Table Of ContentMathematics and Visualization
Xue-Cheng Tai · Egil Bae
Marius Lysaker Editors
Imaging, Vision
and Learning Based
on Optimization
and PDEs
IVLOPDE, Bergen, Norway,
August 29 – September 2, 2016
Mathematics and Visualization
Serieseditors
Hans-ChristianHege
DavidHoffman
ChristopherR.Johnson
KonradPolthier
MartinRumpf
Moreinformationaboutthisseriesathttp://www.springer.com/series/4562
Xue-Cheng Tai • Egil Bae (cid:129) Marius Lysaker
Editors
Imaging, Vision and
Learning Based on
Optimization and PDEs
IVLOPDE, Bergen, Norway, August 29 –
September 2, 2016
123
Editors
Xue-ChengTai EgilBae
DepartmentofMathematics NorwegianDefenceResearch
UniversityofBergen Establishment
Bergen,Norway Kjeller,Norway
MariusLysaker
UniversityofSouth-EasternNorway
Porsgrunn,Norway
ISSN1612-3786 ISSN2197-666X (electronic)
MathematicsandVisualization
ISBN978-3-319-91273-8 ISBN978-3-319-91274-5 (eBook)
https://doi.org/10.1007/978-3-319-91274-5
LibraryofCongressControlNumber:2018956324
MathematicsSubjectClassification(2010):35-XX,49-XX,65-XX,90-XX
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Preface
It has become an established paradigm to formulate problems within image
processingandcomputervisionaspartialdifferentialequations(PDEs),variational
problemsorhigh-dimensionaloptimizationproblems.Thiscompact,yetexpressive
framework makes it possible to incorporate a variety of desired properties of the
solutions and to design algorithms based on well-founded mathematical theory.
Applications range from early image formation through compressive sensing, to
low-levelimageenhancement,restorationandfeaturedetection,andtohigher-level
imageunderstanding,segmentationandclassification.Morerecently,thesametools
have also shown great promise in more general applications of data analysis and
machinelearning.
InAugust2016,weorganizedaconferencetitledImaging,VisionandLearning
based on Optimization and PDEs (IVLOPDE) in the city of Bergen, Norway.
The conference was intended to foster collaboration and exchange of new ideas
withinthesemathematicaltechniquesforthebroadrangeofapplicationsinimaging
science, computer vision and machine learning. The 5-day event included invited
presentations from 18 internationally leading experts within the field, and 16
contributed poster presentations. Plenty of time was also set aside for informal
discussions, such as a full-day excursion to the fjords and mountains of western
Norway. After the conference, the participants were invited to submit full papers
based on their presentations, or based on new ideas that may have emerged
during the course of the event. Each submitted article was evaluated by 2–3
expertreviewers,whoweremostlyselectedamongtheotherinvitedspeakers.The
reviewersprovidedalotofusefulfeedback,whichinsomecasesledtonewinsights
thattheauthorsincorporatedinrevisedversionsoftheirarticles.
Thisbookconstitutestheconferencepost-proceedingsofIVLOPDE.Itcontains
11 original research articles that were selected from the submitted full papers
after the peer-review process. The articles present various novel techniques and
analyticalresultswithin optimization,variationalmodelsandPDEs, togetherwith
experimentalresults on applications ranging from early image formation to high-
level image and data analysis. To guide the reader, the articles have been divided
into four topical sections: (I) image reconstruction from incomplete data, (II)
v
vi Preface
image enhancement, restoration and registration, (III) 3D image understanding
and classification, and (IV) machine learning and big data analysis. Each section
featuresabalanceoftheoreticallyorientedarticlesandapplicationorientedarticles.
Thebookwill benefitall researcherswithinmathematics,imagingscience ordata
science who would like to become more familiar with this active field, as well as
expertswhowouldliketolearnaboutthelatestdevelopments.
We would like to thank all the reviewers for their valuable suggestions and
careful evaluations, the Research Council of Norway (through ISP-matematikk
project 239033/F20)for providingfunding for the conference, and Ruth Allewelt
and Martin Peters at Springer for their excellent support and patience while we
werepreparingthisbook.
Bergen,Norway Xue-ChengTai
Kjeller,Norway EgilBae
Porsgrunn,Norway MariusLysaker
April2018
Contents
PartI ImageReconstructionfromIncompleteData
1 Adaptive Regularizationfor Image Reconstructionfrom
SubsampledData........................................................... 3
MichaelHintermüller,AndreasLanger,CarlosN.Rautenberg,
andTaoWu
2 AConvergentFixed-PointProximityAlgorithmAccelerated
byFISTAforthe(cid:2) SparseRecoveryProblem.......................... 27
0
XueyingZeng,LixinShen,andYueshengXu
3 Sparse-DataBased3DSurfaceReconstruction
forCartoonandMap....................................................... 47
BinWu,TalalRahman,andXue-ChengTai
PartII ImageEnhancement,RestorationandRegistration
4 VariationalMethodsforGamutMapping
inCinemaandTelevision.................................................. 67
SyedWaqasZamir,JavierVazquez-Corral,andMarceloBertalmío
5 FunctionalLiftingforVariationalProblemswithHigher-Order
Regularization .............................................................. 101
BenediktLoewenhauserandJanLellmann
6 OntheConvexModelofSpeckleReduction............................. 121
FamingFang,YingyingFang,andTieyongZeng
PartIII 3DImageUnderstandingandClassification
7 Multi-DimensionalRegularExpressionsforObjectDetection
withLiDARImaging....................................................... 145
ToddC.Torgersen,V.PaúlPauca,RobertJ.Plemmons,DejanNikic,
JasonWu,andRobertRand
vii
viii Contents
8 Relaxed Optimisation for Tensor Principal Component
AnalysisandApplicationstoRecognition,Compression
andRetrievalofVolumetricShapes...................................... 165
HayatoItoh,AtsushiImiya,andTomoyaSakai
PartIV MachineLearningandBigDataAnalysis
9 AnIncrementalReseedingStrategyforClustering..................... 203
XavierBresson,HuiyiHu,ThomasLaurent,ArthurSzlam,
andJamesvonBrecht
10 Ego-MotionClassificationforBody-WornVideos...................... 221
ZhaoyiMeng,JavierSánchez,Jean-MichelMorel,
AndreaL.Bertozzi,andP.JeffreyBrantingham
11 SynchronizedRecoveryMethodforMulti-RankSymmetric
TensorDecomposition...................................................... 241
HaixiaLiu,LizhangMiao,andYangWang
Index............................................................................... 253
Part I
Image Reconstruction from Incomplete
Data
