From Global to Local Statistical Shape Priors: Novel Methods to Obtain Accurate Reconstruction Results with a Limited Amount of Training Shapes

270 Pages·2017·13.47 MB·English

by  Carsten Last (auth.)

Studies in Systems, Decision and Control 98
Carsten Last
From Global to
Local Statistical
Shape Priors
Novel Methods to Obtain Accurate
Reconstruction Results with a Limited
Amount of Training Shapes
Studies in Systems, Decision and Control
Volume 98
Series editor
Janusz Kacprzyk, Polish Academy of Sciences, Warsaw, Poland
e-mail: [email protected]
About this Series
The series “Studies in Systems, Decision and Control” (SSDC) covers both new
developments and advances, as well as the state of the art, in the various areas of
broadly perceived systems, decision making and control- quickly, up to date and
withahighquality.Theintentistocoverthetheory,applications,andperspectives
on the state of the art and future developments relevant to systems, decision
making,control,complexprocessesandrelatedareas, asembeddedinthefieldsof
engineering,computerscience,physics,economics,socialandlifesciences,aswell
astheparadigmsandmethodologiesbehindthem.Theseriescontainsmonographs,
textbooks, lecture notes and edited volumes in systems, decision making and
control spanning the areas of Cyber-Physical Systems, Autonomous Systems,
Sensor Networks, Control Systems, Energy Systems, Automotive Systems, Bio-
logical Systems, Vehicular Networking and Connected Vehicles, Aerospace Sys-
tems, Automation, Manufacturing, Smart Grids, Nonlinear Systems, Power
Systems, Robotics, Social Systems, Economic Systems and other. Of particular
valuetoboththecontributorsandthereadershiparetheshortpublicationtimeframe
and the world-wide distribution and exposure which enable both a wide and rapid
dissemination of research output.
More information about this series at http://www.springer.com/series/13304
Carsten Last
From Global to Local
Statistical Shape Priors
Novel Methods to Obtain Accurate
Reconstruction Results with a Limited
Amount of Training Shapes
123
CarstenLast
Institut für Robotik undProzessinformatik
Technische UniversitätBraunschweig
Braunschweig
Germany
ISSN 2198-4182 ISSN 2198-4190 (electronic)
Studies in Systems,DecisionandControl
ISBN978-3-319-53507-4 ISBN978-3-319-53508-1 (eBook)
DOI 10.1007/978-3-319-53508-1
LibraryofCongressControlNumber:2017930419
©SpringerInternationalPublishingAG2017
Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart
of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations,
recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission
or information storage and retrieval, electronic adaptation, computer software, or by similar or
dissimilarmethodologynowknownorhereafterdeveloped.
The use of general descriptive names, registered names, trademarks, service marks, etc. in this
publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfrom
therelevantprotectivelawsandregulationsandthereforefreeforgeneraluse.
The publisher, the authors and the editors are safe to assume that the advice and information in this
book are believed to be true and accurate at the date of publication. Neither the publisher nor the
authors or the editors give a warranty, express or implied, with respect to the material contained
hereinorforanyerrorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregard
tojurisdictionalclaimsinpublishedmapsandinstitutionalaffiliations.
Printedonacid-freepaper
ThisSpringerimprintispublishedbySpringerNature
TheregisteredcompanyisSpringerInternationalPublishingAG
Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland
For my wife Carolin.
Without you I could not have done this.
Preface
ThepresentthesisoriginatesfrommyscientificworkasemployeeattheInstitutfür
Robotik und Prozessinformatik, Technische Universität Braunschweig, Germany.
However, the completion of this thesis would not have been possible without the
help of others.
Atfirst,IwouldliketothankProf.Dr.-Ing.FriedrichM.Wahl fordirectingme
towards the interesting topic of medical image segmentation and giving me the
freedomtodevelopmyownideas withinthisfield.He providedmewith excellent
technical resources and a great working environment, and he gave me the oppor-
tunitytopresentmyideasatvariousnationalandinternationalconferences.Iwould
also like to thank Prof. Dr. Thomas Vetter for his effort to review this thesis as a
secondrefereeandforprovidingthemorphablefacemodelaswellastheadditional
face scans that are used for evaluation.
My thanks go especially also to Dr.-Ing. Simon Winkelbach for his continuous
support in developing and discussing new ideas, but as well for proofreading this
thesis.Hisinputhadagreatinfluenceonthefinaloutcome.Ialsohavetothankthe
whole staff and all students of the Institut für Robotik und Prozessinformatik for
creating such a nice and friendly working atmosphere.
Additionally,IwouldliketothanktheGermanResearchFoundation(DFG)for
funding parts of my research within the project Roboterunterstützte,
erwartungskonformeEndoskopführunginderendosalenChirurgie.Inthisregard,I
would like to thank Prof. Dr. med. Dr. h.c. Friedrich Bootz from the Klinik und
