Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging: Mathematical Imaging and Vision PDF
Preview Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging: Mathematical Imaging and Vision
Ke Chen Carola-Bibiane Schönlieb Xue-Cheng Tai Laurent Younes Editors Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging Mathematical Imaging and Vision Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging Ke Chen • Carola-Bibiane Schönlieb (cid:129) Xue-Cheng Tai (cid:129) Laurent Younes Editors Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging Mathematical Imaging and Vision With553Figuresand72Tables Editors KeChen Carola-BibianeSchönlieb DepartmentofMathematicalSciences DepartmentofAppliedMathematicsand TheUniversityofLiverpool TheoreticalPhysics Liverpool,UK UniversityofCambridge Cambridge,UK Xue-ChengTai HongKongCenterfor LaurentYounes CerebrocardiovascularHealth DepartmentofAppliedMathematicsandStatistics Engineering(COCHE) JohnsHopkinsUniversity Shatin,HongKong,China Baltimore,MD,USA ISBN978-3-030-98660-5 ISBN978-3-030-98661-2(eBook) https://doi.org/10.1007/978-3-030-98661-2 ©SpringerNatureSwitzerlandAG2023 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. 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Preface Therapiddevelopmentofnewimaginghardware,theadvanceinmedicalimaging, the advent of multi-sensor data fusion and multimodal imaging, as well as the advances in computer vision have sparked numerous research endeavours leading to highly sophisticated and rigorous mathematical models and theories. Motivated by the increasing use of variational models, shapes and flows, differential geome- try, optimisation theory, numerical analysis, statistical/Bayesian graphical models, machine learning, and deep learning, we have invited contributions from leading researchersandpublishthishandbook toreviewandcapturethestateoftheartof researchinComputerVisionandImaging. This constantly improving technology that generates new demands not readily met by existing mathematical concepts and algorithms provides a compelling justification for such a book to meet the ever-growing challenges in applications and to drive future development. As a consequence, new mathematical models have to be found, analysed and realised in practice. Knowing the precise state-of- the-art developments is key, and hence this book will serve the large community of mathematics, imaging, computer vision, computer sciences, statistics, and, in general,imagingandvisionresearch.Ourprimaryaudienceare (cid:129) Graduatestudents (cid:129) Researchers (cid:129) Imagingandvisionpractitioners (cid:129) Appliedmathematicians (cid:129) Medicalimagers (cid:129) Engineers (cid:129) Computerscientists Viewingdiscreteimagesasdatasampledfromfunctionalsurfacesenablestheuseof advancedtoolsfromcalculus,functionsandcalculusofvariations,andoptimisation and provides the basis of high-resolution imaging through variational models. No otherframeworkcanprovidethecomparableaccuracyandprecisiontoimagingand vision. v vi Preface Although our initial emphasis is on the variational methods, which represent the optimal solutions to class of imaging and vision problems, and on effective algorithms,whicharenecessaryforthemethodstobetranslatedtopracticalusein various applications, the editors recognise that the range of effective and efficient methods for solving problems from computer vision and imaging go beyond variationalmethodsandhaveenlargedourcoveragetoincludemathematicalmodels and algorithms. So, the book title reflects this viewpoint and a big vision for the referencebook. All chapters will have introductions so that the book is readily accessible to graduate students. We have divided the 53 chapters of this book into 3 sections, namely (a) ConvexandNon-convexLarge-ScaleOptimisationinImaging (b) Model-andData-DrivenVariationalImagingApproaches (c) ShapeSpacesandGeometricFlows tofacilitatebrowsingthecontentlist.However,suchadivisionisartificialbecause, these days, research becomes increasingly intra-disciplinary as well as inter- disciplinary,andideasfromonetopicoftendirectlyorindirectlyinspireortranspire anothertopic.Thisisveryexciting. For newcomers to the field, the book provides a comprehensive and fast track introductiontothecoreresearchproblems,tosavetimeandgetonwithtacklingnew andemergingchallenges,ratherthanrunningtheriskofreproducing/comparingto someoldworksalreadydoneorreinventingsameresults.Forresearchers,exposure to the state of the art of research works leads to an overall view of the entire field soastoguidenewresearchdirectionsandavoidpitfallsinmovingthefieldforward andlookingintothenext25yearsofimagingandinformationsciences. The dreadful Covid-19 pandemic starting from 2020 has affected lives of everyone, of course including all researchers. We are still not out of the woods. The editors are very much grateful to the book authors who have endured much hardshipduringthelast3yearsandovercomemanydifficultiestohavecompleted their chapters on time. We are also indebted to many anonymous reviewers who provided valuable reviews and helpful criticism to improve presentations of our chapters. The original gathering of all editors was in 2017 when the first three editors co-organised the prestigious Isaac Newton Institute programme titled “Variational methods and effective algorithms for imaging and