets is achieved with an averagelandmark distance after registration of 0.96 mm. Furthermore, the effectiveness of ourtailored discretization is confirmed by a reduction of memory consumption by 95 %and run times that are superior to those of related LDDMM methods. While otherauthors report run times of more than one hour for their LDDMM algorithms whenregistering two lung CT scans on powerful computer clusters, our registration takesabout 20 minutes on a standard desktop computer.The proposed methods are suitable for a wide range of clinical applications for diffeo-morphic lung CT registration like lung ventilation estimation, follow-up registration,radiotherapy, and COPD staging. Due to the flexible choice of distance measures ourmethods can be properly adapted to other data types and applications.

AB - In this thesis three diffeomorphic image registration methods are proposed. ADiscretize-then-Optimize approach is used to derive these methods from optimalcontrol formulations in the Large Deformation Diffeomorphic Metric Mapping (LD-DMM) framework. We give a condensed overview of the theoretical background ofLDDMM and discuss the two major groups of algorithms: relaxation and shootingapproaches. Afterwards, we examine the connection to optimal control and derivethe relaxation and shooting models that are used for registration in this work. Aparticular focus of this dissertation is the discretization of the proposed models andthe solution of the constrained numerical optimization problem. The latter includesthe consistent solution of the arising partial differential equations (like transport andcontinuity equations) that are the constraints of the optimization problem. As we dealwith large-scale problems, explicit fourth-order Runge-Kutta methods are employed,which offer a good compromise between fast computation and small errors.Key elements of the proposed techniques are the flexible choice of arbitrary differ-entiable distance measures, the memory-efficient discretization of velocity fields andtransformations as well as the generation of diffeomorphic transformations in thediscrete setting. Experiments on computed tomography (CT) data of the lungs (com-prising large deformations and pathologies) demonstrate that our algorithms achievestate-of-the-art accuracy: The second-best of all published results on the DIR-Labchronic obstructive pulmonary disease (COPD) datasets is achieved with an averagelandmark distance after registration of 0.96 mm. Furthermore, the effectiveness of ourtailored discretization is confirmed by a reduction of memory consumption by 95 %and run times that are superior to those of related LDDMM methods. While otherauthors report run times of more than one hour for their LDDMM algorithms whenregistering two lung CT scans on powerful computer clusters, our registration takesabout 20 minutes on a standard desktop computer.The proposed methods are suitable for a wide range of clinical applications for diffeo-morphic lung CT registration like lung ventilation estimation, follow-up registration,radiotherapy, and COPD staging. Due to the flexible choice of distance measures ourmethods can be properly adapted to other data types and applications.

M3 - Doctoral Theses

ER -

Large Deformation Diffeomorphic Metric Mappings -- Theory, Numerics, and Applications

Abstract

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