Poliklinik für Hals-Nasen-Ohrenheilkunde/Chirurgie at the Universitätsklinikum
Bonnforprovidingmewiththeparanasalsinusesdatabasethatisbeingusedwithin
this thesis. Also, I would like to thank my former colleagues Dr.-Ing. Ralf
Westphal, Markus Rilk, and Dr. med. Klaus Eichhorn for the fruitful and friendly
cooperation within this project.
vii
viii Preface
Specialthanksgotomyfamilyfortheircontinuousmoralandfinancialsupport
throughoutallmyyearsofstudyandtomywifeCarolinforthecountlesshoursthat
she spent discussing and proofreading this thesis.
Braunschweig, Germany Carsten Last
December 2016
Contents
1 Basics. .... .... .... .... .... ..... .... .... .... .... .... ..... 1
1.1 Naming Conventions . .... ..... .... .... .... .... .... ..... 1
1.2 Vector Calculus . .... .... ..... .... .... .... .... .... ..... 2
1.2.1 Pixels and Voxels.. ..... .... .... .... .... .... ..... 2
1.2.2 The Gradient and Necessary Condition for a Minimum ... 3
1.2.3 Directional Derivative.... .... .... .... .... .... ..... 3
1.2.4 Descent Direction.. ..... .... .... .... .... .... ..... 3
1.2.5 Descent Methods .. ..... .... .... .... .... .... ..... 4
1.3 Calculus of Variations .... ..... .... .... .... .... .... ..... 4
1.3.1 The Functional Derivative. .... .... .... .... .... ..... 6
1.3.2 Differentiation Rules..... .... .... .... .... .... ..... 7
1.3.3 Functionals of Functions with Multiple Arguments . ..... 7
1.3.4 Functionals of Multiple Functions .. .... .... .... ..... 8
1.3.5 The Functional Differential.... .... .... .... .... ..... 9
1.4 Level Set Methods... .... ..... .... .... .... .... .... ..... 9
1.4.1 Level Set Function. ..... .... .... .... .... .... ..... 9
1.4.2 Level Set Evolution ..... .... .... .... .... .... ..... 11
1.4.3 Level Set Methods for Image Segmentation Problems .... 13
1.5 Variational Image Segmentation.. .... .... .... .... .... ..... 16
1.5.1 Geodesic Active Contours .... .... .... .... .... ..... 16
1.5.2 Active Contours Without Edges.... .... .... .... ..... 18
2 Statistical Shape Models (SSMs) .... .... .... .... .... .... ..... 21
2.1 Definition of Shape .. .... ..... .... .... .... .... .... ..... 22
2.2 An Explicit Linear Parametric Statistical Shape Model .... ..... 24
2.3 An Implicit Linear Parametric Statistical Shape Model .... ..... 31
2.4 Rigid Shape Alignment ... ..... .... .... .... .... .... ..... 39
2.4.1 Similarity Transformation. .... .... .... .... .... ..... 41
2.4.2 Rigid Alignment of Two Shape Configurations .... ..... 41
2.4.3 Rigid Alignment of Multiple Shape Configurations . ..... 43
ix
x Contents
2.5 Problem: Limited Training Data.. .... .... .... .... .... ..... 44
2.5.1 Artificial Enlargement of Shape Variations.... .... ..... 46
2.5.2 Relaxation of Model-Constraints.... .... .... .... ..... 48
2.5.3 Model Partitioning . ..... .... .... .... .... .... ..... 49
3 A Locally Deformable Statistical Shape Model (LDSSM) .... ..... 53
3.1 Motivation . .... .... .... ..... .... .... .... .... .... ..... 53
3.2 Mathematical Formulation of Our LDSSM . .... .... .... ..... 55
3.3 An Iterative Framework to Determine the Weight Fields... ..... 58
3.3.1 General Idea: Demons-Based Approach .. .... .... ..... 58
3.3.2 A Side Note to Optimal Weights for the SSM. .... ..... 60
3.3.3 Determination of the Weights for a Known
Target Shape.. .... ..... .... .... .... .... .... ..... 62
3.3.4 Determination of the Weights for Segmentation
Problems. .... .... ..... .... .... .... .... .... ..... 65
4 Evaluation of the Locally Deformable Statistical Shape Model..... 75
4.1 Segmenting the Nasal Cavity and the Paranasal Sinuses ... ..... 75
4.1.1 Description of the Paranasal Sinuses Database. .... ..... 78
4.1.2 Segmentation with Global Model Information . .... ..... 81
4.1.3 Experimental Setup and Results .... .... .... .... ..... 88
4.2 Segmenting the Bones in the Human Knee . .... .... .... ..... 100
4.2.1 Motivation ... .... ..... .... .... .... .... .... ..... 100
4.2.2 Experimental Setup. ..... .... .... .... .... .... ..... 100
4.2.3 Results .. .... .... ..... .... .... .... .... .... ..... 104
4.3 Fitting the LDSSM to Range Scans of Faces.... .... .... ..... 106
4.3.1 The Basel Face Model: A Meta-Database for 3D Faces... 107
4.3.2 Evaluating the Shape Approximation for Known
Target Shapes. .... ..... .... .... .... .... .... ..... 109
4.3.3 Application: Reconstructing Incomplete Face Scans. ..... 116
5 Global-To-Local Shape Priors for Variational Level
Set Methods.... .... .... .... ..... .... .... .... .... .... ..... 125
5.1 Problems of the Iterative Segmentation Framework... .... ..... 126
5.2 Existing Variational Image Segmentation Approaches
with Shape Priors.... .... ..... .... .... .... .... .... ..... 127
5.2.1 Linear Subspace-Constrained Approaches. .... .... ..... 127
5.2.2 Approaches with Additional Flexibility... .... .... ..... 132
5.2.3 Drawbacks of Existing Approaches . .... .... .... ..... 137
5.3 Variational Formulation for a Global Shape Prior .... .... ..... 138
5.3.1 Problem Formulation .... .... .... .... .... .... ..... 139
5.3.2 An Exemplary Segmentation Problem ... .... .... ..... 141