vision” (https://www.newton. ac.uk/event/vmv/), partially supported by UK EPSRC GR/EP F005431 and Isaac Newton Institute for Mathematical Sciences. During the programme, Mr Jan HollandfromSpringer-Naturekindlysuggestedtheideaofabook.Wearegrateful to his suggestion which sparked the editors’ fruitful collaboration in the last few Preface vii years. The large team of publishers who have offered immense help to us include Michael Hermann (Springer), Allan Cohen (Palgrave) and Salmanul Faris Nedum Palli(Springer).Wethankthemall. Finally,wewishallreadersahappyreading. Theeditorialteam: Liverpool,UK KeChen(Lead) Cambridge,UK Carola-BibianeSchönlieb Shatin,HongKong Xue-ChengTai Baltimore,USA LaurentYounes February2023 Contents Volume1 PartI Convex and Non-convex Large-Scale Optimization inImaging............................................. 1 1 ConvexNon-convexVariationalModels........................ 3 Alessandro Lanza, Serena Morigi, Ivan W. Selesnick, andFiorellaSgallari 2 Subsampled First-Order Optimization Methods with ApplicationsinImaging ..................................... 61 Stefania Bellavia, Tommaso Bianconcini, Nataša Krejic´, andBenedettaMorini 3 Bregman Methods for Large-Scale Optimization with ApplicationsinImaging ..................................... 97 MartinBenningandErlendSkaldehaugRiis 4 FastIterativeAlgorithmsforBlindPhaseRetrieval:ASurvey .... 139 HuibinChang,LiYang,andStefanoMarchesini 5 Modular ADMM-Based Strategies for Optimized Compression,Restoration,andDistributedRepresentations ofVisualData.............................................. 175 YehudaDarandAlfredM.Bruckstein 6 ConnectingHamilton-JacobiPartialDifferentialEquations withMaximumaPosterioriandPosteriorMeanEstimators forSomeNon-convexPriors.................................. 209 JérômeDarbon,GabrielP.Langlois,andTingweiMeng 7 Multi-modality Imaging with Structure-Promoting Regularizers ............................................... 235 MatthiasJ.Ehrhardt ix x Contents 8 DiffractionTomography,FourierReconstruction,andFull WaveformInversion ........................................ 273 Florian Faucher, Clemens Kirisits, Michael Quellmalz, OtmarScherzer,andEricSetterqvist 9 ModelsforMultiplicativeNoiseRemoval ...................... 313 XiangchuFengandXiaolongZhu 10 RecentApproachestoMetalArtifactReductioninX-RayCT Imaging ................................................... 347 SoominJeonandChang-OckLee 11 DomainDecompositionforNon-smooth(inParticularTV) Minimization .............................................. 379 AndreasLanger 12 FastNumericalMethodsforImageSegmentationModels ........ 427 NoorBadshah 13 OnVariableSplittingandAugmentedLagrangianMethod forTotalVariation-RelatedImageRestorationModels........... 503 Zhifang Liu, Yuping Duan, Chunlin Wu, and Xue-ChengTai 14 Sparse Regularized CT Reconstruction: An Optimization Perspective ................................................ 551 ElenaMorottiandElenaLoliPiccolomini 15 RecentApproachesforImageColorization..................... 585 FabienPierreandJean-FrançoisAujol 16 NumericalSolutionforSparsePDEConstrainedOptimization ... 623 XiaoliangSongandBoYu 17 GameTheoryandItsApplicationsinImagingandVision........ 677 Anis Theljani, Abderrahmane Habbal, Moez Kallel, andKeChen 18 First-OrderPrimal–DualMethodsforNonsmoothNon-convex Optimization............................................... 707 TuomoValkonen Volume2 PartII Model- and Data-Driven Variational ImagingApproaches................................... 749 19 LearnedIterativeReconstruction ............................. 751 JonasAdler Contents xi 20 An Analysis of Generative Methods for Multiple Image Inpainting ................................................. 773 Coloma Ballester, Aurélie Bugeau, Samuel Hurault, SimoneParisotto,andPatriciaVitoria 21 Analysis of Different Losses for Deep Learning Image Colorization ............................................... 821 Coloma Ballester, Hernan Carrillo, Michaël Clément, andPatricia Vitoria 22 Influence of Color Spaces for Deep Learning Image Colorization ............................................... 847 AurélieBugeau,RémiGiraud,andLaraRaad 23 VariationalModel-BasedDeepNeuralNetworksforImage Reconstruction ............................................. 879 YunmeiChen,XiaojingYe,andQingchaoZhang 24 BilevelOptimizationMethodsinImaging...................... 909 JuanCarlosDelosReyesandDavidVillacís 25 Multi-parameterApproachesinImageProcessing .............. 943 MarkusGrasmairandValeriyaNaumova 26 GenerativeAdversarialNetworksforRobustCryo-EMImage Denoising.................................................. 969 HanlinGu,YinXian,IlonaChristyUnarta,andYuanYao 27 Variational Models and Their Combinations with Deep LearninginMedicalImageSegmentation:ASurvey ............ 1001 LuyingGui,JunMaandXiaopingYang 28 BidirectionalTextureFunctionModeling ...................... 1023 MichalHaindl 29 RegularizationofInverseProblemsbyNeuralNetworks ......... 1065 MarkusHaltmeierandLinhNguyen 30 Shearlets:FromTheorytoDeepLearning ..................... 1095 GittaKutyniok 31 LearnedRegularizersforInverseProblems .................... 1133 SebastianLunz 32 Filter Design for Image Decomposition and Applications toForensics................................................ 1155 Robin Richter, Duy H. Thai, Carsten Gottschlich, andStephanF.Huckemann
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